Talk:Marginal utility/Archive 3

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Gender

A standard practice in academic discourse by economists is to achieve gender-neutrality by toggling back-and-forth between genders as hypothetical people are introduced. This has two advantages over “he or she” disjunctive constructions. First, the awkwardness that they sometimes entail is avoided. Second, when just two people exist, they can be simply distinguished by being given distinct genders.

For some reason (leaning against the wind?) it has also become standard to make the first hypothetical person female.

Anyway, at one stage, I had a hypothetical “her” which someone changed to a “her or his”. No big deal. But now there are two more hypothetical people in that section. Hence, I have restored the feminine gender of that first hypothetical, made the second male, and the third female. I hope that people will accept this convention for this article. —SlamDiego 03:06, 18 March 2007 (UTC)

That's just people with political agendas that hijacked the language for their own POV pushing into the culture, the language used to have a whole lot more forms in archaic form and the usage of "he" in a text has no sexual-meaning what so ever. It derives from the words themselves being classified as male or female. Much like the usage of "one" in text to describe oneself, the word "one" doesn't have anything to do with the number '1' it is an archaic heritage in our language. Don't let the politicans hijack the language. No one ever writes: *read out loud*, "He or she must ask himself or herself whether his or her sensetive style could allow himself or herself to write like this?", that would be insane and that is what those people would want. As Orwell paraphrases, people who controls the meaning of the words controls the minds of people. 81.227.10.205 20:13, 22 April 2007 (UTC)

Utility as pleasure

The hedonic notion of utility is that of pleasure per se. But note that “Grenz·nutzen” literally translates as “border use” or “use at the border”, without any presumption that the use is pleasure itself. Granted that one feels happiness of a sort as one moves towards a goal, but that doesn't make the happiness itself (nor the contentment at arrival) the goal. (I am reminded of the many Playboy Playmates who listed as one of their goals “To be successful!”) Now, given the ordinary sense of “pleasure” (sensory and so forth), pleasure can be a goal, but the article should not presume that it must be, let alone that it is ultimately the only goal. —SlamDiego 23:22, 18 March 2007 (UTC)

Nomination

Ackh! This nomination comes while one of the sub-sections is still a stub! —SlamDiego 15:29, 8 April 2007 (UTC)

Sorry about my hasty nomination... I suppose we just have to speedily finish the section in question. Lord Metroid 16:03, 8 April 2007 (UTC)

Well, it's not a particularly easy section to complete. On the one hand, it shouldn't be overly long. On the other hand, it should simply participate in the common confusions about where differences did or didn't lie. —SlamDiego 16:42, 8 April 2007 (UTC)

I think that the section is now passable. (The section and this article more generally still has plenty of room for improvement.) —SlamDiego 17:07, 9 April 2007 (UTC)

Marginal Disutility

Marginal disutility is a concept made use of by John Maynard Keynes as well as his predecessors in the classical school of economics. Unfortunately there is no page on this concept, and it is not 100% clear to me that it is directly related to marginal utility. However, if it is directly related, than someone more knowledgeable than me should add a section explaining it, as well as a Marginal Disutility page that redirects here. Also, under "quantified marginal utility", it would be good to mention whether or not M.U./M.D. are measurable quantities, and how to measure them if they are, and also whether they are comparable quantities, I.E. can you compare the utility for Bob of watering his roses with the utility for Fred of Watering his dog, and can we (really) compare the disutility for Bob of working 40 hours a weak with the utility of the money he is making - or do we simply assume that the disutility is less if Bob doesn't quit. Also, how do these concepts play out when we are talking about groups of people? If they continue to be meaningful when we talk about groups of people, does that imply that they are not subjective concepts? —Comiscuous

Please do not place your comments out of order on the talk page of this or any other article.

My apologies for placing my comments out of order, and thank you, Slam, for your insightful response. I actually don't care whether M.D. is discussed here or in the article on utility. My reason for bringing it up here is that Keynes only seems to be talking about marginal disutility, not disutility itself. He is always talking about situations where (dis)utility can be compared with other forms of (dis)utility

I'm not sure what would be added by a specific discussion of marginal disutility, but I'm open to suggestions. Please bear in mind that this article cannot possibly present all the significant implications of marginal utility. Also, understand that Keynes essentially subscribed to the Marshallian conception of utility, which gets us back to the presumption that the ultimate use is hedonic; that is a special case assumption.

I'm not sure what you mean by “the classical school of economics”. Keynes used “classical” to refer to a sort of caricatured version of the economics of Pigou. Marx used it in a different, but similarly self-importantly idiosyncratic manner. Most modern economists nowadays use it to refer to mainstream economists from Smith to Mill. In this last case, they certainly didn't make use of marginal disutility.

I think Keynes was talking about mainstream economists from Smith to Mill. At least I assume Smith is included as a "classical economist". He doesn't mention him explicity, but the term is certainly not limited to Pigou. See "The General Theory..." chapter 1, first footnote. I misspoke, I think, when I said that the M.D. concept was made use of by the classical school in general. I had assumed that someone else must have made explicit use of the term, in another context if not in this very same one. Upon a rereading of chapter 2 of "The General Theory" I see that I was very wrong to make that assumption. Keynes is only arguing that there are two postulates assumed by the classical school, not that they explicitly mention them. Still, I doubt that Keynes invented the concept, or he would (most likely) have given it more explanation. —Comiscuous

Keynes implicitly presented himself as-if talking about a mainstream up-to-but-not-including Keynes when using the term “classical”. But what he presents is a caricature which most nearly approximates Pigou. —SlamDiego 01:51, 25 April 2007 (UTC)

There are numerous preconditions for utility to be measurable in practice, including but not confined to utility being quantified. Entire books have been written about this subject. It is questionable whether this article should wrestle with the issue, especially as there is a separate article on utility (albeit presently shot-through with confusions). It would be more sound to have a separate article, to which this one (and that on utility more generally) might be linked, discussing the preconditions.

I agree —Comiscuous

While a change can effect an increase in pleasure of some sort simultaneously with an increase in pain of some sort, that is not a simultaneous increase in utility and disutility, even if we accept a hedonic notion of utility. Exactly one of four relations must hold between any two states $S_{1}$ and $S_{2}$:

• $S_{2}$ is preferred to $S_{1}$
• $S_{1}$ is preferred to $S_{2}$
• $S_{2}$ equivalent to $S_{1}$
• $S_{2}$ is incomparable to $S_{1}$

The last two cases do not correspond to $S_{2}$ being preferred to $S_{1}$ simultaneously with $S_{2}$ being preferred to $S_{1}$, hence a move from $S_{1}$ to $S_{2}$ is neither useful nor “dis”·useful

Situations in which uses are not partially orderable by desirability (id est when there is incomparability) are outside of the scope of this article. If Bob cannot compare the state in which he has no money but lots of leisure with a state in which he has no leisure but lots of money then he is Buridan's ass.

I take it that you mean to say that disutility is not a measure of "undesirability" only, but of undesirability relative to another possibility. My question concerning measurability and comparability revolves around the possibility of measuring the utility of a choice outside of any consideration of its preference to an alternative. If this is impossible, than what good is the concept of utility? In other words, what else is implied by saying "x has greater utility than y", beyond what is expressed by "x is preferred to y"? The reason that I ask is that Keynes' assessment of the classical economists has them assuming two propositions: 1) that the wage is equal to the marginal product of labor 2)that the utility of the wage when a given volume of labour is employed is equal to the marginal disutility of that amount of employment, subject to certain inefficient disturbances in equilibrium. I want to know how to measure disutility and utility so I can know if proposition 2 is a tautology, and if it is not, why not. As far as Bob goes, I'm not sure that there is room for him to be buridan's ass, because he has no choice but to either work or not work. No matter what he does, he seems to be making a statement regarding the utility of employment whether he knows it or not. —Comiscuous

1. Measurement is always against something.
2. Ultimately, the difference between discussion in terms of utility versus discussion in terms of preferences is just a difference in framework. However, it is easier to engage in some mental operations in on framework than the equivalent operations in another. This is perhaps most clearly seen in the case of expected utility analysis for decision-making under uncertainty. Ramsey &alii demonstrated that a relatively small set of plausible axioms about such decision-making imply and are captured by the existence of utility and probability functions, and the required operations are very simply performed using those functions. But even if we confine ourselves to the static case, it remains true that it is often easier to convey or to hold a thought in terms of utility than in terms of preference.
3. The second proposition is not tautological, and actually rather dubious.
   • It assumes that working is necessarily a bad (rather than, for example, a good that competes with others for one's time).
   • It presumes not simply quantification of utility, but a utility function that comes down to just $U(W,L)$ (with $W$ being wages and L being labor).
   • It assumes that money and labour are continuously divisible so that limits can be reached.
   • It assumes that competition amounts employer and amongst labourers is sufficient that limits will be reached.
   • It assumes that boundaries will not bite.
4. If we accept the underlying assumptions of the proposition, then it is no more or less tautological than any other theorem.
5. The essence of the problem of Buridan's ass is not that the ass has n choices; it is that it is paralyzed by indecision about the two best within its feasible set. Both the ass and Bob have a decision imposed upon them by the frame. —SlamDiego 01:51, 25 April 2007 (UTC)

When groups attempt to order their desires, Arrow's impossibility theorem applies.

Only when they vote on it, I think. When a group of people makes a utility judgement that it is better to delegate their decisions to a single member of the group or a small group of members (for strategic advantage, say), the group itself makes a choice (utility judgement?) that is independent of the utility judgements of all the individual members. I wouldn't pass any judgements on groups regarding fairness of their collective decisions, even if they purported to be representative decisions, because fairness has yet to be defined to my satisfaction. —Comiscuous

If by “vote” you mean voting of the ordinary sort, then: No, not only when they vote on it. Arrow's impossibility theorem applies to any collective decision-making process, and can be expressed as a statement about social welfare functions. Ordinary voting is one way of aggregating preferences. But we could also have voting schemes that allowed weighting, multiplications of weighted votes across persons, &c; in other words, every social welfare function corresponds to a sort of voting, and vice versa. —SlamDiego 01:51, 25 April 2007 (UTC)

Unless you accept a majoritarian metaphysics, there is no reason to see collective agreement as transcending subjectivity. —SlamDiego 03:40, 24 April 2007 (UTC)

I do not accept a majoritarian metaphysics, I was just wondering if the fact that a utility judgement is made by a group meant that there was some way of measuring that judgement. I'm not sure there is in any case, nor am I sure that the concept of utility has any non-tautological meaning. —Comiscuous 15:24, 24 April 2007 (EST)

The issues of measurability and subjectivity are somewhat orthogonal in this context. And a collective with perfectly harmonious preferences would be no more or less subjective than Robinson Crusoe, who (at least until Friday appeared) also did not meet with dissent. —SlamDiego 01:51, 25 April 2007 (UTC)

Passed v0.7 nomination

Very nice article. Consider a peer review, and sending to WP:FAC after that. Titoxd^{(?!? - cool stuff)} 17:40, 27 April 2007 (UTC)

Possible confusion to readers

The openning sentence of this article may be confusing to some readers. As an introductory decription the one found at [1] is an example of a more easily understood definition. [Unsigned comment by Axiomsofchoice]

That simpler definition is not correct as a generalized statement. It assumes that utility may be measured by satisfaction. Many marginalists assumed just that, but the article is careful to distinguish this conception as a special case. A general principle is at play here: Confusion may result from over-simplification. —SlamDiego 04:28, 22 May 2007 (UTC)

The confusion arises simply because the jargon is virtually unintelligible to an average reader who might prefer plain English. Whilst the article cited above may not be true in the general case it is clearly far easier to understand. --Axiomsofchoice 18:50, 22 May 2007 (UTC)

• Easier-to-understand-but-wrong is not acceptable.
• There is no jargon in the definition. No word in that definition is used in a way peculiar to some discipline. —SlamDiego 04:33, 23 May 2007 (UTC)

Hayek's suggestion

This line: "(On the other hand, Hayek or Bartley has suggested that Marx, voraciously reading at the British Museum, may have come across the works of one or more of these figures, and that his inability to formulate a viable critique may account for his failure to complete any further volumes of Kapital before his death.)" is speculation, and from an ideological perspective. It does not matter who speculates - it is still speculation and adds nothing of worth to the article. —Preceding unsigned comment added by 24.27.23.241 (talk • contribs)

Nope, it does matter who offers a theory. Wikipedia editors are not entitled to offer their own, original theories theories, nor to present theories of others as if they are fact. But this is a theory from a notable source, presented as a theory and properly attributed.

In fact, your edit history shows that you've allowed all sorts of theorizing from those with ideological perspectives to remain unmolested. You are here simply trying to push a POV. I caution you that a pattern of POV-pushing will get you blocked.

What is aded of worth by noting the theory in the article is not simply discussion of important possible interplay between the development of Marxism and that of Marginalism, but the point that the claim that Marginalism was a reaction to Marx can be stood almost (albeit not quite) on its head. That is to say that, if Hayek/Bartley is correct, while Marginalism was not much shaped in reaction to Marx, Marxism was left unshaped in reaction to Marginalism. —SlamDiego_←T 11:27, 5 June 2007 (UTC)

Please don't accuse me of POV when you capitalize Marginalism in every instance. As to what you say here:

"the claim that Marginalism was a reaction to Marx can be stood almost (albeit not quite) on its head. That is to say that, if Hayek/Bartley is correct, while Marginalism was not much shaped in reaction to Marx, Marxism was left unshaped in reaction to Marginalism."

Can this section of the article be changed to reflect this meaning, instead of positioning the lack of further volumes of Das Kapital to Marx' inability to fathom or incorporate marginal utility?

It really seems like Hayek is presupposing that marginal utility is correct (it is certainly very good at modeling economic behaviour), and is taunting or belittling Marx for not discovering it.

Examples:

"*may* have..."

This means it is speculation.

"his *inability* to..."

Was it Marx' task to describe marginal utility?

"his *failure* to..."

Was it ever Marx' goal to incorporate marginal utility with his works?

The point you make is fine, but it need not be with such wording. Marx did not write subsequent volumes because of deteriorating health; Engels and Kautsky were left to finish the work from Marx' notes after he died. This reason is reason enough, and has some validity to it. Hayek's speculation, even though it is from Hayek, is a superfluous layer. You can say what you want to say without including ideologically-driven (yes, it is) speculation. —Preceding unsigned comment added by 24.27.23.241 (talk • contribs)

1. Capitalizing the word “Marginalism” here doesn't demonstrate POV. It is an artefact of following the convention that the names of belief systems should be capitalized. (I don't do this in the article simply because that's not the style that prevails in Wikipedia.)
2. Any theory can be labelled “speculation”. However, we don't, for example, delete reference in the articles on Marx or on Marxism to his speculations. Properly, we instead make sure that they are presented as theories, rather than themselves as facts.
3. Hayek and/or Bartley offer a theory. It isn't presented in the article as a fact. (What is a fact is that the theory was offered.) You flatly reject that theory in favor of another theory. (One does not have to question whether Marx's health was failing to question whether this failure was the sole source or principal source of his failure to complete Das Kapital.) But that one can subscribe to a different theory is merely illustration that each is a theory.
4. It is the task of any economist to apprehend whatever significance marginal utility might have. Whether Marx had this as a goal is another matter. The theory offered by Hayek or Bartley suggests that Marx did. (Similarly, the old Marxist theory that Marginalism began in a response to Marxism presumed that Jevons, Menger, and Walras had a goal of responding to Marx. The dates of things falsified that theory.)
5. What you want is for the theory to be erased; or, failing that, to be presented in mincing terms so that readers will be coaxed into disregarding it.

—SlamDiego_←T 13:26, 6 June 2007 (UTC)

Ok, you'll just have to block me, because the little section you defend is just too snide not to be POV.

There's nothing snide about it it. And an attitude of “you'll just have to block me” demonstrates that you are presently not proceeding in an acceptable manner. —SlamDiego_←T 16:34, 6 June 2007 (UTC)

I'll remove it again, you'll block me, and I'll just wait for someone else with integrity to continue where I left off.

