Talk:Bucklin voting

removing FairVote reference.

FairVote is not a "reliable source" for Wikipedia, being an advocacy organization (at least for facts; it is a reliable source for arguments being used by IRV advocates) and the page cited, which was the source for material in the article which I have also removed, was argumentative. The reason given for voters not to add second rank votes is simply an opinion, it appears, one designed to promote Instant Runoff Voting. As a note for further research, I found this reference: [1] which then cites other relevant cases. It appears that Brown v. Smallwood, in particular, was cited by other courts in outlawing the Hare system. I.e., STV. I have written elsewhere that Brown v. Smallwood would appear to apply to IRV as well as to Bucklin, and that the argument that Brown v. Smallwood was only about the additional votes involved in the Approval-like Bucklin method is spurious, apparently based on a shallow reading of the case, which appears to have disallowed all kinds of alternative votes. This is a current controversy in Minnesota, as it appears the IRV elections set up there are headed for judicial review.

This is what I removed:

Like other variants of approval voting, in Bucklin voting indicating support for a lesser choice will count against a higher choice -- for example, if both your first choice and second choice advanced to the second round, your ballots would cancel each other out. For this reason, in high stakes elections in which voters have strong favorites, most voters opted to "bullet vote" and protect the interests of their favorite choice be withholding any alternate choices. In Alabama, for example, in the 16 primary election races that used Bucklin Voting between 1916 and 1930, on average only 13% of voters opted to indicate a second choice. Even in hotly contested multi-candidate gubernatorial primaries, over two thirds of voters selected only a single choice. Between 1916 and the system's repeal in 1931, in no case did the addition of the second choice votes give the winner a majority.

Note that the primary purpose in major elections of a system like Bucklin (or IRV) is to eliminate the "spoiler effect," and to do this, in a two-party system, it is only necessary for a relatively small percentage of voters to use additional preference expressions. In the election invalidated by Brown v. Smallwood, however, many voters did use the additional preferences, and they turned the election. The bugaboo of second choices hurting your first preference is only relevant if your first and second preferences are both frontrunners, in which case an ordinary voter would quite easily and properly vote for one only. So low usage of second preference votes is not an argument against Bucklin at all. It would be expected in a two-party system, where third party supporters are at most a few percent of the electorate. In any case, my point is not to establish *my* argument here, but to note that FairVote was presenting *their* argument, not known facts, presented in a balanced way. --Abd 02:33, 11 November 2007 (UTC)

References

Problems with the example

The use of the geographical example is one which has value because it shows an underlying rationale for voting; indeed, it assumes that voters will follow distance as a basis for their votes. However, that example really is designed for Range voting; if voters vote to minimize their distance, and if they vote sincerely, the overall distance traveled to the capital by all voters will be minimized.

However, in real public elections, multiple majorities will be quite unusual. Normally, in most public elections, there are no more than two front-runners, and for a multiple majority to occur, as with the geographical voting example, there must be a large number of voters who vote for *both* front-runners, which is, shall we say, extremely unlikely; this would be the equivalent of having voted for Bush and Gore in U.S. Presidential 2000. The article notes that there is an advantage to "bullet voting," under some circumstances, but then the example shows all voters voting all ranks. Which is implausible for political elections; we can expect that if voters are free to vote as few ranks as they like, that many will vote for one only, and that is perfectly rational, and perfectly legitimate. No voter should be forced to vote for anyone, and requiring full ranking requires that all voters essentially vote (conditionally) for all candidates except one, the one they bottom-rank. Bucklin is not designed for that. Like Approval voting, its pure-rating cousin, bullet voting would be the *norm*, and it is the supporters of candidates not likely to win who would add additional votes for candidates more likely to be real contenders.

