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Hi, there is a mistake in this article. The statement "Daniel Bernoulli (1738) gave the earliest known written statement of this hypothesis" is not correct. Cramer described the utility function in 1728 in a letter to the Nicolas Bernouilli (the cousin of Daniel Bernouilli)! Is it ok to adapt this??? PhDB Phdb (talk) 10:19, 10 August 2008 (UTC)

Noted. -- Beland (talk) 20:59, 29 August 2008 (UTC)

VNM formulation

This section was dumped from material contributed on this talk page (since archived) and should be verified and referenced. See e.g. [1] as a starting place. -- Beland (talk) 21:18, 29 August 2008 (UTC)

poker example

i deleted the example because it is wrong. I added a hidden comment in the section. —Preceding unsigned comment added by 81.210.230.253 (talk) 15:26, 12 October 2008 (UTC)

Your change was reverted. It was a large removal of material... I really don't know about this, but if there material's going to be there it really needs references. I don't know that it belongs in the article even with references, though. Why should poker get such a highlight when craps or investing or education etc. dont? CRETOG8(t/c) 16:13, 12 October 2008 (UTC)

invariance axiom

I know it's supposed to be here, but it's not —Preceding unsigned comment added by 193.157.201.173 (talk) 10:47, 10 November 2009 (UTC)

Bernouli's formulation

Hi, i am not sure about this statement. "Daniel Bernoulli proposed that a mathematical function should be used to correct the expected value depending on probability ". the utility is the subjective value of the outcomes and does not talk about probabilities. It was later in prospect theory that weighted probabilities were taken into account. Kpmiyapuram (talk) 13:06, 20 May 2009 (UTC)

The "mathematical function" referred to in this passage is the expected utility function, which explicitly takes into account probabilities. Duoduoduo (talk) 16:48, 22 May 2010 (UTC)

Behavioral decision science: Deviations from expected utility theory

Myerson's book on game theory (ISBN 0674341163) has a good discussion on that, including some counterexamples cited from empirical studies. It's in the first chapter, pp. 22-26. Tijfo098 (talk) 22:22, 21 March 2011 (UTC)

Moral expectation

A couple more links on Moral Expectation and Mathematical Expectation:

Hope this helps. Jheald (talk) 21:37, 24 March 2011 (UTC)

Page needs revision

Someone needs to go through this page. Sample from the page.. "It is well established that humans find logic hard, mathematics harder, and probability even more challenging". This line in itself makes the page a joke. —Preceding unsigned comment added by 64.206.141.60 (talk) 05:17, 9 April 2011 (UTC)

Also, in "criticism" it says: For example, in 2000 behavioral economist Matthew Rabin proved mathematically that the utility of wealth cannot explain loss aversion and attempts to so use it will fail. Obviously it is referring to "Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion," chapter in Choices, Values, and Frames, Daniel Kahneman and Amos Tversky, editors, New York: Cambridge University Press, 2000, 202-208. Well, although this paper is important, nothing is MATHEMATICALLY proved in that paper. This again makes the page a joke.

preference reversal

"Many studies have examined this "preference reversal," from both an experimental (e.g., Plott & Grether, 1979)[16] and theoretical (e.g., Holt, 1986)[17] standpoint, indicating that this behavior can be brought into accordance with neoclassical economic theory under specific assumptions."

This suggests the irrationality of preference reversal can be explained within "neoclassical economic theory". My understanding of Plott & Grether is that they couldn't explain it, so this article needs to explain how it's explained. Earcanal (talk) 10:35, 3 September 2014 (UTC)

Dr. Volij's comment on this article

Dr. Volij has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:


In the Risk Aversion section, the sentence "Since the risk attitudes are unchanged under affine transformations of u, the first derivative u' is not an adequate measure of the risk aversion of a utility function. Instead, it needs to be normalized. "

should be changed to

"Since the risk attitudes are unchanged under affine transformations of u, the second derivative u is not an adequate measure of the risk aversion of a utility function. Instead, it needs to be normalized. "


We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Volij has expertise on the topic of this article, since he has published relevant scholarly research:


  • Reference : Oscar Volij, 1999. "On Risk Aversion and Bargaining Outcomes," Economic theory and game theory 010, Oscar Volij.