I have indeed requested immediate intervention. There is no lack of integrity involved in reporting the Hayek/Bartley theory as a theory, which nearly inverts the old Marxist theory, but unlike that theory is unfalsified. —SlamDiego_←T 18:47, 6 June 2007 (UTC)

The view so espoused is fringe and irrelevant to the topic of the article. I'd suggest removal, because it's simply not important enough to be included here, and I'm sure there are alternative views too which are conveniently missing. The wording as it stands is extremely weasly, even if it is sourced. I'm sure there are plenty of other equally snide but equally sourceable comments. -- infinity0 18:35, 9 June 2007 (UTC)

The suggestion came from the work of one of the most famous economists of all time. It is further notable because it demonstrates that a chronologically falsified Marxist theory (of the relationship between Marxism and Marginalism) becomes a workable theory when nearly turned on its head. Your claim that the wording is “weasly, even if it is sourced” flies in the face of the MoS definition:

Weasel words are words or phrases that seemingly support statements without attributing opinions to verifiable sources

especially as the source is provided before the suggestion. And the suggestion is no more snide that that old Marxist theory that Marginalism was formulated in response to Marxism, which theory I never saw dismissed as snide, and which was treated in this article without such dismissal. —SlamDiego_←T 19:15, 9 June 2007 (UTC)

I have included some Marx quotes to try to keep this section of the article balanced. It also makes a lot of sense to draw from the works and ideas of the very person listed in the section heading, instead of just posturing a rival's speculation. My prediction: SlamDiego will be furious that Marx so besmirches Hayek's precious proddings that the offensive words will be removed, and I will be blocked. -Mookie

If you're going to be blocked again this time, it will not be for adding the passages, but for your incivility. The first passage that you cited from Marx seems appropriate enough (albeit not having the effect that you imagine) and the second is perhaps as well (but see below), even if some of your wrapping of them was problematic. —SlamDiego_←T 16:26, 11 June 2007 (UTC)

BTW, you need to get a handle on two things:

1. Marginalism isn't simply acknowledgement that utility has some significance. (Most pre-marginalists understood that utility has significance.) Marginalism is focussed upon marginal utility.
2. Marginalism isn't simply recognition of the concept of marginal utility, it is also the working out of its significance.

That's why the passages that you cite aren't an effective rebuttal of Hayek/Bartley; they don't show Marx having any answer to Marginalism. —SlamDiego_←T 17:26, 11 June 2007 (UTC)

No, it does not refute Hayek's speculation. (Don't take this to mean that I concede that that line ought to be in there. It adds NOTHING to the article.) I still think your inclusion of it is POV, but because Marx does not specifically address MU (or, if he does, the quick research I did was not enough to find it), nothing I have will "refute" it. What it does do is show that Marx was aware of these ideas, and suggests that while his analysis took note of them, he did not address them more vigorously as part of his theory, not because he couldn't do it (as Hayek suggests), but because it was not his goal.

Modern economics may be based on marginal utility, but in his time it was not, so his critique of political economy began from labour value. Expecting a dead person to adhere to an economic understanding that was developed and honed a great deal after he died is ridiculous. Speculating (as a noted rival) that he couldn't finish his works because he couldn't include these ideas is definitely POV.

I will not try to remove it again, because the addition of those Marx quotes provides an opportunity for readers to see the extent of Marx's dealings with the subject, as opposed to just Hayek's. The quotes themselves add little value to the article, but, then again, neither does Hayek's speculation. Both could be removed to make the article more streamlined. —Preceding unsigned comment added by 24.27.23.241 (talk • contribs)

It is quite alright to make clear that Marx had given some thought to the significance of utility, though I rather think that it would more need explicit statement if he had not, insofar as such failure would set him apart.

Marx wasn't attempting to simply exhibit properties of the preëxisting theoretical framework; he was trying to see the underlying truth of the human world, and claimed to have done so. Nor can one really imagine Marx, confronted with Marginalism, defending his work as if it were a board game rather than science.

One of the things about the Hayek/Bartley suggestion that seems to have escaped you is that it imputes to Marx enough intelligence to see (before 1883) that marginalism presented a very great challenge. Since the second generation of Marginalists were already publishing years before Marx's death (Jevon's, Menger, and Walras having first published in 1863, in 1871, and in 1874, respectively), this imputation is not a great stretch.

As you have repeatedly been told, reporting on a PoV (or the product thereof) is not the same thing as endorsing a PoV. Wikipedia reports points-of-view, and the products thereof. If the Hayek/Bartley suggestion were reported as fact, then (in the absence of sound evidence in its support) the neutral point-of-view policy would be violated. As it is, it isn't even reported that Hayek or Bartley believed it, merely that one of them suggested it as a possibility.

—SlamDiego_←T 20:19, 11 June 2007 (UTC)

More on Marx

I don't know much about marginal utility (I came to learn), but I have read a lot of Marx. There are some fundamental errors here.

"to Marx labor was the ultimate source of value." This may be contributable to Marxists but not Marx. The person who wrote this has conflated the two. Marx:

Labor is not the source of all wealth. Nature is just as much the source of use values (and it is surely of such that material wealth consists!) as labor, which itself is only the manifestation of a force of nature, human labor power. http://www.marxists.org/archive/marx/works/1875/gotha/ch01.htm

Critique of the Gotha Programme is very good for identifying the differences between Marx and Marxists (he wrote it as a criticism of the United Workers' Party of Germany.)

There is a problem of conflating use-value with value here also. According to the political economists that Marx was critiquing, they are not the same thing. There is also no mention of exchange-value here either which is fundamental to an understanding of use-value.

"[...] utility was considered as all or nothing; it was unnecessary to describe variable use-value". I don't understand this. Isn't "It is, moreover, determined not only qualitatively but also quantitatively" sufficient to completely explode this idea? I mean, it's even quoted in the text! Perhaps I don't understand what the wikipedian is getting at. We need to explain what is meant by "utility was considered as all or nothing". Marx would consider commodity x to have more use-value for one person (or a group for that matter) than commodity y. Commodity x would also have different use-value over time. A steam-powered machine, for example, has a high use-value for a capitalist in the 19th century, but might be completely useless in the 20th century. The use-value would therefore be variable right? I can provide references (from Capital) where Marx talks about the necessity to keep machines running because running or not running their use-value dissipates (through becoming obsolete or simply rusting.)

"The doctrines of marginalism and the Marginal Revolution are often interpreted as somehow a response to Marxist economics." This is again a paradigmatic shift. Only a Marxist would say there are Marxist economics. Marx was not positing the LTV as his economics, he was criticising it. You need to make this cristal clear.

As for: "his inability to formulate a viable critique may account for his failure to complete any further volumes of Kapital before his death," it is useless speculation, I don't care if it is referenced. Maybe if Marx had said somewhere "Look I cannot get me head around this marginal utility thing maybe I should hold off on publishing" then it might be interesting.

My recommendation for this section on Marx is that it be scrapped in its entirety. The first paragraph seems to be entirely incorrect. The second is speculation and the third is only useful given that the first two exist.

Ledpup 03:29, 9 October 2007 (UTC)

Passages from Marx

I have corrected a few substantive problems in the wrappings on the passages from Marx:

1. “in language similar to marginal utility.”

   This imposes the editor's (odd) opinion in interpretation. As far as I can see, Marx is simply noting the (previously noted) point that money will cease to circulate as such if its value-in-exchange drops below its value-in-use.

   Additionally, I had undone the silent insinuation of emphasis in the passage by the editor, and in the wrapping changed “limit” to “natural limit”, so that the reader will note the term that the editor wished to emphasize, without spurious imputation of the emphasis to Marx himself.

2. “Utility is considered all or none, not along a continuous curve”

   Continuity is not the only alternative to dichotomy, as the writer should recognize even if the article hadn't carefully made the point that generalized marginalism doesn't assume continuity.

3. “most likely for the sake of simplicity”

   Most Marxists have not read this as mere simplification. (Certainly Marx did not declare that it as such.) What could be appropriate here would be citation of an authority who believes that it was for the sake of simplification, not a bald declaration of 24.27.23.241's interpretation as “most likely”.

—SlamDiego_←T 16:22, 11 June 2007 (UTC)

Some of this analysis came from Morishima's Marx's Economics, some parts I remember from pgs 8-15. I don't know how to cite non-web resources so could not include it. If you want to degrade me for this ignorance, by all means do, but please refrain from telling me what I know and don't know. You have been most uncooperative and heavy-handed this entire ordeal. Instead of meeting me halfway and acknowledging like you should have that Hayek's speculation adds nothing (read it again) to the article, you blocked, belittled, and insulted me. —Preceding unsigned comment added by 24.27.23.241 (talk • contribs)

It isn't incumbent upon me to meet you “halfway” by erasing a piece of historical truth. (Imagine, indeed, how each an every article in Wikipedia would be reduced to nothing by humoring such demands in series!) Again, you are willing to see that

Marxists believe X.

can be a established fact regardless of whether X itself is a fact at all. To be consistent, you'd see that, likewise,

Hayek suggested Y.

can be a established fact regardless of whether Y itself is a fact at all. —SlamDiego_←T 20:40, 11 June 2007 (UTC)

Second passage from Marx

Bearing in mind that this article is about marginal utility: What relevant insight is exhibited by the second passage from Marx that isn't already exhibited by the first? If this article were about utility more generally, I could see how we might want to capture what Marx wrote about utility more generally. But, as it is, the first passage shows that Marx knew that utility had significance, then the second simply has him talking about it without affirming, denying, or acknowledging a significance of marginal utility. —SlamDiego_←T 17:56, 11 June 2007 (UTC)

Hayek's speculation adds even less to the article section on Marx and marginal utility and should, if honesty and integrity are valued criteria, be removed outright. At least now Marx has a voice in a section that purports to show how marginal utility supersedes his ideas. That they weren't present before tells me that SlamDiego is not interested in a fair and balanced article, but instead one based on ideologically-driven speculation. —Preceding unsigned comment added by 24.27.23.241 (talk • contribs)

1. The relevance of the parenthetical note on the Hayek/Bartley suggestion has already been thoroughly explained.
2. Since you admit that the second passage doesn't add anything (but offer it as a ill-conceived tit-for-tat), I'm going to remove it.

—SlamDiego_←T 19:41, 11 June 2007 (UTC)

Actually, since above you admit that the first passage shouldn't be read as about marginal utility, I'll remove it and keep the second, which does a better job of exhibiting his thought on utility in general, as opposed to its relation to whether a commodity circulates a money or as a good. —SlamDiego_←T 19:46, 11 June 2007 (UTC)

“closest”

An assertion that the marginal use was merely “closest” to the margin would suggest that there might yet be some distance between that use and the margin; but that wouldn't be coherent. The margin is located by that use. —SlamDiego_←T 08:31, 12 July 2007 (UTC)

Questions for Slam

Thanks for your message on my talk. There are three things in particular that I don't understand about your approach, the:

• Convoluted (and to me redundant) "that of its" in the first sentence.
• Combining of two definitions ("...in other words"...) in the first sentence
• Including in the first paragraph the term's origins, which to me should be a separate par.

Can you explain your reasons for these? Grant | Talk 02:26, 13 July 2007 (UTC)

Okay:

• “that of its”:

  The attempt is to produce a definition that is fully correct, yet recognizable to those who have conceptualized utility as satisfaction as does mainstream economics. I mentioned isomorphism to you on your talk page because, actually, anything that can be said here about satisfaction could be said about use and vice versa, but that's a subtle point around which people would have trouble wrapping their heads. Consider three paths:

  1. Start the article not by defining “marginal utility” but by explaining utility.
  2. Write an enormous definition of “marginal utility” that explains utility in its course.
  3. Write a definition of “marginal utility” which postpones an explanation of utility.

  That last is what I've done. Let's look at the phrase from which that “that of its” is extracted: “The marginal utility of a good or service is that of its least urgent possible use”. This could of course be unpacked to “The marginal utility of a good or service is the utility of its least urgent possible use”.

  • If utility is just use, then this becomes: “The marginal utility of a good or service is the use of its least urgent possible use” which would indeed be convoluted. However…
  • If utility is satisfaction, then this becomes: “The marginal utility of a good or service is the satisfaction from its least urgent possible use”, which on the surface is not convoluted.

  So the definition is recognizable to those used to conceptualizing utility as satisfaction.

• Two definitions?

  What you're calling a second definition doesn't really have an independent life, so I don't see it as a second definition. The whole purposes of the phrase “the use that is just within the margin of constraints” is exactly and only to explain what the devil the word “margin” is doing in the term. There isn't really a new idea in the phrase, there is just synonymy.

• Term origin in the first paragraph:

  The first paragraph is primarily definitional. I don't see why one would want to separate the etymology from the definition into a one-sentence paragraph. (I'm not generally opposed to one-sentence paragraphs, but I think that one needs a positive reason for their sentences to be separate from others.)

—SlamDiego_←T 03:21, 13 July 2007 (UTC)

Thanks for replying. In general, I would sum up my difficulties with the present wording of the intro by saying that I think we need to explain jargon, and therefore need to expand the intro and break it down for general/lay readers. Similarly, following from what you have said about the definition, I think we should point out in the very first sentence that the definition is fraught with controversy, and provide two or more distinct definitions. That would be an "encyclopedic" way of handling it.

You say the definition should be "recognizable to those used to conceptualizing utility as satisfaction." I think this is the wrong approach for the very first sentence of an article in a general encyclopedia, because only certain schools of economists conceive of it in that way, whereas few general/lay readers would.

"In other words" means that it is a different/separate definition, even if it does not conflict with the first definition.

To me, definitions, etymology and historical origins are all quite different/separate things. As I alluded above, I think the whole intro should be expanded, which would solve the problem of one-sentence paragraphs. Grant | Talk 04:33, 13 July 2007 (UTC)

• But the definition isn't fraught with controversy; it's fraught with confusion that is under-recognized. Providing two distinct definitions would embrace rather than clarify that confusion.
• One of the criteria that any WIkipedia article has to meet — often quite unfortunately — is that it must be achieve consensus support. Personally, I would love to be able to write the definition itself without worrying about editors from solely a neoclassical background coming along and rewriting it into something that was recognizable to them but not fully correct.
• I don't deny that what you're calling a second definition is at least very close to being one. It could become one with a trivial amount of rewriting. But that second definition would be nearly opaque. (It would beg the question of which uses are at the margin and why.) Again, the only function of what follows “in other words” is to explain the presence of “marginal”. I'm not saying that it would be intolerable to break the point into a separate sentence; but I simply don't see good reason to do so.
• The word “etymology” actually comes from the Greek for true history, and the English word literally refers to the study of the history of a word.

—SlamDiego_←T 06:12, 13 July 2007 (UTC)

BTW, the proper place to present a thorough-going explanation of different conceptions of utility is definitely not in this article, but in the article on utility. Right now, that article is grossly inadequate. I have seen complaints on its talk page, some of them years old, but they don't seem to have resulted in the necessary reform. —SlamDiego_←T 06:25, 13 July 2007 (UTC)

Problems with that replacement definition

1. “good” — That rolled “good or service” into jargon without good cause.
2. “to a person” — We'd normally be talking about a person, but that's not intrinsic to the concept.
3. “successive” — The concept of succession is essential to the “law” of diminishing marginal utility, but it is not essential to the concept of marginal utility itself.
4. “income or the budget constraint” — The concept does not require there to be anything like money, and a more abstract reading of “income” and of “budget” is again return to jargon.
5. “marginal utility indicates the value of the marginal unit, given the budget constraint” — Lost the whole purpose of the original second sentence, which was exactly and only to draw attention to the point that the margin is the constraints.

—SlamDiego_←T 22:38, 14 July 2007 (UTC)

Thomas— This article is laden with references that make plain that the neoclassical conception of utility is a special case. The article takes great care to be fully correct, which requires it to be fully general. Not all of the original generation of marginalist used what was to become the mainstream conception, and there are marginalists to-day who are not using that neoclassical conception. —SlamDiego_←T 00:07, 15 July 2007 (UTC)

As to whether utility is use or somehow instead indicates use: What is now the second sentence was (until a few days ago) just a clause “in other words, the use that is just in the margin of constraints” (which did not thus presume an equation), and I was happy with it; its present form was accepted to mollify another editor, and actually a distinction between indication and equality would not be as meaningful as you perhaps think. —SlamDiego_←T 00:34, 15 July 2007 (UTC)

Problems with the current definition

Thank you for comments, Slam, and for your willingness to engage in discussion with improvement of the article as our common goal. I cannot do full justice to the above now but hope to do so in the next week. Meanwhile, I hope that attention might be given to fixing problems with the current 1st 2 sentences of the article, whether addressed by you or others:

(A) The marginal utility of a good or service is the utility of its least urgent possible use, from the best feasible combination of actions in which its use is included. In other words, marginal utility is that for the use that is just within the margin of constraints.

Here's what I think it's trying to say, or what it should have tried to say, although still cumbersome:

(B) The marginal utility of a good or service is the utility of the last unit of that good, given the highest level of utility from use of income on all but that unit. In other words, marginal utility is the extra utility from the good that leaves the highest-utility use of income other than the additional unit unchanged.

That's an interpretation that is at least closer to that of for example Paul Samuelson and William Nordhaus's Economics (2001, p. 769) textbook definition in its Glossary (which cites econ. dictionaries, encyclopedias, etc.) Here's a paraphrase of their definition:

The additional satisfaction from 1 added unit of a good, holding constant the quantity of other goods consumed.

It is also consistent with mathematical treatments of subject.

There is no citation for (A) above. You would add credibility if you cited such a source, and conversely. I am very skeptical that there is any such source, needless to say, but would be delighted to be proved wrong. The problem is in the wording.