I do not think that the Memphis voters would add second rank votes. However, the voters in other cities might. The Nashville voters would likewise know that adding second rank votes might hurt them, if they second rank Memphis, since the front-runners (for first preference) are Memphis and Nashville. However, the other two cities would be likely to add second preferences; Knoxville and Chattanooga might add each other. And then they might add Nashville as a third preference. The result would be, again, that the counting would go to the third round, with Nashville winning. Unless the Knoxville and Chattenooga voters refused to add Nashville third, in which case there would be majority failure. If the rules allow a plurality win at that point (as IRV generally would), Memphis would win, an undesirable result for Knoxville and Chattanooga, which is why I think they would cast those extra votes. Basic rule for Approval (and it applies to Bucklin): vote for one of the two front-runners, at least somewhere in your preferences. --Abd 04:03, 11 November 2007 (UTC)

The source of the example was before I started editing, and was designed for a simple example to use in multiple election methods. There was a discussion about it (somewhere), about its usefulness, I don't remember, but it was moved for all method to a common article now called Effects of different voting systems under similar circumstances. Anyway I have no great affection for the example. I probably did originally add it to Bucklin, and yes with any specific method, sincere ranking may not be the best strategy, so the example must be more considered as a demonstration rather that a serious analysis on how people might vote - WHICH would anyway be original research perhaps, so it can't really be much more than it is! Tom Ruen 06:19, 11 November 2007 (UTC)

The other problem with the example is a misleading claim:

Chattanooga voters could cause their candidate to win by bullet voting.

This does not appear to be true in the example given, since Chattanooga voters cast their second place rank for Knoxville, which is not a contender in the second round. Perhaps something different was originally intended?

See, this all depends on how "don't-care" votes are counted. If "don't-care" equals "ranked dead last", then there is a strong incentive to bullet vote. Conversely if "don't-care" means "ranked as high as possible", then there's a strong disincentive to bullet vote, but don't-care votes may distort the results of the election in an undesirable way (or even find some other use in tactical voting). If "don't-care" means that every unranked candidate is given 1/n votes per don't-care rank, then bullet voting merely defers your vote to people who actually fill out their ballots, neither helping nor harming the unranked candidates. The pathological incentives of setting don't-care votes to dead-last was what caused Bucklin to fail so miserably historically. MarcT 107.129.249.144 (talk) 02:21, 14 May 2019 (UTC)

Unconstitutional Why?

Any details as to why it was found to be unconstitutional? (i.e. What constitutional principles did it breach?) -- 00:02, 9 January 2008 (UTC)

See 1915 Minnesota Supreme Court decision, Brown v. Smallwood: :Tom Ruen (talk) 00:18, 9 January 2008 (UTC)

• [2]
• [3]

Those are both FairVote propaganda pages about Bucklin and Brown v. Smallwood. If you want the real skinny, read Brown v. Smallwood itself! You can find it from an article on the case that I wrote and then Warren Smith edited, at [4]; there is a link there to a PDF of the actual case.

Meanwhile, the first source (FairVote) has this on Bucklin:

"In the United States, IRV election laws were first adopted in 1912. Four states -- Florida, Indiana, Maryland, and Minnesota -- used versions of IRV for party primaries. Seven other states, used a different version of preference voting known as the Bucklin system. Bucklin was found to be defective as it allowed a voter’s second-choice vote to help defeat a voter’s first-choice candidate. With Bucklin voting, most voters refrained from giving second choices, and the intent of discovering which candidate was favored by a majority of voters was thwarted."

The claim that "most voters refrained from giving second choices" is false for nonpartisan elections, and the best counterexample was the election of a judge which was the basis for Brown v. Smallwood. As to *partisan* elections, in the context of a two-party system, we would expect most voters, voting sincerely, to vote for only one, there is no reason to do otherwise, it would be moot at best. Only for what is, by definition, a minority, would additional votes become important. An example would be Nader supporters in Florida in 2000. As to major party supporters, what would we expect, additional votes from a Gore supporter for Bush? Now, *some* major party supporters might indeed add some additional votes, say a Democrat for Nader if the voter wanted to push the favored party in the Green direction, or a Republican for Badnarick (or whoever the Libertarian was in Florida that year) who wanted to push the party in a Libertarian direction. (And some Democrats might like to do that too!)