ExpertIdeasBot (talk) 20:33, 1 July 2016 (UTC)

Dr. Dhami's comment on this article

Dr. Dhami has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:


This is quite a misleading and confused write-up. Many sentences are confusing, which is matched only by the number of claims that are just wrong. The article may superficially look nice--but the reader should be warned of the pitfalls. There are many excellent sources for lucid and reliable treatments of the subject matter. Any of the main undergraduate or graduate book in microeconomics may be relied on. The central problem with expected utility theory is the empirical refutations--and by now there is a very large number of well established refutations. For one comprehensive treatment of this material and a proper statement of the results on expected utility, see:

Sanjit Dhami (2016) The Foundations of Behavioral Economic Analysis. Oxford University Press. To be published by mid October 2016. (https://global.oup.com/academic/product/the-foundations-of-behavioral-economic-analysis-9780198715528?lang=en&cc=gb)

Some mixture model estimates now show that it could be that about 20% of the people follow expected utility theory and the rest follow prospect theory. This 20% figure is based on whether people follow linear or non-linear weighting of probabilities. However, if other domains of comparison are allowed, such as reference dependence and loss aversion, this figure is much more likely to drop. For a reference, see Bruhin, A., Fehr-Duda, H., and Epper, T. (2010). Risk and rationality: uncovering hetero- geneity in probability distortion. Econometrica. 78(4): 1375-1412.

There are also good evolutionary reasons why people may follow something like prospect theory that allows for reference dependence and loss aversion.

Here are some specific comments on different sections of the wiki entry on expected utility:

1. The term "moral expectation" in the introduction is archaic and misleading. 2. The following sentence in the introduction is confusing: "From relatively early on, it was accepted that some of these conditions would be violated by real decision-makers in practice but that the conditions could be interpreted nonetheless as 'axioms' of rational choice." The axioms that lead to an expected utility representation of preferences are indeed known as the axioms of rationality. Any empirical rejection of the axioms is itself a rejection of expected utility. 3. There are inaccuracies in the section titled "Bernoulli's formulation". The following sentence is just wrong "Daniel Bernoulli proposed that a mathematical function should be used to correct the expected value depending on probability". The relevant correction was made to the utility of an outcome (by replacing a linear utility function with a concave function). 4. The second paragraph in the section titled "Infinite expected value — St. Petersburg paradox" is either misleading or unclear. A proposal was made to use a concave utility function to explain the St. Petersburg Paradox. Whether this is "the utility function used in real life" or not an entirely empirical matter. There are alternative explanations of the same paradox that rely on non-linear probability weighting and loss aversion but this is not clear at all from the commentary. 5. In the section on "Von Neumann–Morgenstern formulation" there is confusion between utility from an outcome and the expected utility from a lottery. The following sentence is incorrect "The von Neumann–Morgenstern formulation is important in the application of set theory to economics because it was developed shortly after the Hicks–Allen "ordinal revolution" of the 1930s, and it revived the idea of cardinal utility in economic theory.[citation needed] Note, however, that while in this context the utility function is cardinal, in that implied behavior would be altered by a non-linear monotonic transformation of utility, the expected utility function is ordinal because any monotonic increasing transformation of it gives the same behavior." Expected utility is invariant with respect to an affine transformation of utility (not monotonic transformation). This is correctly stated in the next section on "Risk Aversion". 6. In the section on "Risk Aversion", the following sentence is completely unclear and probably incorrect: "A decision that maximizes expected utility also maximizes the probability of the decision's consequences being preferable to some uncertain threshold (Castagnoli and LiCalzi,1996; Bordley and LiCalzi,2000;Bordley and Kirkwood, )." Neither are these fundamental and commonly cited references in the area, as far as I know. There is very little discussion about why we need CARA and CRRA utility functions. 7. In the section on "Criticisms" the words "normative" and "first order approximation" in the following sentence are vacuous: "It has a normative interpretation which economists particularly used to think applies in all situations to rational agents but now tend to regard as a useful and insightful first order approximation." On the whole this section is poorly written and deserves much development. It should be at least 40-50 percent of the total article. 8. I am quite dismayed at the sections following "Criticims".



7.


We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Dhami has expertise on the topic of this article, since he has published relevant scholarly research:


  • Reference : Sanjit Dhami & Ali al-Nowaihi, 2007. "Optimal income taxation in the presence of tax evasion: Expected utility versus prospect theory," Discussion Papers in Economics 07/10, Department of Economics, University of Leicester.

ExpertIdeasBot (talk) 02:06, 2 October 2016 (UTC)

inaccurate description of rabin paper

This description is not an accurate gloss of Rabin's 2000 paper explaining how EU can't account for loss aversion: "For example, in 2000 behavioral economist Matthew Rabin argued that mathematically the utility of wealth cannot explain loss aversion and attempts to so use it will fail. Bernoulli's theory on the utility of wealth assumed that if two people have the same wealth all other things being equal the people should be equally happy. However, where two people have US$1m but one has just prior to that had US$2m but lost US$1m whereas the other had US$500k and had just gained US$500k they will not be equally happy." The reason is that it implies that if you are risk averse to many modest gambles you have an expected utility curve which would imply that your risk aversion is implausibly high. For example, if someone turns down a 50/50 gain $100 loss for welath levels above 350k, we know they would turn down a 50/50 $4k loss vs $635k gain gamble at a wealth of $340k. — Preceding unsigned comment added by 73.231.138.128 (talk) 02:27, 10 October 2018 (UTC)

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