Your 21:48, 14 July 2007 Edit summary says an "earlier definition is in fact more technically correct" than mine which you replaced. I won't speak about "more," but (A) is unrecognizable as the non-special case asserted by you above. You don't say that the "special case" is wrong, but, if your general defininition is unrecognizable as a generalization of the special case, then it needs rewriting. I know that you've put a lot into trying to improve the article. I hope that you would be able to do a little more. Thanks. --Thomasmeeks 23:21, 15 July 2007 (UTC)

First, it is 'not trying to express the thought of (B). Definition (B) implicitly involves the ability to perform addition and subtraction on whatever it is that we call “utility”. I draw your attention to the fact that I have repeatedly objected to the presumption that utility is necessarily quantified. (I am not simply talking about the usual distinction between “cardinal” and “ordinal” utility. What is usually labelled “ordinal” utility is still a quantification, merely not treated as a uniquely valid quantification.)

When you say that (B) is “consistent with mathematical treatments of subject”, that really amounts to nothing more than that the British/neoclassical conception has been mathematically formalized. In fact, so has (A); and, had it not been, that lack of formalization wouldn't be particularly meaningful. (The mathematics of (A) is relational algebra.)

Now, for (A), I would direct you to the following works cited in the article:

• Georgescu-Roegen's article ““Utility”, in which the difference (yet coherence) of the Mengerian conception is recognized.
• Mc Culloch's article, which mathematically formalizes that Mengerian conception.
• Menger's Principles.
• Böhm-Bawerk's Positive Theory, from which the comes the passage below, for which definition (A) will fit and definition (B) will not.

I am aware that the present definition isn't ideally transparent. While I will resist any attempt to simplify it at the cost of making it wrong, I have some hope that discussion with you or with others will lead to its improvement. On the other hand, I note that anyone who has got himself locked-in to one definition can have peculiar difficulty in understanding another. —SlamDiego_←T 00:33, 16 July 2007 (UTC)

On (B):

An ordinal utility function is commonly represented as complete and transitive (and therefore reflexive). It does not imply additivity. Ir does require only being able to rank commodity bundles as more, less, or =ly preferred, unique only up to a linear transformation. Think a Silly Putty thermometer. Best of all is when the MUs (unobservable directly) drop out in favor of price ratios, which are observable.

(A) is obviously not in BB. I haven't seen McC (yet), what I read is consistent with the valuational measurement of MU, which you reverted.

Are referring to the following articles?

N Georgescu-Roegen - International Encyclopaedia of the Social Sciences, 1968 "Utility"

J. Huston McCulloch,"The Austrian theory of the marginal use and of ordinal marginal utility," Journal of Economics 37(3-40 September, 1977

The latter does not look very general to me. From what I've read I doubt that it is in the former, which is close to my definition. I also doubt it's in Georgescu-Roegen, but I'm not afraid to look.

A utility function can have different properties of interest. If you can one common denominator, it might be kind of boring. If you find one that has testable implications (such as the "law" of demand) that seem supported by common experience, so much the better. And by statistical testing, better still. --Thomasmeeks 02:21, 16 July 2007 (UTC)

I am well-versed in the properties of what mainstream economics calls “ordinal” utility. But not only is the quantification of utility not essential to the concept, it in fact improperly rules-out orderings that cannot be fit to a quantified proxy. (The presumption that a proxy could always be found is mathematically equivalent to de Finetti's Conjecture, which was disproved by Kraft, Pratt and Seidenberg in “Intuitive Probability on Finite Sets”, Ann. Math. Statist. Volume 30, Number 2 (1959), 408-419.)

(A) obviously fits Böhm-Bawerk. And (B) plainly does not because the marginal change is not, in fact, grain-by-grain, even though he plainly notes that the farmer could have allocated other than by whole bags; in other words, the notion of marginality is different (because it is not intrinsically atomic). Now I will grant you that the example doesn't show Böhm-Bawerk actively rejecting quantification of utility, but neither does he show it playing any rôle in the decision-making process; it's an unnecessary assumption. And since an “ordinal” utility functions cannot be fit to some rational preferences, but the Mengerian conception can, that distinction is more than a mere concern for parsimony.

Yes, exactly as I said, I was referring to works noted in the article.

Whether or not you will see any of these articles as themselves attempting to be general is not essential to proving that the neoclassical conception does not fit the thinking of some important marginalists and hence is not itself the general conception.

McCulloch's doesn't begin as if presenting a generalization. But what he overtly does ab initio is to show that the Mengerian conception isn't the neoclassical conception. As I said below, one of the things that we might want to discuss is whether the Mengerian conception is parallel or subsuming. Even if it were parallel, the point would remain that the neoclassical conception does not contain the Mengerian as a special case, and is therefore not acceptable as a general conception.

(To show that the Mengerian conception is not subsuming, one needs to find something positively in it that is not in the neoclassical conception, just as quantification is not in the Austrian School conception. McCulloch explicitly notes that the v. Neumann-Morgenstern model is mathematically a special case of the Austrian School concept; the same could be said of neoclassical models more generally, since all the features that distinguish the v. Neumann-Morgenstern from the more general neoclassical notion are amongst the features that distinguish it from the Mengerian notion.)

Why should it have been presumed that you feared to look in Georgescu-Roegen? Again, the point to note is that Georgescu-Roegen noted that the Mengerian system doesn't employ a quantification of utility.

I have no idea whether you will be bored or excited if and when you recognize the generalization. As with what the neoclassical economists typically take to be the definition, there isn't enough in the general definition by itself to get things such as the “law” of demand, but one doesn't have to accept any of the distinctive apparatus of the neoclassical definition or assumptions to get that “law”.

In any case, even if the general definition is boring or were of no scientific use, it should still be identified and described. Alleged scientific uselessness would be a thing to discuss in a “Criticisms” section, or in sections explaining peculiar merits of the neoclassical conception.

—SlamDiego_←T 03:45, 16 July 2007 (UTC)

(1) An economic theory that fits every hypothetical problem is fine to talk about, but a more practical approach is try solving real or theoretical problems as they present themselves. Your citation is about probability with no reference to economic theory. If there is a connection, the source should be shown.

(2) There is nothing obvious about (A), much less that it fits BB who could be a model of clarity, as your quotation nicely illustrates.

(3} The scaling of quantity units (lbs., oz., etc.) is arbitrary, and they can be as small or large as necessary to fit the problem.

(4) A point of ordinalism, as mentioned above, is to show that absolute quantification of utility is unnecessary. Another is not its necessity but its convenience in connecting theory to observational counterparts (price, quantity) to test implications of the theory. It does not, contrary to your suggestion above, have "any rôle in the decision-making process." Rather its role is s to model the decision process. It is purely an analytical convenience. Necessity has nothing to do with it.

(5) You write as though neoclassicals were not marginalists, which of course they were, at least in common terminology. The entire entry in New Palgrave: A Dictionary of Economics for "neoclassical economics" is "See MARGINALIST ECONOMICS"

(6) Useful scientific theories are a subset of all scientific thoeries. They are special theories. Their usefulness is what makes them special. Generality by itself does not make a theory interesting or useful.

(7) "Georgescu-Roegen noted that the Mengerian system doesn't employ a quantification of utility" does not make (A) coherent. Manger may not have employed a quantification of utilitym, but the "utility" article in New Palgrave: A Dictionary of Economics, v. 4, p. 778. states that Mangere treated utility as cardinally measurable.

(8) None of the above remarks clarify (A). It is at this point unsubstantiated. Moreover what you have said does not suggest (A) can be substantiated with page-specific references in the sources you mention. Can you help satisfy Wiki requirements with page-specific references? The burden of evidence is on the person defending a passage. Thank you. --Thomasmeeks 15:14, 16 July 2007 (UTC)

1. McCulloch makes use of the the cited work. (In any event, you and I both know that economic theory doesn't have to be know to be, or even just to be, practical to be economics, and the de Finetti conjecture concerns ordering assumptions that you should recognize from economic theory.)
2. (A) is just (B) with the non-essentials discarded. (A) doesn't presume that utility is quantified, doesn't assume that changes in the good or service are small or of regular size, &c. Thus, it should be obvious to you that it fits Böhm-Bawerk, even if it is not. We can go over it bit-by-bit, but I fear that you will first have to recognize that (B) is not correct before you are receptive.
3. Alleged “units” whose size can change at any instance are not units at all; they are merely quantities.
4. As I said, I am well-versed in the properties of what mainstream economics calls “ordinal” utility. Menger doesn't build his theory with quantification; Böhm-Bawerk doesn't build his theory with quantification; Mises (work also noted in article) declares that quantification is impossible (and produces a mistaken attempt at proof thereöf) yet proceeds with marginal utility analysis; and McCulloch provide the mathematical formalism of the Mengerian approach for those who needed it. Meanwhile, you've already seen that “ordinal” utility won't fit all rational orderings, so it isn't even a proxy for a general marginal utility.
5. I write in rejection of the neoclassical insistence that they are marginalists. I do so because neoclassical economics not only was not thorough-going in its application of the marginal utility concept, but even (from the ascendancy of the Hicks-Allen approach until the ascendancy of EU maximization) walked away from marginal utility analysis. There is a large literature which makes the same distinction as do I. The two groups whom I observe treating “neoclassical” as synonymous with “marginalist” are just some of the neoclassicals themselves, and the Marxists.
6. Whatever you and I might or might not jointly or separately believe about the importance of operationalizabiliy isn't relevant to the problem at hand. The Mengerian tradition isn't going to be excluded here based upon some philosophy of science. Again, deficiencies can be addressed in a “Criticisms” or perhaps in the exposition of rival views.
7. I said earlier that (A) is just (B) with the non-essentials discarded. If you can prove me mistaken in that, then it will be improved.
8. Under the formulation that you are now attempting, if I can show that your neoclassical candidates are mistaken, but no one produces an explicit reference that merely omits the errors of the neoclassical candidates (while keeping the portions about which economists can agree), then we shall have no definition. That result would be sufficiently grotesque that it wouldn't survive arbitration, and it's not a trump card for anyone here, Thomas. In any case, (A) was clarified, but perhaps not sufficiently. (I had hoped to proceed through this discussion in a more orderly fashion, but you launched a sort-of neoclassical charge; you're going to have to live with the fact that the path upon which you've put us will get us to resolution in a messy manner if at all.)

—SlamDiego_←T 19:17, 16 July 2007 (UTC)

Tangential Datum: The coinage of “neo-classical” was by Veblen, specifically in “The Preconceptions of Economic Science” (1899), and in his very first use of it, he explicitly says that the Austrian School is almost like the neo-classical, which of course meant that they're not the same. The Austrian School, for its part, has always resisted the label “neo-classical” (with and without hypenation). (At this time, I have no idea how the Pareto &alii felt about the label or otherwise about being tossed-in with the neoclassicals.) —SlamDiego_←T 11:29, 17 July 2007 (UTC)

There ought to be at least page-specific reference(s) for (A) (referenced above) in the lead. (That still wouldn't save it, b/c it is unintelligible.} --Thomasmeeks 16:12, 17 July 2007 (UTC)

I keep telling you that I'd welcome a more transparent definition so long as it remained fully general. I have never been happy with any of the definitions in the article, including those that I've written. As to it being unintelligible, every version that I wrote was tested on some non-economists to see if they could get it, and they did. This article was positively reviewed by the Version 1.0 Editorial Team. It a real deficiency that the presentation has been a problem for some who have been preconditioned to see utility in general and marginal utility in particular with Benthamite or neoclassical presumptions, but let's recognize the boundaries of that problem.

As to a citation for the definition per se, that would be good, but I can plainly demonstrate that a definition that requires quantification, small or unitary changes, &c is not fully general. So, one way or another, the central definition of the article can not treat these things as essential. —SlamDiego

I take it that you do not have a source you can cite for (A). That's pretty crucial. Context and language matter. I'm sure that you see the connection of (A) to MU. I try to put myself in the shoes of the innocent reader, & I don't see the connectionn without connectiog a lot of dots that I don't see in (A). As for non-economist test groups, well, it's human nature to want to please others or to want to see something that others see. Whether agreement carries over to more rigorous tests is something else. For a more general definition, there needs be be a WP-citeable source, if it is challenged. Thanks. --Thomasmeeks 01:40, 18 July 2007 (UTC)

I admit to not having a source immediately in mind or at hand; I've not yet begun looking. You're still threatening to play a card that wouldn't work. If taken to arbitration, I will cite sources to prove that any definition which treats quantification as essential is false. Arbitration is then going to require that whatever definition is selected will not make that presumption. I will be happy to work with you to arrive at a definition that will be more accessible; I am willing and was planning to look for a concise source. But, in any case, there will be no cheap imposition of neoclassical conceptions here.

The Version 1.0 Editorial Team is not in the business of flattering editors, and some of the people on whom I tested it were asked to apply it.

—SlamDiego_←T 02:04, 18 July 2007 (UTC)

"Essential"? That is not a real issue. Arch-neoclassical Kenneth Arrow pronounced measurable ordinal utility meaningless in his 1951 classic. It's obviously unnecessary, since it drops out of the marginal conditions. Indeed he showed in the volume honoring Samuelson how Samuelson's FEA ordinalism [could] be restated without loss of generality to remove even the measurable-to-a-linear tranform assumption.

The article is not about utility, but marginal utility. Arguably, measurability of utility is neither here nor there, literally.

May I ask what would you consider a reasonable time to track down your definition? Thanks. --Thomasmeeks

You are confusing various concepts of measure and of measurement. (I have consistently linked the article to “Measure (mathematics)” rather than to “Measurement”.) The point of using what neoclassicals (badly) labelled “ordinal” utility is that no measure is presumed to have unique significance. However, so long as one is able to perform the operations of the calculus, or even merely the operations of arithmetic than underlie them, then there is a measure essentially involved, even if there is not a measurement. And so long as there is a measure essentially involved, the conception does not fit that of one of the major players in the Marginal Revolution, and some rational orderings are unnecessarily excluded. (It is perfectly fine to note that the quantified special case gains tractability when it sacrifices some robustness; I did that in the lead that I wrote.)

Measurability, which corresponds to measurement is indeed not here.

I think that anyone and everyone who wants this article to be as good as possible should look for a source until one is found. Again, I've presented the sources that show that the neoclassical conception is not fully general. Ideally, you would help forge a more accessible expression of a fully general definition and/or see if you can find a concise expression in the literature, rather than attempting to compel the reader to think inside the neoclassical box. —SlamDiego_←T 03:31, 19 July 2007 (UTC)

A search for the perfect, as distinct from an available referenced, definition is, I believe, an exercise in futility, well illustrated by much of the above. Presenting and defending an incomprehensible, unsourced definition in the article is sad. A well-referenced source that fits actual, not hypothetized or Pickwickian, use should be the objective. --Thomasmeeks 18:03, 19 July 2007 (UTC)

The ideal definition would be both correct and associated with a concise expression in the literature. No incorrect definition is acceptable, even if the alternative is to use one that summarizes an article or chapter or monograph, rather than corresponding to a single sentence therein. —SlamDiego_←T 02:33, 20 July 2007 (UTC)

Slam, I know that you object to quantification of utility. I would guess that you you also object to quantification of goods (1 apple, 2 apples, etc. of given quality, etc.). Am I right? --Thomasmeeks 19:52, 19 July 2007 (UTC)

No, I wouldn't raise that objection. First, it's one thing to show that C0 is a generalization of C1; another to show that it should be called by the same name; I've not encountered a marginalist school that notes some possibility of unquantifiable goods or services, and applies what it calls “marginal utility” to the analysis thereof. Second, I am skeptical that such a generalization is possible; while I can think of bivalent cases, where quantification might seem a tad silly (but would just represent the use of a dummy variable), I cannot think of any case in which it would be formally incorrect. (If you can, then I'd be very glad to be exposed to it!) —SlamDiego_←T 02:33, 20 July 2007 (UTC)

Böhm-Bawerk quotation

A pioneer farmer had five sacks of grain, with no way of selling them or buying more. He had five possible uses: as basic feed for himself, food to build strength, food for his chickens for dietary variation, an ingredient for making whisky and feed for his parrots to amuse him. Then the farmer lost one sack of grain. Instead of reducing every activity by a fifth, the farmer simply starved the parrots as they were of less utility than the other four uses; in other words they were on the margin. And it is on the margin, and not with a view to the big picture, that we make economic decisions.

---

Indeed a nice quotation. It is relevant for refuting a misapplication of marginal utility. Too bad the farmer so misconstrued the use of marginal utility theory. Of course a proper understanding would make the 2 goods: grain for parrots vs. the remaining bags for the composite good. What would change is a little less in the other uses of grain (unless the parrots were considered too much of a luxury).