The primary motive for election reform is to deal with the spoiler effect, and Bucklin quite handily deals with it. The argument given by FairVote above is a red herring, and, in addition, I've seen no proof for it. They simply assert it without sourcing, other than to their own research (not to sources from the time, beyond Brown v. Smallwood, which they radically misinterpret).

FairVote is interested in promoting IRV, hence this claim: "Bucklin was found to be defective as it allowed a voter’s second-choice vote to help defeat a voter’s first-choice candidate." That is not what Brown v. Smallwood says, beyond *one* passage in the decision which can be read that way. Given the rest of the decision and the reconsideration, however, that was not the intended meaning. Now, does Bucklin behave in this way? Sure, *in theory*. In practice, the problem only arises for a voter if the first and second choice are both frontrunners! Have you ever felt that way about an election? I haven't, not with any public elections for major offices! It would take a practically insane voter to vote first choice, one frontrunner, and second choice, another, in most contexts. Yes, in nonpartisan elections, it could happen; likewise a voter who has no idea about "frontrunners" and who imagines that the voter's first and second choices are both frontrunners. We should be so lucky! (I feel that way about the Democratic primaries, actually, I like *every* major candidate on the Democratic side, I'd be tempted to approve them all. But Bucklin would encourage me to single out a favorite and second favorite, and then the third rank would allow me to approve everyone one whom I actually would support. If these later votes "hurt" my favorite, I'd still be quite happy. I actually want the party to nominate the candidate -- among this set -- most likely to win the general election, and this implies choosing the candidate whom the party can most effectively unite behind. This is more important to me than choosing my personal favorite. In other years, it might be different.

Now, as to the second source given, it's to an article by Tony Anderson Solgård and Paul Landskroener. Who are these people? Well at the end of the article, we have, helpfully: "TONY ANDERSON SOLGARD is chair of the board of FairVote Minnesota, a nonpartisan, nonprofit organization educating the public about voting systems and their effect on the quality of democracy. PAUL LANDSKROENER is a lawyer and graduate of Valparaiso University School of Law. He practices in Edina."

On the other hand, there exists legal review by at least one presumably neutral attorney that Brown v. Smallwood *does* apply to IRV, and that is my own reading of the case. Solgard and Landskroener argue that this phrase from Brown v. Smallwood controlled the decision:

"The preferential system directly diminishes the right of an elector to give an effective vote for the candidate of his choice. If he votes for him once, his power to help him is exhausted. If he votes for other candidates he may harm his choice, but cannot help him.'

Now, this is not a reference to one-person, one-vote, it is to a tactical voting decision. But there is lots more in Brown v. Smallwood. In particular, the reconsideration of the case included this very specific language, which applies to IRV as much as to Bucklin:

"We reached the conclusion that a system of voting, giving the voter the right to vote for the candidate of his first choice, and against the first choice of another voter, and, in addition, by a manipulation of second and additional choice votes, vote for different candidates all against the first choice of another voter to a number of times limited only by the number of candidates, was contrary to the intent of the Constitution; and that it was none the less so because such other voter was permitted to engage in a like manipulation of second and additional choice votes. [...] We do right in upholding the right of the citizen to cast a vote for the candidate of his choice unimpaired by second or additional choice votes cast by other voters." (Brown v. Smallwood, 130 Minnesota Reports, p. 508.)

This is *not* an argument proceeding from a claim that a voter is going to hurt his first choice by casting a second choice vote. FairVote wants to read the case that way because, they claim, IRV never does this. However, in some circumstances, it does; for example, the IRV legislation proposed for Vermont by Terrill Bouricius must face a majority election requirement in the Vermont Constitution, and the "last round majority" that IRV necessarily generates is not a true majority; if a majority *of ballots cast* -- including exhausted ballots -- is not attained by the end of the process, the top three candidates go to the Legislature for a secret ballot *plurality* election. Thus adding additional votes *can* hurt your first choice, by allowing a majority to form for your second choice, whereas if there is majority failure, your first choice will still have a chance.