Composite goods are relevant for generalizing consumer theory including marginal utility in relation to the demand for a good. For the benefit of our vast readership, Hicks (1939}) shows that the composite good can be treated like a single good as to analyzing the substitution and income effect of a change in price or income. So, that there is no loss in generality in going from the 2-good case to the n-good case in keeping ordinal utility but with diminishing marginal utility to analyze demand, a neat trick. --Thomasmeeks 22:00, 15 July 2007 (UTC)

No, Thomas, the fact that one can reananlyze the problem from the perspective of the British/neoclassical tradition doesn't somehow make v. Böhm-Bawerk's presentation not marginalism or wrong marginalism. And that passage is a presentation of marginal utility theory by one of the most important early marginalists.

The function here of the quote is to illustrate that the marginalism of Menger, v. Böhm-Bawerk, &alii clearly employs a different conception of marginal utility than what the neoclassical economists have slipped into thinking is simply the conception. (Your response neatly illustrates that presumption.) So, then, some questions are: Is the conception used by Menger &alii coherent? If so, are these two entirely different conceptions (as some who answer “yes” to the first question believe)? Are they parallel, or does one subsume the other? (The Mengerian conception plainly isn't a special case of the neoclassical conception, but can it be the other way around?)

If you'll back off on presuming that v. Böhm-Bawerk must be wrong because his approach doesn't fit the neoclassical conception, then we can productively deal with those questions, and perhaps with others. —SlamDiego_←T 23:25, 15 July 2007 (UTC)

I agree with BB that the farmer would be misapplying MU theory. The composite-good approach shows just how as to the income effect: a bit less of several things rather than only one. BB was making his point in a way that would have made Frédéric Bastiat#Works smile: what's important is not all-or-nothing (or the total utility of the parrots), but a little less or more of this, that, and so forth. --Thomasmeeks 01:10, 16 July 2007 (UTC)

Böhm-Bawerk does not say that the farmer misapplied marginal utility (the farmer isn't even indicated to be conscious of the notion); Böhm-Bawerk used the example as a simple exemplar of the concept. You're simply going to have to swallow hard than and accept that we have here an example of a conception different from that of the neoclassical tradition. —SlamDiego_←T 01:23, 16 July 2007 (UTC)

BB doesn't have to say it. It would be a misapplication to so use MU theory. BB's point was not to so misapply it but to illiustrate the usefulness of a theory that explains how people respond to circumstances that affect them at the margin. English writers learned something from BB & other Austrians (Kirzner, "Austrian School of Econonomics," v. 1, p. 147). From the premise that Austrians made important contributions it does not follow that no one else did, as I believe the above illustrates. Far from showing the incompatility of BB's insights, the above demonstrates the opposite. --Thomasmeeks 12:25, 16 July 2007 (UTC)

1. The farmer isn't using (or misusing) marginal theory any more than any other typical economic actor is using economic theory. 19th century farmers were not presumed to have read or discussed the works of the Marginal Revolution.
2. You keep asserting that this is a misuse, yet nothing about it is economically irrational. I would find it grotesque to starve the parrots, but economic rationality does not have a component of morality or aesthetics. Someone else might find the parrots a complement to exercise (or somesuch); the farmer is evidently a man of simple tastes. And rationality does not require an additional assumption that there is some sufficient quantity of parrots such that one wil give up a tiny amount of whisky (or whatever) to have them, let alone that these quantities (large and small) are feasible in this discrete case.
3. Claiming that Böhm-Bawerk here silently meant us to see this as a mistaken use is no different from someone trying to use the same formulation to exclude anything that you might cite. (“Samuelson really meant us to take Foundations as just a grand joke, dontcha know?”)
4. No one here claimed that no one else made important contributions. And I know the history of marginal utility theory rather well.
5. So far, I have actually used the Böhm-Bawerk quote to one purpose, to rebut the standard presumption that marginal changes are by definition “very small” or even unit changes. You seem essentially prepared to do without that assumption, though we may have to wrestle with the concept of unit more before you do.
6. You have insisted that the definition (A) fits the quote. Setting aside the unit issue, it does, but only in the same sense as also does “cardinal” utility. The reason that you don't insist that the quote illustrates “cardinal” utility is because nothing in it calls upon absolute measureability. Well, nothing in it calls upon measurability at all.
7. I do have other purposes to which I will put this quote should they prove relevant, but I hadn't put it to any purpose when you jumped-in feet-first. (You had, after all, indicated that there could be a delay of days before you were free to take up discussion.)

—SlamDiego_←T 20:09, 16 July 2007 (UTC)

(1-3) Well, my point was that BB provided a reason, an economic reason for the farmers action, just not a good one (unless the parrots were such a distinct luxury good, say if the farmer was otherwise on the edge). And his point was that people are not likely to act in that grotesque way. Rather BB's MU approach was closer to explaining how they likely would act.

(5) That's a separate point, which earlier referenced by the water-diamond paradox and the related difference between value in use (we might say total utility of a good) and MU of one more unit of a good.

(7) I meant taking up discussion of my suggested gloss (B) of (A) to make it more intelligible and consistent with standard definitions. That didn't preclude discussion of (A) on its own terms. --Thomasmeeks 15:20, 17 July 2007 (UTC)

(1-3) Böhm-Bawerk does not critique the behavior as grotesque. “The past is a different country. They do things differently there.” And some of what they do seems grotesque to us. (Amundsen, by plan, ate his frickin' dogs!) Again, the farmer's behavior is economically rational (as perhaps was Amundsen's); Böhm-Bawerk does not critique it as wrong in any way wrong.

(5) Of course it's a separate point. But it was one of the two points that I actually had in mind when I posted the quote for future reference. And we evidently did have to deal with the issue of units.

(7) I do not know why you think your (7) to be a response to my 7, which only notes that I might reference the passage for other purposes, and that your attempts at preemption have create a bit of a mess. Again, your (B), with it s reference to a unit of the good or service, didn't fit the passage from v. Böhm-Bawerk. —SlamDiego_←T 01:16, 18 July 2007 (UTC)

On your (1-3) OK, delete the word 'grotesque', which I which was your characterization, and my (1-3) statement still stands. --Thomasmeeks 23:06, 18 July 2007 (UTC)

Did doesn't matter what negative word we apply, the point is that the farmer's behavior is unusual by the standards of one time and place, and not by those of another. Unless it is shown to be economically irrational or we can find v. Böhm-Bawerk objecting to it somewhere, there is no case that he intends this as an example of misuse of any sort. —SlamDiego_←T 03:06, 19 July 2007 (UTC)

So, I'm gathering, the right reading of BB is one that renders MU theory less relevant to explaining how a normal person might act. --Thomasmeeks 13:45, 19 July 2007 (UTC)

Well, that's not how I put it; but, yes. It is more generalized than some conceptions might be. My whole point has been to make the article generally correct. —SlamDiego_←T 02:10, 20 July 2007 (UTC)

I assume that your comment is in response to my previous comment. But the most plausible interpretation in that light is that you are saying BB is more generalized by explaining less about the real world. That doesn't compute. So, you must have had something else [in mind]. --Thomasmeeks 02:13, 21 July 2007 (UTC) 10:57, 21 July 2007 (UTC)

It computes just fine. Just as a general explanation of mammalian behavior won't necessarily predict the specifics of canine behavior, a general explanation of economically rational behavior won't necessarily predict the specifics of typical economically rational behavior. And it is to this extent that your previous characterization of what v. Böhm-Bawerk was saying is correct. —SlamDiego_←T 03:16, 21 July 2007 (UTC)

The point of the entire dialogue above has been how to interpret the BB quotation. Rationality (which may be construed as rational choice theory) was never the issue (at least for me), only how to apply it to the BB quotation. Your remarks offered one interpretation. I described it as "more generalized by explaining less about the real world." You did not disagree with the description. I offered another interpretation. As to your last sentence above, I haven't figured out what the relation of the transition phrase "And it is to this extent that" to what precedes or follows it. I don't doubt, however, that the sentence is well intended. --Thomasmeeks 10:57, 21 July 2007 (UTC) Thomasmeeks 11:31, 21 July 2007 (UTC)

1. “And it is to this extent that” is there because multiple possible interpretations could be made of your earlier remark. Operating under one interpretation, I had agreed with it, only to have you declare that “That doesn't compute.” However, it does compute; I am forced, then, to allow for the possibility that you meant something other than what I took to be the natural meaning of your words is (natural or otherwise) not their intention. That allowance is not a commitment to the presumption that you meant something different.
2. If you never challenged the economic rationality of the farmer, then the point of your comment of 16 July 2007 at 01:10 becomes mysterious.
3. Whatever may be the case there, the Böhm-Bawerk passage illustrates that various presumptions in standard treatment of the theory of marginal utility and of the history of that theory are mistaken (though it does not plainly illustrate all deficiencies in standard accounts).

—SlamDiego_←T 11:33, 21 July 2007 (UTC)

{1} I was trying to apply the principle of charity to your intents and thought that you could not have meant what I was inferring from your words. I was floored that you agreed with my inference.

[2] I challenged the relevance of the reason attributed by BB to the relevance of MU as usually construed. It is not that such behavior or reasoning is impossible, just irrelevant for most market disturbances on average. And I believe that that was BB's point, just as a positive-sum game may escape some of a certain persuasion in describing a market economy, to the detriment of their analysis. Economic action is typically "at the margin," rather than going from all of 1 commodity to all of everything else from a price change. A theory that predicted the latter would be irrelevant for describing most market behavior. BW, Slam. --Thomasmeeks 17:15, 21 July 2007 (UTC)

1. Part of your surprise may be an artefact of not noting that what isn't presumed in definitions can still be accepted in overt assumptions.
2. Your reading, then, presupposes a mainstream that hadn't yet formed when v. Böhm-Bawerk wrote that passage. And it is one thing to have an approach that can speak of marginal utilities when the relevant change is large or leads to dramatically different marginal application of the commodity, and entirely another to have an approach that can only speak of such changes. Böhm-Bawerk wasn't committing to a world in which marginal changes were always or even usually so different from the sort that neoclassical economists now routinely suppose; but he had not need to set aside marginalism when he wasn't in the realm of such changes. (As to his actual point in providing the example, there is no reason to see it as any more than to drive home that as means are cut, the ends regarded as most expendable are discarded. In this case, the b_st_rd farmer starved the birds.)

—SlamDiego_←T 18:06, 21 July 2007 (UTC)\

Slam, on your (2), end, your reading is most consistent with the BB text. I've waated a lot of your time. Many regrets. --Thomasmeeks 02:20, 22 July 2007 (UTC)

Let's try to resolve this debate by explaining clearly and historically why it is so contentious

My lordy, what an awful article. SlamDiego will probably accuse me of being neoclassical, or something like that, but it took me almost an hour to understand why the definition included the words "the least urgent possible use". If I'm not mistaken, the reason those words are included is that a given frenchfry might be the first frenchfry you eat (and thus "inframarginal") or the last one you eat (and thus "marginal"); the marginal one you eat is the least urgent one. Is that what you're driving at, Slam? I'm sure there are many subtle errors in this rapid description, but it's the best I could do in less than an hour. I hate to think how long it would take most of the remaining millions of English speakers (or the millions of English-language students taking social science classes) to understand your definition.

Listen, folks, we have to find a better way to write this article. Let's think out of the box a bit here. Some people want a comprehensible definition. Some people want a correct (and entirely general) definition. Nobody has found a way to do both.

So instead, let's follow the example already given us (probably by Slam?) and include some historical context here, in addition to the mention of Friedrich von Whatsit. Utilitarian philosophers and economists intended the concept to mean roughly what your Econ 1 student thinks it means: the extra happiness you get from consuming one more unit of a given good. (I'm sure you will correct me if I'm wrong, Slam...)

BUT, as they started thinking hard and arguing about the concept, they discovered that it was muchmuchmuch more subtle than they originally thought. (I'm sure you will correct me if I'm wrong, Slam...) For many reasons (such as the fact that the first frenchfry and the last frenchfry are not necessarily identifiable as instances of the same good), and most importantly because many thinkers question the notion that the numbers we attach to utility have any meaning beyond providing a partial ordering over consumption bundles, saying how much "extra" utility you get from "one more unit of the good" is very difficult.

Therefore, I propose the following rewrite of the introductory section. And I am going to paste it there immediately. (I'm sure you will revert it if you disagree, Slam... but really, if you disagree with my version, maybe you can help us write a brief description of what MU is INTENDED to mean, accompanied by a comprehensible explanation of why things are not that simple.)

  The marginal utility of a good or service is a
  concept in economics that is intended to mean the increase in utility
  obtained by consuming or using one more unit of that good or service.  
  However, this apparently simple definition hides some subtle philosophical issues.
  In particular, many economic thinkers argue that utility is not quantifiable: 
  even if we can say that one consumption bundle is more desirable
  than another, that does not imply that there any meaningful scale of units to measure
  satisfaction or happiness.  Therefore, "how much utility increases" when one more
  unit of some good is consumed is, according to this argument, a meaningless question.

  A definition of 'marginal utility' which avoids any assumption of quantifiable
  utility is the following.  For a given unit of a good or service, the marginal utility
  to a given decision maker is the utility of its least urgent possible use, 
  out of the best feasible combination of actions in which its use is included 
  by that decision maker.  In other words, its marginal utility is 
  the utility obtained when using it just within the 'margin' of the constraints
  faced by that decision maker.

  Under either of these definitions, the same object may have different marginal utilities 
  for different people, reflecting different “tastes” or individual circumstances. 
  The concept grew out of attempts by economists to explain the determination of price. 
  The term “marginal utility” arises from a translation of “Grenznutzen”, 
  coined by the Austrian economist Friedrich von Wieser.
   

P.S. When I say the article is awful I am referring to the introduction, which is the part most users will read. Most of the rest is really very good and very interesting. But the article MUST start with a comprehensible explanation of the concept, even if that comprehensible version refers to a very special case. I would be delighted if anyone can marginally increase the comprehensibility of my version.

Your changes to the introduction and elsewhere are based upon a conjectured and false history of the origins of the confusions and of other things. (For example, if you will read Hicks' actual paper, then you'll see that he didn't punt just “cardinal” utility; and it is still to-day easy to find micro textbooks that would discard utility altogether as ostensibly wrong.) Your discourse above is a combination of such conjecture with personal attacks against me; along with a misunderstanding of what is under contention. I have already more than once stated to Thomasmeeks that I am receptive to the notion that the definition ought to be more transparent. So long as Thomasmeeks believes that the neoclassical definition is correct as a general definition, your thought “outside the box” provides no resolution whatsoever; it would merely offer a preface that led to an assertion of a general definition to which he objects. If and when he recognizes it as correct, he may well be able to help re-present it more transparently. In the meantime, you are just throwing gasoline. —SlamDiego_←T 23:40, 16 July 2007 (UTC)

I've been trying for a while to understand exactly what you meant above by "merely offer a preface". If you thought my reference to "the increase in utility obtained by consuming or using one more unit of that good or service" was merely intended as a preface to a better definition, then you misinterpreted me. On the contrary, I intended that wording as an entirely correct, but not entirely general, definition of marginal utility. There is nothing wrong with that definition, if one starts from a cardinal theory of utility. However, it is not completely general, because it is an incorrect definition under many other theories. If you prefer, we could replace "is intended to mean" by "is", but preface the definition by saying "Under the assumption of cardinal utility, the marginal utility of a ..." --Rinconsoleao 17:48, 17 July 2007 (UTC)

1. A definition of “dog” that fits only beagles is not a correct definition of “dog”. It would not do to say “It is a correct definition of ‘dog’ so long as we start with by thinking of dogs as beagles.” It is not coherent to think that a definition of X which only fits a subset Y is an entirely correct definition of X “but not entirely general”.
2. So long as a definition is presented as more general that Thomasmeeks insists is not more general or is otherwise incorrect, calling it a correct and more general will not resolve the dispute.

—SlamDiego_←T 00:28, 18 July 2007 (UTC)

Dear Slam, I cannot see any personal attacks in my comments. I described the article as awful, which I still believe is a fair description of an article with an incomprehensible opening sentence. I also used sarcasm to complain about your apparent unwillingness to accomodate rewriting of this page. Perhaps if your name included "meek" rather than "slam" I would have addressed you in a softer tone, but my impression was that you were willing to engage in robust argument. I apologize (really, I do) for any offence caused. But I insist: this article needs a clear introduction easily understood by the lay reader. I will continue demanding changes until it is improved. And I was sincere and attempting to be constructive when I suggested that a more historical approach to the opening paragraph might be what we need. --Rinconsoleao 15:58, 17 July 2007 (UTC)

By the way, I really did think that the issue under contention was defining MU in a way acceptable both to people who regard utility as quantifiable, and those who do not. If that's not the issue, could you please briefly explain what is the issue, for those of us who have trouble digesting this 11516-word debate? --Rinconsoleao 16:38, 17 July 2007 (UTC)

Well, you are making valiant efforts, none of them wasted in the larger scheme of things. But as of the 17:30, 17 July 2007 article, the lead pretty much avoids history. I think history is interesting, but gets in the way of stating more interesting things. I believe that the best way to lure readers into reading more is to present approaches compellingly and clearly enough that they are not put off by history. Stated otherwise, history should be a reward, even a dessert, for attention, not a reason to stop reading. With the exception of para. 2, the current lead satisfies this standard, I believe most readers would judge. --Thomasmeeks 18:05, 17 July 2007 (UTC)

If you cannot see any personal attack in your comments, then I suspect that you go through life oblivious to how much offense you offer. To follow up your claim that you cannot see yourself as having made personal attacks with further personal attacks is perverse. I cannot accept an apology given in such context; it is nearly meaningless. What there actually was constructive in your comments could have been offerred without persoanl attack, and it could have been left on the talk page until it was discussed, so that, for example, its misrepresentation of history could have been fixed.

Since, as has already been noted to you, I have repeatedly told Thomasmeeks that I am receptive to the notion that things can be improved, your assertion “I will continue demanding changes until it is improved.” is the sort of rhetoric best forgone.

You also could have asked whether you properly understood the issue before presenting what you thought to be the resolution. The known issues are or have been:

1. Whether marginal utility can be meaningfully defined without explicit or implicit quantification. In insisting that a definition that implies quantification is fully general, Thomasmeeks has said that it is not.

   (Nothing that I've put in the article rejects the possibility of quantified utility; and I took care to include such things as the section “Quantified marginal utility”, to allow readers to see how quantification is normally incorporated.)

2. Whether marginal changes in the good or service are of fixed size. Thomasmeeks appears willing to let go of terms such as “unit”, so I believe that we are passed that issue.

Additionally, setting aside the purely mathematical properties of utility, we might have to discuss to what it refers. Alternately, we might find ourselves in effective agreement.

—SlamDiego_←T 00:28, 18 July 2007 (UTC)

"Criticism of the marginalist explanation of the paradox..."

I don't understand why this paragraph is needed. Obviously any neoclassical who believes that marginal utility affects prices also understands that the marginal cost of production affects prices (unless, purely for simplicity, one focuses on a situation of pure trade, instead of the more realistic case of production and trade). I would suggest inserting a brief mention of marginal cost in the previous subsection, and delete entirely the "criticism" and its response. (Though the Whately quote is rather nice.) --Rinconsoleao 20:22, 17 July 2007 (UTC)

First, note that it is not a paragraph; it is two paragraphs. The first originated as part of a Marxist attempt to turn this article into an ostensible debunking of Marginalism. I corrected its factual errors, and included the second paragraph. There are many aspects to the structure of this article that represent making what concessions can be made to the demands of other editors while remaining within the constraints of being correct. —SlamDiego_←T 22:53, 17 July 2007 (UTC)

In addition, a citation would be required to demonstrate that someone actually takes this seriously as a criticism of marginalism or of marginal utility. --Rinconsoleao 20:33, 17 July 2007 (UTC)

I don't see that such a citation is required, as anyone familiar with the Marxist discourse has encountered such assertions many times; it would be like citing an asserion that cats have fur. But, if you feel that a citation is needed, then by all means provide one. The practice of some editors of deleting passages without citations, rather than instead just finding the citations, is very bad. —SlamDiego_←T 22:53, 17 July 2007 (UTC)

Seems fair to assume in today's world that those "familiar with Marxist discourse" may be rather few. I wouldn't know where to find such a criticism. If you do, it would be helpful. Anyway, I'm relieved to know you were more involved in paragraph 2 than paragraph 1... --Rinconsoleao 23:14, 17 July 2007 (UTC)

The point of Wikipedia is not to tell people what they already know, nor should it overtly footnote everything that it tells them. (Amongst other things, the readership would be driven away by the nightmare of footnotes. If you really feel that this passage should have a footnote; then you can google to find Marxist pontifications. I am already dealing with enough pile-on here as it is.

The article as I found it is easily found in the history. There have, since, been various parties trampling-in with mud on their boots; I have cleaned-up what I can. —SlamDiego_←T 23:41, 17 July 2007 (UTC)

Question

Was it Marshall who adopted von Wieser's "Grenznuzen" into English as "marginal utility"? --Rinconsoleao 20:49, 17 July 2007 (UTC)

That seems unlikely if the last ref. of the current lead is correct about "unjustly." After all, if Marshall originated the translation, who would know better than he where he got the term from? On the other hand, Marshall might not have been the first in print but could have been the originator of the term, so notorious was he in delaying publication. Assume Wieser coined the German term in his 1884 publication. If "MU" was around earlier, Wieser could not have been the source. --Thomasmeeks 21:47, 17 July 2007 (UTC)

Almost certainly, the first translator would have been William Smart. In any case, if anyone has found an earlier instance of “marginal utility”, then he or she has kept it to his- or herself. There were various other terms used by others. For example, Clark (an independent reïnventor) had been calling it “special effective utility”, which is a rather good term.

Marshall did not respond well to the Austrian School criticisms of his theory of the supply curve. Part of what followed was successive erasures of the Austrian School from Marshall's discussion of the history and development of Marginalism. Reässigning credit for the term to Gossen would fit that pathology. —SlamDiego_←T 23:25, 17 July 2007 (UTC)

Jevons quote

I put back the Jevons quote, because without it the statement that "the concept grew out of attempts to explain price" lacks context. The Jevons quote doesnt actually use the word 'marginal', but it does clearly refer to a continuous, cardinal conception of utility, and states that trade continues until the 'next' (i.e. marginal) unit sold has the same utility as that bought.

If this seems the wrong place to put it, or if it seems inappropriate because 'marginal' does not literally appear, feel free to move it or delete it... --Rinconsoleao 22:23, 17 July 2007 (UTC)

The problem with the preface that I first removed is that it proceeded on the assumption that all the Marginalists had essentially started with a Utilitarian conception, so that the Mengerian conception would have evolved from that. That's simply not the case.

OK, my mistake. --Rinconsoleao 23:15, 17 July 2007 (UTC)

I have only glanced at the present state of the preface, but it doesn't seem to repeat that mistake. There is nothing wrong in principle with prefacing, nor with including in that preface the conception more familiar with some prior exposure to Utilitarianism or to its children. One question to ask would be of whether the quote is the most accessible presentation of that conception. —SlamDiego_←T 23:04, 17 July 2007 (UTC)

This is the WP:LEAD of the article. IMO, an interested but but innocent reader should not have see the subject exactly through the words of Jevons at that writing. Surely he'd have clarified it for exactly the purposes needed in the present context if he could have. As it is, it's asking the reader a lot to boil Jevons down to get the right context. If we can't find the right quote, better not to use any quote that's not clear enoough for the general reader. A better quote might be in Walras who worked out the math that might have allowed him to make the proportionality of MUs to Ps in equilibrium. The right emotion is empathy for the contemporary reader, not admiration for Jevons, so I believe. --Thomasmeeks 00:33, 18 July 2007 (UTC)

I've not yet looked closely at the lead, because I have been concerned to read (and to reply to) what has been said on the talk page before further edits. But I am inclined to doubt that such a quotation is appropriate in the lead. I am also inclined to believe that, because of considerations of length, the use of quotations in the body of the article should be very limited. I would not delete the passage if Rinconsoleao put it in the body, for the same reason that I left one of the passages from Marx in “The Marginal Revolution and Marxism”; but I really hope that Rinconsoleao will agree to a modern paraphrase. —SlamDiego_←T 01:23, 18 July 2007 (UTC)

“cardinal” utility v. “ordinal” utility

In his edits, Rinconsoleao has repeatedly associated the dispute with the distinction between “cardinal” utility and “ordinal” utility; he has further linked to the articles thereon. Unfortunately, this is not the relevant distinction. The problem is that the names of these two conceptions (“cardinal” and “ordinal”) are not good descriptions — both in fact represent a sort of quantification. They were named under a presumption corresponding to de Finetti's Conjecture or something very much like it, so that the only remaining question was of whether some measure were in some way uniquely meaningful (hence absolute). It would have been better had they been named something such as “strong cardinal” and “weak cardinal”, but that's not going to be changed here. —SlamDiego_←T 02:22, 18 July 2007 (UTC)

POV?

Could someone show me where in A Reconsideration of the Theory of Value the assumption of convexity of the indifference curve is other than a bald assumption? (I'll try later to dig up a page number on Hicks' admission in VC to that effect, but this is obviously low priority, as the present version of the paragraph is okay.) —SlamDiego_←T 19:00, 21 July 2007 (UTC)

Comment on definition in 3rd paragraph of the article

I don't see that the present state of the definition in the third paragraph has moved in the direction of transparency. But I am, for the most part, going to wait for the attempt to stabilize before I make or suggest specific revisions.

I would reïterate that the Mengerian conception proves to be a general one, of which the neoclassical conception proves to be a special case. If an editor finds himself instead presenting a mere alternate special case, then I contend that he has taken a wrong turn. (However, if I could somehow be proven wrong in my contention about the Mengerian conception, then we nonetheless owe it to the reader to present a general definition.)

—SlamDiego_←T 11:42, 27 July 2007 (UTC)

Well, definition (A) above (in the article from which the present definition descends) wasn't "ideally transparent" (Talk:Marginal utility#Problems with the current definition, SlamDiego←T 00:33, 16 July 2007, last para.). Both discussants of that section agree on that. The 3rd paragraph has additions meant to make more explicit the (presumed) terms in that definition, and, more pertinently, to the terms in the current definition. It is not enough to say that the earlier words meant what they said. If there is no context for determining what they meant, the definition and discussion are not transparent and need more work. Wieser takes a couple of pages to give context to his definition. The third para. attempts to do the same thing in one para. Does it succeed? One response is, "in comparision to what?" "Improvements in transparency" (presumably including clarity) are fine if do clarify, rather than leaving it for the reader to "figure it out" on the basis of only untransparent terms that are supplied or omitted necessary terms. If 'transparency' means cutting unnecessary words, that's fine too, provided there is no loss in helpful context. --Thomasmeeks 18:14, 27 July 2007 (UTC)

Transparency comes down to the ability of readers to apprehend the what is written. I think that it may be that the new definition (as it stood when I wrote the above) would be one through which a neoclassical economist could more readily work, but it had become more intimidating for lay readers. (I've not read whatever changes may subsequently have been made.)

I continue to hold and admit that the earlier definition wasn't ideally transparent; I don't believe that we are faced with a dilemma of having to chose that or the definition which last I read.

—SlamDiego_←T 00:14, 28 July 2007 (UTC)

If "lay readers" were not intimidated by the earlier definition, it is b/c they supplied a context in spite of the the text (as for [1A] below) or an impossible context (as for [2A] below). Here is the relevant earlier article Edit definition of SlamDiego 11:16 21 July 2007:

The marginal utility for a quantity used of a good or service is the use of that quantity that stands at the margin of feasible uses.<fn omitted> In other words, marginal utility is the least valuable use amongst those in the best possible combination of uses. (Italics added.]

Here are comments on each of the italicized phrases above:

'Quantity' in the above does not distinguish total quantity from marginal quantity. The current counterpart does (as does every standard exposition).

'Stands at the margin of feasible uses' is in the eye of the reader who might or might not guess what is referred to. There is no context in the para. that allows the reader to determine what it means, unlike the current para., which explicitly defines the term.

The 'in other words' sentence is a non sequitur (logic). Marginal utility is distinct from diminishing marginal utility, which requires an additional assumptions. Nothing in the MU definition requires diminishing MU. The current para. makes that clear by defining MU first, then stating the assumption required to derive the separate proposition of diminishing MU.

For ease of comparison, here are relevant comparative statements earlier (A), then current (B):

[1A] The marginal utility for a quantity used of a good or service is the use of that quantity that stands at the margin of feasible uses.

[1B} Then the marginal utility for a quantity used of a good (say, the fifth unit) is the utility of that quantity that stands at the margin of feasible uses.

[2A] In other words, marginal utility is the least valuable use amongst those in the best possible combination of uses.

[2B] In other words, marginal utility of a quantity at that point corresponds to the lowest-valued use of that good that would be selected.

Surely there is no dispute about the clarification of the earlier first sentence with its current counterpart. What is at least as important is an explanation of the first sent. missing before [1A] & supplied by the current version Before [1B]:

(B1B] First, let the ‘margin of feasible uses’ refer to the highest quantitative utilizaton of goods (including services), such that the total quantity of one available good is maximized for available total quantities of all but that good.

To expect the lay reader to know that (or something like it) to understand (1A) is not reasonable.

As for the 2nd sentences, they look very close. But [1B] is falsely equated to [1A] in the earlier version. Diminishing MU is different from MU, contrary to [1B]. [2B] is not, however, equated to [1B] (for the good reason that they are not equivalent). Rather [2B] is immediately preceded by this new statement

[B2B] Combinations of goods are then assumed to be selected from highest-valued (urgent) quantities to successive lower-valued quantities out to the point where all such feasible quantities are used. This ensures that only higher-valued quantities will be selected at the margin of feasible uses compared to quantities not selected.

[B2B] is not logically equivalent to [1B]. It is an additional assumption from which [2B] follows. To paraphrase from my first statement in this section, Wieser (1889) in the omitted fn. provides enough context to make sense of [1B] & [2B]. That context is lacking as to [1A] and is impossible to supply for [1B] as equivalent to [1A].

For ease of reference, the earlier [A] and current [B] para. from the article in their entirety (except for fn. omissions] are respectively:

[A] A definition which avoids any assumption of quantifiable utility is the following: The marginal utility for a quantity used of a good or service is the use of that quantity that stands at the margin of feasible uses. In other words, marginal utility is the least valuable use amongst those in the best possible combination of uses.

[B] A definition that avoids any assumption of quantifiable utility is the following. First, let the ‘margin of feasible uses’ refer to the highest quantitative utilizaton of goods (including services), such that the total quantity of one available good is maximized for available total quantities of all but that good. Then the marginal utility for a quantity used of a good (say, the fifth unit) is the utility of that quantity that stands at the margin of feasible uses. Combinations of goods are then assumed to be selected from highest-valued (urgent) quantities to successive lower-valued quantities out to the point where all such feasible quantities are used. This ensures that only higher-valued quantities will be selected at the margin of feasible uses compared to quantities not selected. In other words, marginal utility of a quantity at that point corresponds to the lowest-valued use of that good that would be selected.

--Thomasmeeks 01:28, 30 July 2007 (UTC)

1. I wish that you'd numbered (or otherwise ordinated) the thoughts above. We'll end-up with a mess if we start replying with annotations, but without ordination it can be difficult to see that to which a subsequent point is directed.
2. The definition before I had to wrestle with your edits was the more careful

   The marginal utility of a good or service is the utility of its least urgent possible use, from the best feasible combination of actions in which its use is included. In other words, marginal utility is the use that is just within the margin of constraints.[2]

   and it is against the transparency of that definition that I am gauging the transparency of the present definition. (That earlier definition resulted from compromise with Grant65; a still earlier version was “The marginal utility of a good or service is that of its least urgent possible use from the best feasible combination of actions in which its use is included, in other words, the use that is just within the margin of constraints.”) Although that earlier definition is not ideally transparent, it is far more transparent that what has followed (including what I have written in attempts to reach compromise with you).
3. You have made a sloppy reading of [1A]. It did not say

   The marginal utility for a quantity used of a good or service is the use that stands at the margin of feasible uses of that quantity.

   An expression “marginal quantity” is intrinsically more vague than “quantity that stands at the margin of feasible uses”. If you want to argue that other readers will likewise be sloppy and that we should write the definition to offset such propensities, fine; but understand where the failure occurs.
4. There is a definite and significant flaw in (A1); specifically, when I reordered things (as the earlier “in other words” sentence was a closer paraphase of v Wieser) to produce it, I should have inserted the word “best” in front of “feasible”. In other words, the phrase should have become “quantity that stands at the margin of best feasible uses”. Without that “best”, (A1) leans heavily on (A2), whereas (A1) should be able to stand by itself.
5. Otherwise, a bald declaration that the meaning of “stands at the margin of feasible uses” is in the eye of the beholder would be more convincing if you could show a way to interpret it (according to the grammar and vocabulary of English) that were wrong.
6. No, the “in other words” is not a non-sequitur. Nothing requires a least element to be unique (laypeople are well aware that things may tie for last place); and, indeed, it can be the case that

   $min\left\{X_{1},X_{2},\dots \right\}=\left\{X_{1},X_{2},\dots \right\}$

7. What (B1B) added was a term; it adds nothing conceptually. Any apparent conceptual difference between the definition of that term and “the best possible combination of uses” is in fact illusory. (Indeed the word “best” is not particularly precise, but that it because the concept of marginal utility allows for agents to have all manner of notions as to what might be best. And we would have to likewise intrepret your alternate phrase very broadly and allow production-possibilities frontiers of unusual shapes in unusual spaces to have it be fully general.) Increasing the amount of actually jargon is sometimes very appropriate, but should be done only with trepidation in an article for lay readers; and the present definition for that jargon is forbidding. (Indeed, it implicitly suggests that the reader study production possibilities frontiers!)
8. Again, you're mistaken in your presumption that a least element must be unique.