The legal opinion issued by the FairVote authors is corrupt and disregards the clear text of Brown v. Smallwood. I would guess that it was calculated to encourage Minneapolis decision-makers to go ahead and go for IRV. It may have been a smart political move, since there is, in fact, a good chance that Brown v. Smallwood will be reversed, it was a thoroughly corrupt decision as well, in my opinion. The dissent in the decision points that out quite well. A Michigan court, I noticed a reference just now, appears to have tossed out the "Hare system" of proportional representation in 1920, with reference to Brown v. Smallwood. That's STV, the methodological foundation for IRV, quite explicitly on point.

The majority in Brown v. Smallwood was considering all marks on the ballot to be "votes," and thus Bucklin -- and any preferential voting system -- would violate one person, one vote.

(In the article I originally wrote, Warren Smith comments that the first U.S. Presidential elections were "Approval," but that is an error which can be traced back to the same set of "theorists." He fell for it, apparently. But *Bucklin* is essentially "instant runoff Approval," it clearly satisfies the Majority Criterion, no matter how you slice it (there is argument about that for Approval). The additional approvals are only brought in if there is majority failure in the first round. Thus it behaves like Plurality except when there is majority failure, which is also true for IRV. Yet Bucklin is a much simpler method to count than IRV, it is precinct summable, unlike IRV, and there are no nasty surprises due to candidate eliminations. *It was working, from all accounts I've been able to find, the reasons FairVote gives for its abandonment are not based on known facts, they are simple opinions stated by FairVote, beyond what is seen in Brown v. Smallwood, which I would conclude was about politics, not fairness in elections. Somebody wanted Bucklin dead. Too dangerous to the status quo. Third parties might actually start to get traction, that was a major fear in those days. You know, communists, anarchists, farm and labor parties, Negroes, etc.) --Abd (talk) 05:49, 9 January 2008

Absolute majority?

There is a sentence in the article that states "A majority is defined as half the number of voters, similar to absolute majority." I believe this to be factually incorrect for two reasons:

1. A majority, whether simple or absolute, requires more than half, not just half.
2. An absolute majority is defined as being based on the total number of possible voters, whether present or not. This is not a requirement of the Bucklin system as far as I can tell, nor is this really common to the theory of voting systems in general.

As such, I am correcting what I believe to be errors. Please discuss here if you disagree with the changes. Derelk (talk) 22:44, 31 March 2008 (UTC)

That definition of majority was incorrect, not so much because of "absolute majority," but because majority means "more than half." An exact half is not a majority. "Absolute majority" is used differently in different places, so the comment could be confusing, though it is correct if we understand the basis, the "membership," so to speak, as being all those who cast ballots in the election. It can be variously defined for Bucklin, sometimes it might mean all ballots containing a vote for an eligible candidate, including eligible write-ins. The change Derelk made was an improvement. --Abd (talk) 15:56, 20 May 2010 (UTC)

Condorcet loser criterion?

OK, Bucklin does fail. But in order for it to fail, you need an incredible balance. It's impossible with 3 candidates, and with 4, I can't do it with fewer than 23 voters of 11 different kinds; I'm sure this can be improved marginally, but I doubt by too much.