—SlamDiego_←T 14:05, 30 July 2007 (UTC)

The following the comments refer to their numbered counterparts immediately above:

[2T] The definition in (2) is of course def. (A) in Talk:Marginal utility#Problems with the current definition. It is highly controverted there. The definition in (2) is copied below with bolding added:

The marginal utility of a good or service is the utility of its least urgent possible use, from the best feasible combination of actions in which its use is included. In other words, marginal utility is the use that is just within the margin of constraints

There is nothing in the definition that gives the bolded terms sufficient context to assign a determinate meaning to the definition (really 2 definitions, b/c the last sentence is not equivalent to the first (on which, see [7] below). Yes, those already knowledgeable about the subject could try to attach determinate meanings to the relevant terms -- despite the words, not b/c of them. But the proper standard is to read it through the eyes of a reader unacquainted with the context of the bolded terms. All my efforts on the 3rd para. current-MU definition counterpart were aimed at providing additional context and specificity. To repeat from above, Weiser (1889), the cited English source finally provided (by me) for the current definition, gave context, unlike the definitions in (2).

[3T] The first definition in (2) is what it is. I did not impute the interpretation ascribed to it in (3). To impute a "sloppy reading" of the definition in (2) for a definition in [B] that is a descended from the definition in (2) is not a careful ascription. Above at Talk:Marginal utility#Let's try to resolve this debate by explaining clearly and historically why it is so contentious

Rinconsoleao recalls it taking "almost an hour to understand why the definition included the words 'the least urgent possible use'." Judging from Wiki contributions elsewhere, Rinconsoleao's is quite well informed in economics. What does that suggest about the likely success rate of other readers trying to figure it out?

[4T] As for the failure in (1A) to use the phrase "quantity that stands at the margin of best feasible uses." see [2T] above with necessary changes.

[5T] If I state that 4 is an integer between 1 and a million, there's nothing wrong with that, except aa definition of 4. Using ill-defined terms to define another term does not make the other term well defined.

[6T] & [8T] I did try to address these points in Edits.

[7T] (7) states that:

What (B1B) added was a term; it adds nothing conceptually. Any apparent conceptual difference between the definition of that term and “the best possible combination of uses” is in fact illusory.

[B1B] defines the later term 'margin of feasible uses' in the [1B] definition of MU. The 'best possible combination of uses' in Slam's [2A] is an undefined term there. Slam's [2A] corresponds to my [2B], the last sentence in my [B] above. Slam's [2A] is like a theorem, that is, the last line of a proof. What is missing is the rest of the "proof." The 2 sentences before the last sentence are present in [B] but not [A]. They provide the assumptions from which [2B] follows. If Slam is saying that [A] and [B] reach the same conclusion, I would not argue against that. And not just to be agreeable. --Thomasmeeks 03:40, 7 August 2007 (UTC) (sp. Thomasmeeks 11:18, 7 August 2007 (UTC))

“lower” v. “less”, and all that

One way or another, it is a struggle to avoid language such that readers will infer quantification. Especially since the 17th century, there has been a tendency in Western cultural to presume that things are quantified. (That propensity exists exactly because so many quantifications have proved successful.)

As to “lower” v. “less”, I note that in graphing orderings if there is a $\sim$ relation, then $X_{1}\succ X_{2}$ is normally indicated by placing $X_{2}$ lower that $X_{1}$ on the paper. Meanwhile, the name of the arthimetic $<$ relation is normally “less than”, and “less $5” would often mean “minus $5”. My suggestion, then, is that “higher” and “lower” are more suitable than are “greater” and “less”/“lesser”.

—SlamDiego_←T 19:51, 3 August 2007 (UTC)

I don't know about graphing relations in the present context except as related to indifference curves where what is graphed is not MU but marginal rates of substitution between goods (economics) (commodities). I am familiar with ranking notation of R, such as can be used to represent an "ordering" in the sense of a complete and transitive relation (though not necessarily continuously differentiable). This is for example the notation of Arrow's Social Choice and Individual Values#terminology. My verbal translation here agrees with that of indifference curve#Preference relations as to strict preference ("x is more [or less] preferred than y" or "x is strictly [less] preferred to y") or weak preference ("at least as good as" [in terms of being chosen]). That in turn agrees with leaning toward "more valued", "less valued", etc., not "higher-valued" or "lower-valued". "Less valued" is "less valued," with no intimation as to how much less. To me "lower-valued than" suggests a next question: "Well, how much lower-valued?" which is the direction that the paragraph presumably finds it unnecessary (and/or impossible) to answer. (If the terminology referred instead to 'ranking', I'd lean toward "higher ranked", "lower ranked," etc.) --Thomasmeeks 23:52, 3 August 2007 (UTC)

At some point, you want to grab and skim or scan a math book on graph theory. The graphs in question are not (except in special cases) conceptualized as graphs in a Euclidean space. You might think of them as paths, networks, or somesuch.

In the case of partial ordering (of which full orderings are a special case), the relevant graph would in particular be a digraph (directed graph). Digraphs of more general relations might be shown by putting arrow-heads on the connectors, but in the case of a patial ordering, for every $X_{m}$ and $X_{n}$ such that $X_{m}\succ X_{n}$, we can just draw $X_{n}$ below $X_{m}$, and draw the connectors without arrow-heads. (We can also forgo drawing many of the connectors.)

I don't believe that people are going to be more inclined to ask “How much lower?” than “How much less?” My intuition is that it is quite the opposite.

I do think that they are less inclined to ask such things about rank. (Nonetheless, some people will try to offer measures of the relative difference between corporal and sergeant as opposed to that between sergeant and lieutenant. Likewise for any other sort of ranking.)

—SlamDiego_←T 01:03, 4 August 2007 (UTC)

As to my perusing a book on graph theory, hey, life is too short (; ). But I do appreciate the invitation. On your 2nd to last paragraph, there is I believe this additional advantage of "less-valued" over "lower-valued" [quantities] in para. 3 of the article. The "lower-valued quantity" suggests a "lower value" (not merely valuation, a more general term) attached to the quantity and somehow associated with MU. But para. 3 is ostensibly written to deny the necessity of such an inference of MU quantification. The idiomatic counterpart of a ""less-valued quantity" is not a " less value" attached to the quantity but a "lesser value," which suggests MU quantification. Using "less-valued" (as opposed to "lesser-valued") avoids that suggestion, but using "lower-valued" does not avoid that suggestion. --Thomasmeeks 12:25, 7 August 2007 (UTC)

The word “graph” notwithstanding, graph theory doesn't intrinsically demand any pictures, and it is exactly the sub-branch of abstract algebra that underlies the mathematics of preference theory. So if you really want to ponder/debate/write about these issues, then it would probably be in your interest to at least give graph theory a glance.

Again, my intuition is that you are inviting more misapprehension with “less-” than with “low-”, though I know of no lexicon that will express the relevant notions without the possibility of misapprehension.

—SlamDiego_←T 08:49, 9 August 2007 (UTC)

Right, no reason to "demand" it, but I believe that someone (not I) at the 19:51, 3 August 2007 Edit above (last para.) introduced the graph-theory convention (to make a point about "lower" vs. "less") that "in graphing orderings if there is a $\sim$ relation, then $X_{1}\succ X_{2}$ is normally indicated by placing $X_{2}$ lower that $X_{1}$ on the paper." someone (not I) at the 19:51, 3 August 2007 Edit So far as I can determine, there is no claim that graph theory differs in any material way from standard ordering theory for the purpose at hand.

Intuitions can differ from one person to the next. I believe that citing the disadvantage of a parallel usage is a more relevant guide. Here, my intuition is guided by Popper, Objective Knowledge (1979, p. 136), --Thomasmeeks 12:01, 9 August 2007 (UTC)

(Bolded text above indicates material restored to my 12:01, 9 August Edit from a typographical error of my 13:47, 9 August Edit, shown below. The latter Edit also erroneously added material, shown as crossed out above. --Thomasmeeks 18:19, 11 August 2007 (UTC))

The point of the reference to graph theory at that time is that in hierarchial diagrams (which are graphs), lower has meaning that doesn't imply quantity. I wrote on the presumption that you'd be familiar with such things under the name of “graph”; you apparently weren't. But people are certainly aware of such diagrams even if they don't know that they may be called “graphs”. —SlamDiego_←T 12:08, 9 August 2007 (UTC)

The someone (not I) at the 19:51, 3 August Edit above referred to "graphing orderings," not "graph theory" mentioned immediately above. There followed in the earlier Edit a verbal description of a graph (on paper no less), not graph theory. --Thomasmeeks 13:47, 9 August 2007 (UTC)

You're confusing things. Yes, I had in mind a visual representation of orderings when I first wrote about graphing orderings. You responded that the only relevant sort of graph with which you were familiar were of indifference curves. That would imply no familiarity with graph theory (as such). At that point, I thought both that I should recommend that you look into the subject and explain why I'd referenced it. My point in subsequently noting that graph theory doesn't demand pictures was as part of an explanation as to why it had a general importance beyond what one might guess; evidently, I shouldn't have bothered. —SlamDiego_←T 14:09, 9 August 2007 (UTC)

I accept all factual statements after the first sentence of the preceding. As to that first sentence, readers may draw their own conclusions by reading my previous 2 Edits and the responses that they evoked. --Thomasmeeks 18:29, 10 August 2007 (UTC)

My 13:47, 9 August Edit above unintentionally altered my own 12:01, 9 August Edit and (garbled it). I have restored my 12:01, 9 August Edit with bolding to indicate material restored and cross-out to indicate material accidentally added. --Thomasmeeks 18:19, 11 August 2007 (UTC)

Why is de Finetti's conjecture relevant?

Point 1: apparent confusion about the meaning of de Finetti’s conjecture

Back on Slam’s talk page where I appear to have been classified as an “orc” (mistakenly, I assure you), I said:

“...if ‘ordinal’ means a complete ordering, instead of a partial ordering, then indeed it would always imply a cardinal ordering too (just numbering by rank).”

and then I clarified

“When I talk about cardinal utility, I mean putting a number on each consumption basket, and ranking consumption baskets according to those numbers. As long as I put a number on every basket, the ordering becomes complete rather than partial... Thus, I think of cardinal utility as a special case of ordinal utility: it does the ranking by assigning numbers.”

Whether or not these are the definitions that are most correctly considered “neoclassical”, I hope I made clear what I meant. Therefore I think the following response from Slam does not actually address what I said:

“Your belief that any full ordering will correspond to a measure is false... I linked to a free, on-line copy of the article by Kraft et. al, which originally provided the mathematics that it is false...”

Notice that I never said that a full (complete) ordering was a measure; I said that any complete ordering could be used to define a numerical ranking. This is obviously true, as long as one bears in mind that in keeping with standard usage in contemporary microeconomics, I was talking about a ranking over ‘bundles’, not a ranking over individual goods.

Therefore, the truth or falsehood of the de Finetti conjecture is unrelated to my comment, because the dF conjecture did not address whether you can put a number on bundles; rather, it addressed whether a utility function over bundles is decomposable in a particular way. Let me explain what the conjecture said... I didn’t know what de Finetti’s conjecture was before I started reading this page, and I’m sure many of us didn’t, so just let me briefly explain what it says in nontechnical notation. You can check the details by reading the FIRST PAGE of Kraft, Pratt and Seidenberg, “Intuitive Probability on Finite Sets”, Ann. Math. Statist. Volume 30, Number 2 (1959), 408-419.) It’s really much clearer than you might expect!

De Finetti’s conjecture: Consider a utility function U over bundles of consumption goods. Suppose that utility function satisfies three properties called comparability, transitivity, additivity (explained in the paper). Then it is possible to decompose the utility function U by assigning a value u(x) to each individual consumption good x, and expressing the utility of a given basket as the sum over all the x in the basket of those values u(x). THIS VERSION IS SLIGHTLY INCORRECT, because the conjecture started from a ranking, not from a utility function. The correct version (though still stated in the most nontechnical way I can) is immediately below. --Rinconsoleao 07:16, 9 August 2007 (UTC)

De Finetti’s conjecture: Consider a ranking R over bundles of consumption goods. Suppose that ranking satisfies three properties called comparability, transitivity, additivity (explained in the paper). Then the ranking implies that we can assign a value u(x) to each individual consumption good x, such that the ranking of baskets by summing the u(x) over all the x in any given basket is equivalent to the original ranking R. --Rinconsoleao 07:16, 9 August 2007 (UTC)

The paper of Kraft et. al proves that de Finetti’s conjecture is FALSE. However, this observation is completely unrelated to standard treatments today of cardinal utility, and also ordinal utility. That’s because standard descriptions of preferences only rank (or give numbers to) bundles. They don’t attempt to do that for individual goods. See for example the discussion of ranking bundles on p.34-35 (Sections 3.1-3.2) of Varian (1987), ‘’Intermediate Microeconomics: A Modern Approach”, ISBN 0-393-95554-0. So the fact that you can’t break utilities of bundles into values of individual goods is in no way a criticism of today’s preference theories. And as I emphasized, it’s certainly not a disproof of my claim that an ordering of all bundles can be used to put numbers on those bundles (put 1 on the first bundle, 2 on the second, etc... or use reals if there is a continuum of bundles).

Any disagreements on these points? --Rinconsoleao 20:55, 8 August 2007 (UTC)

Absolutely. But I'll just note what is wrong with the central point of this section, rather than critiquing everything. Let “$B_{n}$” be one of your bundles.

There is a very great difference between asserting that

$U\left(B_{1}\right)-U\left(B_{2}\right)$

tells us nothing of use beyond its sign, and claiming that it is an impossible operation. Neoclassical economics doesn't deny the possibility of monotonic or of affine transformations of the utility functions; it declares the results meaningless. If, instead, it declared

$U\left(B_{1}\right)-U\left(B_{2}\right)$

to be an impossible operations, then it would also be locking itself out of things such as

${\frac {\partial U}{\partial x}}$

and what goes with it. So let's imagine

$B_{1}=B_{2}\cup \left\{x_{n}\right\}$

De Finetti's conjecture is, in effect, that there will always be a possible

$U\left(B_{2}\cup \left\{x_{n}\right\}\right)-U\left(B_{2}\right)$.

—SlamDiego_←T 22:55, 8 August 2007 (UTC)

De Finetti's claim was much stronger than your last statement. It says that for any ranking over bundles (which satisfies three properties mentioned above), we can come up with a utility function U such that for all $B_{2}$,

$U\left(B_{2}\cup \left\{x_{n}\right\}\right)-U\left(B_{2}\right)=v(x_{n})$.

In other words, we can uniquely define the value $v(x_{n})$ associated with a given good $x_{n}$, regardless of what other goods are in the bundle $B_{2}$. (Here $v$ is exactly the same notation used in paragraph 1 of the Kraft et al. paper.) Such a strong claim is never made in contemporary preference theory, which is why discussing de Finetti appears to me to be a red herring, just like discussing measure theory. Perhaps such claims were made early on in the theory of preferences; Slam obviously knows more history of utility theory than I do. If so, discussing de Finetti might be relevant at some point in the historical part of the article. --Rinconsoleao 08:00, 9 August 2007 (UTC)

I said “in effect” because the thing with which we should here concern ourselves is the marginal implications for the concept of marginal utility. You are still coonfusing allowing addivity is disallowing non-additivity.

I don't know where you think I equated allowing additivity with disallowing nonadditivity.

Explicitly in the next subsection, and implicitly here when claim “Such a strong claim is never made in contemporary preference theory, which is why discussing de Finetti appears to me to be a red herring”. Strength is about what is allowed or disallowed. In confusing the sort of strength to which we should object, you confuse the sort of disallowing to which we should object. —SlamDiego_←T 09:17, 9 August 2007 (UTC)

If DeFinetti's conjecture were correct, then neoclassical “ordinal” utility would allow additivity. (Exactly as I said: “in effect, that there will always be a possible $U\left(B_{2}\cup \left\{x_{n}\right\}\right)-U\left(B_{2}\right)$”.) Since he was wrong, neoclassical “ordinal” utility disallows additivity. That makes it less than fully general. —SlamDiego_←T 08:21, 9 August 2007 (UTC)

Some ordinal preferences (i.e. some orderings over bundles) allow additivity. The counterexample to the de Finetti conjecture simply showed that not all do. Thus ordinal preferences are sufficiently general to allow both cases. Whether some other conception of preferences is more general than this is another issue, about which I would be happy to be informed. --Rinconsoleao 08:56, 9 August 2007 (UTC)

The reason that I put “ordinal” in quotation marks when referring to the neoclassical conception so named is because the that conception always corresponds to a measure.