2	a	b	d	c
2	b	c	d	a
0	c	a	d	b
4	a	d		
2	b	d		
4	c	d		
1	d	a	b	c
1	d	b	c	a
1	d	c	a	b
2	b	c	a	d
2	c	a	b	d
2	a	b	c	d

.... anyway, I know that failing is failing, and I don't want to start a slippery slope of "my system's failure doesn't count", but this is ridiculous. Is there any way to qualify this failure that wouldn't start us down that slope? Homunq (talk) 19:01, 16 February 2010 (UTC)

This is the problem with election criteria, and it leads to other problems. Sourcing. Original research. In the end, though, Wikipedia decisions are made by consensus, and the exact boundaries of allowed sources and "original research" are what consensus can decide. And then, if a discussion "escalates," that decision can change. Bucklin fails certain criteria because of the restriction on "overvoting" in some ranks. That's an artificial restriction, but all of the known Bucklin implementations that I've seen had it, perhaps by habit from plurality or the known alternative at the time, STV.

Election criteria are supposedly neutral criteria that can be applied to a method in order to assess its function. That purpose of criteria is somewhat defeated when a failure is so difficult that it takes an extremely complex situation. Without assessing specific text in context, I don't want to make a blanket statement about this, but one of the obvious and common solutions is to only say about criterion failure what can be found in reliable source, and, unfortunately, reliable source on this topic, i.e., standard formal reliable source, published as described in WP:RS, can be hard to find. Sources have been used in many of the election methods articles that do not meet WP:RS, at least not clearly. My own preference is to try to make sure that articles are accurate, informative, and clear, with less rigid dependence on the formal guidelines and satisfaction of policy in substance if not always in specific form. The only way I know to approach this is through consensus. So let's work on that. If we can agree, for example, that a scenario showing criterion failure is clear from an example, that can be considered the equivalent of doing the math to add up some numbers found in reliable source. Technically, doing math is original research, but if we all sign on to it .... --Abd (talk) 16:11, 20 May 2010 (UTC)

Criteria compliance debate; references needed (was: Dubious)

NOTE: I have copied many of the comments immediately below into the subsections which follow, in an attempt to separate the different points of debate and hopefully make the discussion easier to follow. If you want to avoid reading them twice, skip to the #Is equal rankings a Bucklin system? subsection. Homunq (talk) 17:15, 20 May 2010 (UTC)

If equal rankings and skipped rankings are allowed, Bucklin satisfies both IIA and clone independence. (You have to assume intrinsic rankings - but the IIA criterion makes no sense at all without this assumption, so it's justified.)

Say B wins at rank N. Remove another candidate? B is still ranked the same, so still wins at rank N. Add another non-winning candidate? Same deal. IIA is satisfied. Add a bunch of clones of B? They all tie for a win at rank N. So clone independence is satisfied. Homunq (talk) 22:39, 15 May 2010 (UTC)

Thank you for responding, User:MarkusSchulze. It would be easier for third parties if you'd deign to post here on talk, rather than just edit comments, but I can repost it. You say: "Arrow's impossibility theorem applies to Bucklin voting." You are wrong. Most variants of Bucklin voting do not have an "unrestricted domain" in the sense of Arrow. Ballots cannot express full preferences if there are more candidates than ranking categories; and for a given preference ordering, there is more than one possible ballot if equalities and skipped ranks are allowed. Homunq (talk) 10:23, 16 May 2010 (UTC)

To clarify: if your preferences are A>B>C>D>E and there are 3 ranking categories and no equalities allowed, then you might vote any of A>B>C; A>B>D; A>C>D; or B>C>D. Although A>B>C might seem "more natural", a reasonable voter might choose any of the others to best express their dislike for E. Since these obviously lead to different results, there is no "unrestricted domain". Homunq (talk) 11:02, 16 May 2010 (UTC)

User:MarkusSchulze, I'm not going to be lured into edit warring with you. I've reported you for your earlier 3RR violation, and I hope that in the future you will participate on talk. As to your comment on reverting me: if you feel that my edit is original research, you are within your rights. In that case, the section as it stands is also original research. I am removing it for now, but that makes the article unequivocally worse. I hope that we can come to some compromise, and I would welcome bold edits from you to propose such a comprimise (ie, not just reverts.) Peace, Homunq (talk) 16:40, 18 May 2010 (UTC)