Thanks for making such a strong, specific clarification. I would appreciate it if you could clarify further. If U(x) is a neoclassical utility function (or a list of the numbers associated with a complete neoclassical ranking by order of preference), what is it a measure over? Are you asserting that it is a measure over the space of goods x? Or are you asserting that it is a measure over the space of 'utilities' u? Or are you asserting something else? --Rinconsoleao 09:54, 9 August 2007 (UTC)

Neoclassical economics defines a utility function as a mapping, with certain properties, over real numbers. It would be empty, in neoclassical economics, to call this a mapping over utilities, as utilities would be no more or less than that over which a utility function maps. —SlamDiego_←T 10:10, 9 August 2007 (UTC)

Fine. Now in what sense is that mapping a measure? --Rinconsoleao 10:42, 9 August 2007 (UTC)

Arithmetic performed upon it yields meaning full results. For example, as I stated elsewhere, the signs of differences are meaningful. That is why transformations must be at least monotonic (if not more rigidly restricted) to be accceptable, and why monotonic transformations are possible. I have already made these points. —SlamDiego_←T 10:47, 9 August 2007 (UTC)

OK, but if that's what you mean by measure, then it is not what is meant by measure in measure theory. Therefore, I would again suggest that we eliminate the link to measure theory, which will only confuse readers. A measure, in measure theory (as I assume you do know) is a function that maps sets to the real line, subject to certain regularity conditions. The main regularity condition is that the measure of the union of A and B is at least as large as the measure of A. One can perform meaningful arithmetic on functions which are not measures. --Rinconsoleao 11:07, 9 August 2007 (UTC)

For example, the utility function I constructed in example 3 below is not a measure, because the quantities of apples it evaluates can be regarded as sets of apples, but sometimes an expanded set leads to a smaller utility in this case (i.e. if we consider a set that contains two kilos of apples, and then a set of three kilos of apples that contains the previous set). Nonetheless, arithmetic performed on that utility function yields meaningful results. In particular, we can perform a monotonic transformation on that utility function (over its defined range [0,4]), by adding a constant to U, or by multiplying U by 100, or by taking the log of U, and in all cases, the ranking it implies over consumption bundles is preserved. --Rinconsoleao 11:12, 9 August 2007 (UTC)

No, and we already discussed this point at an earlier time. A utility function might also be a measure of apples, but that doesn't mean that a utility function of apples must be a measure of apples to correspond to a measure. A utility function, to be a utility function, must capture preferences. Thus, a utility function of apples can be a measure of the place that bundles occupy in a preference ranking. —SlamDiego_←T 11:43, 9 August 2007 (UTC)

OK, so we agree that a utility function is not a measure 'of' consumption goods, at least not in general. But now saying it is a 'measure of the place that bundles occupy in a preference ranking', is not a claim that it is a measure in the sense of measure theory. (If you disagree please explain why.) As you know, a measure in the sense of measure theory is a very specific type of function. If we are to have a link to measure theory, either you should explain why a utility function is a measure in the sense of measure theory, or you should explain whether there is some other link to measure theory that has not yet been clear from the discussion. --Rinconsoleao 12:26, 9 August 2007 (UTC)

Again, you're saying “we agree” when the truth is that you've wasted more of our time.

A quick-and-dirty answer is to note that probabilities can be assigned to bundles, which probabilities are measures, without necessarily increasing with the count of apples. I'm unsure what is wrong with your understanding of measure, but I'll leave you to sort it out. —SlamDiego_←T 12:40, 9 August 2007 (UTC)

Of course. Probability functions are measures (and any discussion of probability theory will tell you that). Utility functions are not measures (and if you can find a textbook which asserts that a utility function is a measure, I will be very interested. --Rinconsoleao 12:50, 9 August 2007 (UTC)

I spoke too quickly. Probabilities cannot be assigned to bundles, they are assigned to events. So your quick and dirty answer is based on a misconception. But probabilities are measures, because they are functions over events, which are treated as sets; and they obey the property that the union of A and B is at least as probable as A (i.e. the probability of 'A or B' is at least as great as the probability of A). Utility functions are not (in general) measures; they are defined over bundles (which can be treated as sets) but they do not (in general) have the property that the union of bundles A and B has at least as much utility as bundle A. Nor do they (in general) satisfy the other regularity conditions that define whether or not a function is a measure. --Rinconsoleao 13:12, 9 August 2007 (UTC)

No, now you've spoken too soon. Getting a bundle with $n$ apples is an event; getting one with $n+1$ is another. There is an isomorphism, in other words, between sets of bundles and sets of events. —SlamDiego_←T 13:21, 9 August 2007 (UTC)

No, this shows you don't know what an event means in probability theory. In a model where you receive bundles of apples randomly, 'receiving 6 apples' is not a subset of 'receiving 7 apples'. Instead, it is a subset of 'receiving 6 apples or receiving 7 apples'. Whereas when we treat groups of apples as consumption bundles, a particular set of 6 apples can indeed be a subset of a particular set of 7 apples. There is no isomorphism between these two uses. --Rinconsoleao 13:29, 9 August 2007 (UTC)

No, I didn't say that these events were subcases on of another. I said (correctly) that getting $n$ was an event (as illustrated in the remark below, about EU). And I said (correctly) that probabilities can max-up before the apples are exhausted, just as can utility. I was addressing your actual arguments, not whatever argument you may have intended to make. —SlamDiego_←T 13:37, 9 August 2007 (UTC)

Hence, for example, EU models the utility of a lottery as

$\sum _{i=1}^{n}\left[p\left(S_{i}\right)\cdot u\left(S_{i}\right)\right]$

where $S_{i}$ is a bundle (state-of-the-world), $p\left(S_{i}\right)$ is the probability of that bundle, and $u\left(S_{i}\right)$ is its utility.

—SlamDiego_←T 13:37, 9 August 2007 (UTC)

Those equations in no way address whether utility is a measure, which is the question we are discussing. In that EU function, p(S) is indeed a measure, u(S) is not. --Rinconsoleao 13:43, 9 August 2007 (UTC)

Those equations weren't claimed to show that utility is a measure; they were offered to disprove your absurd claim that probabilities cannot be assigned to bundles. —SlamDiego_←T 13:45, 9 August 2007 (UTC)

Wow, now we are really talking in circles. Strictly speaking, a probability is assigned to the event of receiving a given bundle (or any and/or combination of events of this kind), rather than being assigned to the bundle itself. But we should stick to the issue at hand, which is: are utility functions measures? I have repeatedly asked for an argument to that effect. --Rinconsoleao 13:57, 9 August 2007 (UTC)

Since there is an isomorphism between the event of receiving a bundle and the bundle received, if there is a function that maps from the event to a probability, there is a function that maps from the bundle to a probability, so each bundle has a probability, strictly speaking. (And that is yet another point that I'd already made.)

What you've actually repeatedly done is offered arguments that don't quite work to the effect that utility is not a measure, and asked me to defend the claim that it is in the face of those arguments; so I've shown that they don't work. I'll think about a positive explanation (as opposed to negative arguments) when I get a chance.

—SlamDiego_←T 14:59, 9 August 2007 (UTC)

I will eagerly await any positive argument justifying the claim that utility is a measure. --Rinconsoleao 15:23, 9 August 2007 (UTC)

Many irons were dropped in my fire; they are mostly still in it, so I cannot respond as quickly as I would like.

From the perspective that I believe that you've been making your request, the quantification that neoclassical economics calls “marginal utility” is a measure of the set of uses associated with a bundle. Being careful here, one must either take the bundle to be the complete state-of-the-world, or take there to be a mapping from the bundle to that state, and then from that state to a set of uses, and then the measure to be on the set of uses. A bliss point exists when the inclusion of another unit of a good or services would cause a use of something to be lost. (The unit is then really a magrinal bad or disserivce.) That something could be easily seen, as when one is compelled to expend resources on disposal, but it could also take place at the neuronal level that you introduced in earlier discussion.

Again, responses may be delayed. —SlamDiego_←T 04:21, 19 August 2007 (UTC)

Hi again! (Eliminating indents.) No hurry, bc I am hoping at some point to read the McCulloch paper in more detail, which will take time. Just one comment on that comment: 'use' seems to be an inappropriate issue to bring into the discussion of the neoclassical theory. 'Use' is a fundamental element in the Austrian way of defining MU, but it simply never enters into the neoclassical definition (as far as I know). The neoclassical version just starts out by ranking bundles... don't you agree? --Rinconsoleao 10:17, 19 August 2007 (UTC)

While neoclassical theory at times may lose sight of that significance, it always resides implicitly. What, after all, are the real differences between saying that someone has a use for a good or service and that it has utility for her? (&c.)

The fact that a word doesn't appear doesn't mean that its concept is not present.

Indeed, the word “use” does not appear in most Austrian School definitions of “marginal utility”, even those written in English by Austrian School economists (including Mises). McCulloch uses words in a manner different both from the norm amongst neoclassical economists and from that amongst Austrian School economists. Even setting aside the problems of adopting peculiar nomenclature, I don't see his lexicon as ideal; I advocate that we pay attention to the conceptual content of his article.

—SlamDiego_←T 11:52, 19 August 2007 (UTC)

I was trying to be clear about the concepts, not the words. The only thing that explicitly appears in the neoclassical theory is a ranking. Doubtless there are many ways of interpreting that; some interpretations might involve 'use', but claiming that all do seems to be a very strong claim (so strong it sounds like original research). In contrast, Menger's theory, and McCulloch's development of it, are explicitly based on listing 'uses' (by whatever name) before going on to define marginal utility. That's a really interesting model which I had never encountered before I first read this page, and it's obviously worth pointing out. But I see no reason to claim that that model or theory or interpretation hovers at the background of every neoclassical economist's interpretation of the neoclassical theory. --Rinconsoleao 13:03, 19 August 2007 (UTC)

I understand that you were trying to be clear about the concepts. But explicitness is a matter of words. And the claim that use is in the notion implicitly is not particularly strong, nor “original research” as defined by Wikipedia policy.

I am not claiming that the Austrian School theory hovers in the background of the neoclassical theory; in fact, the neoclassical theory, descended from Benthamite origins, is very like the Austrian School theory turned on its head (which would then derive use from utility). The point, however, is that use is at least implicitly present in neoclassical theory (and explicitly so amongst the more utilitarian neoclassical economists), however ill-considered it may be fit in the model. —SlamDiego_←T 05:01, 20 August 2007 (UTC)

Let me explain explicitly, that the association of use with utility is a matetr of simple tautology (and hence not “original research” as defined internally by Wikipedia). Under the neoclassical conception or otherwise, we are talking about decisions as to which goods and services to use, and how to use them. Try to find a production of utility that cannot be said to result from some sort of use of a good or services. (Even gloating over possession qualifies as a use, and is certainly amongst the uses that the Austrian School theory must include.) —SlamDiego_←T 07:20, 24 August 2007 (UTC)

Backing up a bit, while I was keen to establish in discussion that the neoclassical conception is a measure, I am not insistent that the article link to that on measure theory if you can indeed propose an appropriately concise way within this article to clarify the notion of quantification. So long as people associate the word “quantification” with a rather strong conception, we need other words to make it plain that no quantification need be assumed. —SlamDiego_←T 11:52, 19 August 2007 (UTC)

Good, I agree. I think linking to measure theory is not the clearest way to define quantification. Of course, defining quantification does require explaining what it using other words! I'm still not ready to propose a rewording, but I will give it a try at some point. --Rinconsoleao 13:03, 19 August 2007 (UTC)

Well, you'd earlier declared such a term or term or terms to be available. :-/ In any case, right now the burden is carried by linkage, and I see no reason why in theory it could not be carried by a different linkage, so long as it was to an article that would clarify the general concept of quantification. —SlamDiego_←T 05:01, 20 August 2007 (UTC)

Another issue I was wondering about. You gave the Dewey decimal example as a ranking that is not 'quantified'. Seems like a great example, and maybe it would be helpful to have it in the article. My initial understanding of that example was that it showed that the difference between two ranked items is inherently meaningless, if the ranking is not 'quantified'. I still suspect that is what you mean, since many neoclassical treatments specifically point out that differences are meaningless in ordinal utility (I recently ran into a statement like that in the Kreps textbook). But then I realized that another interpretation of the example is that the Dewey decimal codes simply are not numbers (i.e. they have too many decimal points in them, and often include letters too). Which of these two points were you intending to make... or were you intending both? --Rinconsoleao 10:17, 19 August 2007 (UTC)

We can always map from even the most rococo expression of the Dewey Decimal system to one that contains only digits. (And a system that uses letters only to ordinate is plainly not in principle different from one that uses hexadecimal digits to ordinate.) The point is that ordinates can be numbers without being quantities.

I believe that I owe that example of the Dewey Decimal system to some paper by McCulloch. I suspect that it would be more appropriate to use that analogy in the article on utility than that on marginal utility. The article on marginal utility simply shouldn't bear responsibility for the full functionality of the article on utility.

Again, the neoclassical conception doesn't necessarily want to do much with the quantification, but it wants to do things such as play with signs (as in associating decreasing marginal utility with a negative second derivative). If no quantification can be fit to some rational orderings, then even this relatively modest use of quantification is unacceptable.

—SlamDiego_←T 11:52, 19 August 2007 (UTC)

And note that, in these cases, $p\left(S_{i}\right)$ is not $n$ or more apples, nor $n$ or fewer apples; is just exactly some $n$. —SlamDiego_←T 13:50, 9 August 2007 (UTC)

Your argument as to why utility functions are not measures would also preclude utility functions being measures — again, the probability of bundles of apples could increase to in apples to some point, and then decrease thereafter, analogously to a bliss point. While I don't know of the point being made explicitly in a textbook, it has certainly been made in the literature, as in McCulloch's article. —SlamDiego_←T 13:21, 9 August 2007 (UTC)

Again this is a mistaken interpretation of probability theory and measure theory. Measures increase when they go from subsets to supersets, and probabilities increase as they go from events which are subsets to events which are supersets. Example: the probability of 'receiving two apples' is less than the probability of 'receiving two apples or one apple', which is less than the probability of 'receiving two apples or one apple or seven apples'. That's the kind of monotonicity propertya mathematical description of probability must have. That's why measures are a good type of function to apply to probabilities. There is no analogous property in preference theory, which is why utility functions are not in general treated as measures. --Rinconsoleao 13:37, 9 August 2007 (UTC)

No, now you're effectively inserting words into what I said. I didn't refer to the event of getting $n$ or fewer apples, nor to the event of getting $n$ or more apples; I referred to the event of getting $n$ apples. —SlamDiego_←T 13:43, 9 August 2007 (UTC)

The monotonicity properties of measures only refer to events which are subsets or supersets. So your comment is irrelevant if you are talking about mutually exclusive events such as 'receiving one' or 'receiving two' or 'receiving three'. A monotonicity property is applicable to events like 'receiving one or less', 'receiving two or less', etc., because the former is a subset of the latter. This kind of monotonicity property has no role in utility analysis, which is why utility functions are not measures; probability functions are. --Rinconsoleao 13:48, 9 August 2007 (UTC)

My comment was relevant to refuting what you wrote, and (like every other comment) irrelevant to countless other things that might have been written. —SlamDiego_←T 13:55, 9 August 2007 (UTC)

In other words, it must be possible to decompose a utility function into two functions, one from states-of-the-world to nodes on a preference graph, and one from a preference graph to real numbers. Had you asked “In what sense is that mapping a measure of apples”, I would have answered to explain that it were not (necessarily) quite that. —SlamDiego_←T 12:03, 9 August 2007 (UTC)

Again, a mapping from positions on a preference graph to the real numbers is not a measure in the sense of measure theory. Let's delete the reference to measure theory. --Rinconsoleao 12:26, 9 August 2007 (UTC)

See above. —SlamDiego_←T 12:40, 9 August 2007 (UTC)

Even as they apply monotonic or affine transformations thereby showing that no one measure is particularly significant, they are performing transformations that wouldn't be possible if utility did not correspond to a measure.

(Moreover, I wouldn't have had to wrestle in the very first place with getting another editor to accept a definition without quantification of utility were the “ordinal” neoclassical conception not quantified.)

Now, indeed, you can find economists outside of the neoclassical mainstream whose use of the word “ordinal” is more general. (McCulloch for example tries to reclaim it.) But what we're arguing about here is not how to use the word “ordinal”; it's whether the neoclassical conception (however labelled) is fully general. Again: The disproof of De Finetti's conjecture showed that it is not. —SlamDiego_←T 09:17, 9 August 2007 (UTC)

Point 2: it’s hard to see why we would expect preferences to satisfy the properties in de Finetti’s conjecture

One of the properties assumed in de Finetti’s conjecture is ‘additivity’, which means that if bundle A is preferred to bundle B, and C is a bundle of goods disjoint from A and B, then the bundle of A together with C is preferred to the bundle of B together with C. In clearer English, this says that if two beers are preferred to one, then nine beers are preferred to eight. It is very hard to see why we would want to assume preferences must have that property! Standard treatments of utility usually make allowance for the possibility of bliss points, after which more consumption is bad. See Varian (1987) again, Figure 3.7, p. 43.