You're really trying to make me lose my cool, aren't you? Here's my response. You're wrong for four separate reasons. Before this silly battle, I really did have the utmost intellectual respect for you. Homunq (talk) 18:16, 18 May 2010 (UTC)

Dear User:MarkusSchulze, could you please explain how adding an entire section is "removing" original research? Homunq (talk) 23:14, 19 May 2010 (UTC)

Dear Homunq, please stop trying to change the Bucklin voting article into a majority choice approval article. Markus Schulze 23:23, 19 May 2010 (UTC)

Answer the question. Where are your sources? How can adding unsourced material qualify as "removing original research"? Homunq (talk) 23:28, 19 May 2010 (UTC)

Now you're removing simple tags, without adding references? This is ridiculous. A fact tag does not claim that it passes or fails any criteria. It just says that there are no references. Homunq (talk) 23:41, 19 May 2010 (UTC)

Hello, this is James Green-Armytage. Homunq asked me to have a look at this discussion. Unfortunately I'm finding it hard to figure out precisely what is at issue here. Is there a very specific piece of text that's at issue, or are there multiple disputed points? One of the first disputed pieces of text I found was this:

"If equal rankings are allowed and only the ballots are considered, it also passes the independence of irrelevant alternatives criterion and the independence of clones criterion, although in that case it may violate the majority criterion for the underlying voter preferences."

Homung, are there some proofs of this anywhere? How exactly does Bucklin work when equal rankings are allowed? I don't know if there is a good literature on this, so it might be considered original research, yes. My intuition is that Bucklin probably still fails at least ICC even if equal rankings are allowed. You should be aware that voters may prefer one 'clone' to another; the contrary idea is a common misconception about ICC. I also strongly doubt that Bucklin would satify IIA, even with equal rankings. I hope that this has been helpful. Hermitage (talk) 04:19, 20 May 2010 (UTC)

This is a comment that Tom Ruen posted to his talk page: "Bucklin absolutely doesn't support equal rankings, since the purpose of Bucklin is to treat all ballots equally, so the first round everyone gets one vote, second round 2 votes, etc. Any other interpretation would be something different. Any other interpretation denies the basis of voters to support a multiple vote option as 'fair'. But I don't have sources, or motive to be in an argument. I assume the issue comes out with Approval/Range voting advocates who are forever trying to make a case for multiple votes, and I've never found any resolution/compromise against their agenda. Tom Ruen (talk) 05:06, 20 May 2010 (UTC)" Markus Schulze 11:01, 20 May 2010 (UTC)

OK, let's take this from the top.

Issue 1: Are systems with equal and skipped rankings allowed (such as Majority Choice Approval or the voting system used in Duluth, Minnesota in the early 20th century) properly part of this article? That is, are they forms of Bucklin voting?

My position is that they clearly are. The Duluth system was called "Bucklin voting", among other names, at the time. While it only allowed equalities in the third rank, this clearly demonstrates that the term was (and thus is) broad enough to encompass various systems, including those which allow equal-ranking at all levels. Similarly, today, the same term "IRV" is used for systems with full ranking and those which only allow the top 3 ranks; although this distinction may have a significant impact on the mathematical properties of the system, it is regarded as minor for the purposes of terminology.

Issue 2: Do systems with equal and skipped rankings allowed in all ranks (called =Bucklin below, for short) satisfy (a) the ICC; (b) the IIAC; and (c) the MC?

My position is yes to all three. This does, however, depend somewhat on the definition of the three criteria. For (a), it requires clones to be ranked equally; since this definition of the ICC is called a "misconception" by Hermitage above, this would clearly need to be clarified in the text somehow. For (c), although only I have questioned Bucklin's compliance with MC, this too depends on the definition of the MC, and should probably be clarified somewhere. If the MC is defined as "must elect X if a majority votes solely for X in the top rank", then =Bucklin trivially passes. If it's defined as "must elect X if a majority votes for X uniquely above all other candidates", then it does not.