Any disagreements on these points? --Rinconsoleao 20:55, 8 August 2007 (UTC)

First, you've not quote got a handle on additivity. Additivity would, for example, also be violated if the tenth bed-sheet made the rope long enough for escape. (And this would be true even if yet more sheets remained desirable.)

Second, allowing for addivity is not disallowing for bliss points any more than allowing atheists to serve in Parliament disallows Christians.

Could you please give me an example of an additive utility function with a bliss point? I thought my beer example made this clear. --Rinconsoleao 09:47, 9 August 2007 (UTC)

Stop; pay attention to simple logic. Allowing additivity is not the same thing as requiring additivity.

You haven't (so far) proposed that people must have bliss points (and they're certainly not required for economic rationality); no one has proposed that utility must be additive.

Good, at least we agree on this. Additivity, and having a bliss point, are two properties we might want to consider as possibilities; a theory that considers preferences that can have one or both of these properties is more general than one which does not. --Rinconsoleao 10:09, 9 August 2007 (UTC)

Again, this is not so much agreement as your having wasted our time. —SlamDiego_←T 10:22, 9 August 2007 (UTC)

The point is that economically rational preferences can be additive, and therefore a conception of utility that disallows them is not as general as one that allows them.

—SlamDiego_←T 09:59, 9 August 2007 (UTC)

And my point is that ordinal preferences (meaning an ordering over consumption bundles) can have the additivity property. In that sense they are general. Disproving the dFC simply proves they don't always have that property. But that does not make them less general. --Rinconsoleao 10:09, 9 August 2007 (UTC)

You are abusively switching lexicons. We are not talking about what the Austrian School or some other group calls “ordinal” utility. We are talking about what the neoclassical school calls “ordinal” utility. And because that name is not a proper description — because the neoclassical conception is not fully general — I have consistently used quotation marks to sugegst that there is something off in that name. —SlamDiego_←T 10:22, 9 August 2007 (UTC)

I'm really not trying to gain rhetorical advantage by switching lexicons. I have consistently been trying to make clear which mathematical/econonomic concepts I am talking about, and trying to figure out whether they were the same ones you are talking about. That's why I explicitly said, many times, that I was talking about an ordering over bundles. Which historical schools they can be attached to is a question I have not tried to address. But it would be helpful to know whether 'neoclassical', in your usage, includes standard textbook treatments nowadays (such as the one you have requested that I not cite). --Rinconsoleao 10:53, 9 August 2007 (UTC)

Again, I am focussed on your actions, not on your intentions. You started making declarations of about “ordinal utility” as if these contradicted what I had said about “the neoclassical conception of ‘ordinal’ utility”.

Fine, so I may have made a wrong turn by failing to keep track of exactly which concept you were referring to. But therefore it would again be helpful to me to know whether 'neoclassical', to you, means standard contemporary usage such as Varian, or whether it refers to usages from the early 20th century, or to both, or to something else. --Rinconsoleao 11:32, 9 August 2007 (UTC)

Since I've not been using the past tense or words such as “former”, you naturally should take it as the present definition. (At the dawn of neoclassical economics, the definition would have been more Benthamite.) But I'd refer you to an author such as Kreps, who is far more careful than Varian. —SlamDiego_←T 11:54, 9 August 2007 (UTC)

And your wrong turn has wasted a huge amount of time and drowned this talk page in avoidable nonsense, as you attempted to argue that the issue of de Finetti's conjecture were a red herring. —SlamDiego_←T 11:58, 9 August 2007 (UTC)

That's certainly not the same thing as telling me what you mean by “ordinal utility”; rather, since the meaning of the one didn't match that of the other that's abusive lexicon switching. There is little excuse for it, since I plainly wasn't baldly saying “ordinal utility”, but always putting “ordinal” in quotation marks.

Citing Varian wouldn't at all change that. And implicitly citing Varian at me is not acceptable.

—SlamDiego_←T 11:21, 9 August 2007 (UTC)

Third, allowing for additivity allows for a class of economically rational preferences in the context of various economic circumstances.

Fourth, don't quote Varian at me. Especially don't quote his undergraduate text (or any other undergraduate text) at me.

—SlamDiego_←T 23:13, 8 August 2007 (UTC)

Slam, I am obviously not quoting Varian 'at you'. I am backing up my main points with page-specific references to widely available texts, which is what Wikipedia, wisely, asks us to do. I would hope our discussion will be accessible to many people, no only to the two of us. --Rinconsoleao 06:57, 9 August 2007 (UTC)

Wikipedia asks us to cite sources in articles, not to treat economists on talk pages as if they haven't taken undergraduate economics. I repeat: Do not quote Varian at me. —SlamDiego_←T 07:47, 9 August 2007 (UTC)

Slam, I really sincerely am not trying to talk down to you. And you are not the only person to whom I am directing my comments. My problem with the MU page is that it has never been sufficiently clear. If I quote Varian it is only to allow you (and others) to be sure you know what I mean with my arguments. For example, the page now talks about a 'highest quantitative utilization', three words which I simply could not understand until I clicked and found 'production possibilities frontier'. I did not feel that my intelligence had been insulted by that link. I was grateful for the clarification. --Rinconsoleao 09:01, 9 August 2007 (UTC)

I am less concerned with your intentions (which are not directly observable) than with your actions. You're expecting me to respond to you. Regardless for whose benefit you would do it, don't quote Varian at me. Don't quote any undergraduate text at me. Whatever you might think that you would want in my shoes, you're not in my shoes and I'm not you. —SlamDiego_←T 09:25, 9 August 2007 (UTC)

I am not talking only to you, because many people have been involved in this discussion. If you find it offensive to see that text mentioned, then bear in mind that someone else might want to see it. Where possible, I will always quote the least technical text I can find. --Rinconsoleao 09:31, 9 August 2007 (UTC)

Nonsense. The fact that we presumably have an audience doesn't change the fact that you are talking to me — indeed, if it did then “I am not talking only to you” would be absurd, as the “you” would refer exactly to the people to whom you were talking. And the fact that we have an audience doesn't legitimize quoting undergraduate textbooks at me. If you want to express yourself for their benefit, find a better, acceptable way. —SlamDiego_←T 09:39, 9 August 2007 (UTC)

Point 3: why all this fuss about measure theory?

I was surprised from the beginning when I saw ‘quantified’ utility defined as a ‘measure’, and in particular when that was linked to ‘measure theory’. I always thought of cardinal utility simply as putting numbers on consumption bundles as a way of ranking them. I don’t recall in my studies ever seeing measure theory mentioned in discussions of utility per se (though obviously it is mentioned when you get to expected utility, for example, since expected utility means weighting a bunch of utilities with respect to a probability measure).

It’s true that Stigler uses the word ‘measure’ a lot in the essay cited in this article.(Stigler, George Joseph; “The Development of Utility Theory”, I and II, Journal of Political Economy (1950), issues 3 and 4.) But my reading of that article is that he is using ‘measure’ in the intuitive, nontechnical sense, meaning actually being a quantity of something. In other words, he is asking whether utility has some natural units by which it might, in principle, be measured.

Let me give an example of what that might mean. Suppose we only consume apples, and we measure them in kilograms. That’s something you can actually measure. (The fact that there are other units of measurement that could be used in this context is irrelevant. That’s always true when we measure anything.) Suppose also that utility really is something that could be measured. For example, (JUST for the sake of argument!) suppose utility means milligrams of serotonin per liter of brain juice. Since that’s actually a quantity, we would represent it by a cardinal utility function, and likewise a cardinal marginal utility function. In other words, $a$ kilos of apple give $U(a)$ units of utility (milligrams of...), and likewise, at the margin, additional apples give $u(a)={\frac {d}{da}}U(a)$ units of utility per kilogram of apples.

For example, suppose $u(a)$ is defined for $a\in [0,4]$, because it is impossible to eat less than 0 or more than 4 kilograms of apples, and suppose the marginal utility function is $u(a)=20-10a$. Then by definition we must have

$U(a)=\int _{0}^{a}(20-10x)dx=20a-5a^{2}$

which has a bliss point at $a=2$. Here, we are actually using the measure of apples in the sense of measure theory. Namely, we are integrating with respect to the measure of apples. (I.e. the dx represents a small change in the quantity of apples. And if we changed the units in which we measure apples, we would have to adjust the integral accordingly.) That’s what you do with measures in the sense of measure theory.

In this example, utility is not a measure over apples, because by definition a measure (in the sense of measure theory) gives a larger measure when the set it is measuring is increased to include more members (like a few extra apples). (See Thm. 10.2 in Aliprantis and Burkinshaw (1990), Principles of Real Analysis, 2nd ed., ISBN 0-12-050255-0, or any other real analysis textbook.) What utility $U(a)$ does measure in this example, both in the ordinary sense of the word, and in the measure theory sense of the word, is serotonin. Saying that “the utility of two kilos of apples is $20*2-5*2^{2}=20$” in this context is a statement about the amount of serotonin in your brain juice.

It seems this is where the confusion about the relevance of de Finetti’s conjecture arose. De Finetti’s conjecture is trying (unsuccessfully) to divvy up the utility of a consumption bundle into statements about the utilities of individual goods. In other words, it was conjecturing the existence of a measure over goods. But that’s not what utility functions do. They don’t measure goods. They measure utility, as a quantity, under the assumption (whether it is a reasonable assumption or not) that utility can be quantified.

But my main point here is simply that mentioning measure theory at all is a red herring. It points to a lot of technical issues which there is no reason to go into, because standard treatments of preferences today only rank (or give numbers to) whole consumption bundles. (I can cite many more textbooks that talk about rankings and/or utility functions defined over bundles, without ever mentioning such a function over individual goods, if that would help.) They say nothing about the utility of particular goods. More precisely, they can say something about the utility of a particular good when it is at the margin, but they cannot and do not attempt to attribute utility to a particular good in general. In other words, a utility function is not, and is not intended as, a measure over goods.

Any disagreements on these points? --Rinconsoleao 21:52, 8 August 2007 (UTC)

The distinction between measure theory and measurement theory was already made in discussion with Thomasmeeks.[3] You should not confuse the two, nor attempt to lecture me on either.

Here at least I think we are largely in agreement. In your discussions and in my example above we are both trying to distinguish the mathematical theory called measure theory from the day-to-day concept of measuring something with a ruler or a scale that it tries to formalize. ('Measurement theory' as a way of referring to the day-to-day concept is not standard wording. I would just call it 'measurement'.) --Rinconsoleao 07:35, 9 August 2007 (UTC)

It's not so much that we are in agreement as that you are just wasting my time and your own with misdirected integrals and lectures. —SlamDiego_←T 08:09, 9 August 2007 (UTC)

(There is, in fact, a field of measurement theory. See Basic Measurement Theory by Suppes and Zinnes.) —SlamDiego_←T 15:07, 9 August 2007 (UTC)

Thanks. That is a new one to me. I'll try to look that up. --Rinconsoleao 15:24, 9 August 2007 (UTC)

I have used the term “measure” because that is the mathematical term that applies, and I linked to the Wikipedia article on measure theory accordingly.

My suggestion, instead, is to drop references to measure theory because even though it is accurate and precise, most people don't understand it, and therefore mentioning it raises the possibility that there are deeper issues at stake. But when we ask whether utility could be 'measured' (again, see the Stigler papers you cite) I don't see any issues specifically related to measure theory per se. The question is simply whether there is some real meaning or not when we put a number on utility (for example, does it represent milliliters of serotonin, or any other definable quantitative meaning). If there is some issue where we specifically need techniques from measure theory to address these questions, you should point it out to us, please. --Rinconsoleao 07:35, 9 August 2007 (UTC)

We're not simply worried about numbers but about quantities. I would have been fine with the idea of just using the word “quantity” (and derivatives), quietly wiki-linked to the article on measure theory, except that you proved that the reader wouldn't get it when you barrelled ahead and switched the link to the article on “cardinal” utility. —SlamDiego_←T 08:09, 9 August 2007 (UTC)

The reason for using this term is that it gives accurate and precise mathematical meaning to “quantity”. Your own attempt, in one of your edits to the article to replace this reference with one to “cardinal” utility illustrates that such accuracy and precision is desirable.

Whether my reference to cardinal utility was justified is a separate issue. My usage of the term is coherent, as I explained in Point 1 above, though I'm not entirely sure whether it is the usage that should be called 'neoclassical'. But we can discuss that later. For now, I am advocating eliminating all reference to measure theory in this article, because it merely obfuscates things. --Rinconsoleao 07:43, 9 August 2007 (UTC)

It's not a separate issue. The issue is what keeps the reader from heading off in the wrong direction. You showed that using the word “quantity” wasn't enough; using the word “number” woudl be even worse. —SlamDiego_←T 08:09, 9 August 2007 (UTC)

I don't understand what you mean when you distinguish "quantity" from "number". Sure, I can imagine some distinctions, but I don't know which possible distinction you intend. Could you help me understand this? --Rinconsoleao 09:09, 9 August 2007 (UTC)

Consider the Dewey Decimal system. It assigns numbers to books; those numbers aren't quantities. —SlamDiego_←T 09:52, 9 August 2007 (UTC)

Good, I am getting closer to understanding you. Would it be fair to interpret 'those numbers aren't quantities' as 'those numbers do not represent amounts of anything; instead, they are merely labels'? --Rinconsoleao 10:21, 9 August 2007 (UTC)

Well, they may or may not be merely labels, but the point is that arthimetic performed on those numbers yields just nonsense. By contrast, with the neoclassical conception of “ordinal” utility, the sign of a difference (arithmetic subtraction) is meaningful. Indeed, the sign of the difference-of-differences might also be meaningful. —SlamDiego_←T 10:26, 9 August 2007 (UTC)

DeFinetti's focus was upon probability. The fact that the math applies to utility as well was apparently first recognized by McCulloch.

—SlamDiego_←T 23:29, 8 August 2007 (UTC)

The fact that the de Finetti conjecture is applicable more widely than probability theory was not first recognized by McCulloch (1977). The first page of the Kraft et al (1958) paper makes crystal clear that the conjecture is about rankings in general (such as preference orderings, and in fact the notation used was standard in preference theory in the 1950s) and that the application to probability is a special case (as explained in the third paragraph). --Rinconsoleao 07:22, 9 August 2007 (UTC)

You are again mistaken. The notation was not invented by economists nor for economics; it is a very standard notation for orderings in general, and could and can be found in works by mathematicians who were and are quite oblivious to what economists are doing. And the fact that Kraft &alii applied it to orderings in general does not meaning that they recognized any one specific application other than to probability orderings. (De Finetti's own writing didn't make explicit use of utility, and it took a degree of perspicuity for others to show how it was implicit therein.) —SlamDiego_←T 07:57, 9 August 2007 (UTC)

I did not assert that it was invented by or for economists; yes, you are right, it is mathematical notation; but yes, it was standard notation in economics at the time (Debreu's Theory of Value came out in 1959.) --Rinconsoleao 08:12, 9 August 2007 (UTC)

And I didn't say that you said that it was invented by economists. But what you did do was argue that the common notation illustrated that Kraft &alii had recognized the implications for utility, and I choked-off every argument that might be used to defend that illogical inference; doing so included noting that the authors needn't have got the notation (directly or even indirectly) from economists. —SlamDiego_←T 08:27, 9 August 2007 (UTC)

You are right that the fact that Kraft et al. wrote about orderings in general does not necessarily imply that they recognized that those orderings might be applicable to economics. But Pratt (one of the coauthors of Kraft) made a major contribution to preference theory in 1964 (J.W. Pratt (1964), 'Risk aversion in the small and in the large', Econometrica 32, pp. 122-136). Am I really supposed to believe that he was completely ignorant of the economics applications of orderings in 1958? --Rinconsoleao 08:18, 9 August 2007 (UTC)

Are we really supposed to believe that he did see it and then didn't turn around and say “Hey, guys, about this thing that you call ‘ordinal’ utility and think is fully general…”? Even brilliant people often over-look implications of their own work. I cannot guarantee that McCulloch was the first to see the implications for utility; he was the first to publish, though, which makes it apparent (exactly as I said) that he was the first. —SlamDiego_←T 08:27, 9 August 2007 (UTC)

Of course he would not have turned around and said that, because the disproof of the dFC does not show a lack of generality of 'ordinal' utility. It shows that some ordinal representations of utility satisfy the assumptions of the dFC, and some don't, which is not a lack of generality. --Rinconsoleao 09:30, 9 August 2007 (UTC)

Again: I advised have always referred to what neoclassical economics calls “ordinal” utility. I had Pratt likewise hypothetically use the phrase “this thing that you call ‘ordinal’ utility”. What the Austrian School calls “ordinal” utility is indeed fully general; but what the neoclassical school has been calling “ordinal” utility is not. So the question is: If Pratt was aware of the implications for that neoclassical conception, why didn't he say something? McCulloch did note the implications, and did say something. —SlamDiego_←T 09:46, 9 August 2007 (UTC)