Issue 3: If we do resolve issue 2, does that constitute original research?

I would prefer it if this article were not held to standards that other similar articles are far from meeting. I suspect that well under a quarter of the standards (non)compliances asserted in Wikipedia are adequately referenced. I think that if we're being reasonable, a mathematical proof should suffice, even if it's not published in a strongly reliable source. I'd even be willing to provide such an unpublished proof, if we can agree that it would be adequate; or consider creating an computer-checked proof if necessary. However, if others insist on strict compliance with WP:RS, I will of course have to cede this point, and I won't make an asshole of myself by insisting on the same standard for other articles. In that case, I will of course insist that whatever the article does claim is, as well as being sourced, not positively misleading on the facts; that is, it must not give the impression that any specific system doesn't pass criteria which actually it provably does pass. This is the reason for the current {{refimprove}} tag on the section; I hope we can reach consensus on these 3 points ASAP so as to remove that unsightly tag.

User:MarkusSchulze, can you please state your positions on all three issues, below? Homunq (talk) 14:39, 20 May 2010 (UTC)

I am involving myself here because I'm a bit of an expert on Bucklin voting, just as Mr. Schulze is an expert on a "rival system," a form of Condorcet voting, the "Schulze method," and I was asked by Homung to comment (though the article is on my watchlist). I'm going to suggest that we start by making the article reflect as high a degree of immediate consensus as possible, and if it means stripping out stuff we can't yet agree upon, so be it. Then we work on that, to improve the article, thinking of the readership and basic policy. So far, some of those involved here might be considered somewhat COI on the topic, but that would suggest only what we should already do: work toward consensus through discussion, rather than through revert warring. I am personally pleased to see the participation here of Mr. Schulze, whom I know has deep knowledge of voting systems, and, as well, James Green-Armytage, whose study of voting systems is widely-known. I really want to encourage and protect that. And I think Homung for pinging me. --Abd (talk) 16:24, 20 May 2010 (UTC)

Tom Ruen is not particularly knowledgeable about Bucklin, though he knows more than many, and has previously said that he favors the method, as I recall. I can show RS, however, that original Bucklin generally allowed multiple votes in the third rank. I've seen no argument in the extensive justifications of Bucklin, written at the time by Mr. Bucklin and others, as to why overvoting was prohibited in the first two ranks, but the method does function to seek a majority if possible, and to do that it collapses the ranks so that voters are, in effect, voting for more than one, equally. And it is quite clear from the results of the first Bucklin election (and from stated Bucklin procedure) that ranks could be empty, for in the first election, in Grand Junction, Colorado, there were more votes in third rank than in second. The method is essentially ranked approval, counted in rounds, and from this perspective the requirement that voters only approve one candidate in first and second ranks has no clear justification, it simply requires voters to make a judgment that they may not have adequate preference strength to make. Majority Choice Approval, then, can be seen as a modified Bucklin with only two ranks. MCA with only one vote allowed in first preference is Bucklin with only two ranks, the middle rank being eliminated, that's all. --Abd (talk) 16:37, 20 May 2010 (UTC)

I'm taking the liberty of creating subsections for each of the three issues under debate, and copying positions from above into the relevant sections. Homunq (talk) 17:15, 20 May 2010 (UTC)

Is equal rankings a Bucklin system?

Issue 1: Are systems with equal and skipped rankings allowed (such as Majority Choice Approval or the voting system used in Duluth, Minnesota in the early 20th century) properly part of this article? That is, are they forms of Bucklin voting?

Dear Homunq, please stop trying to change the Bucklin voting article into a majority choice approval article. Markus Schulze 23:23, 19 May 2010 (UTC)

This is a comment that Tom Ruen posted to his talk page: "Bucklin absolutely doesn't support equal rankings, since the purpose of Bucklin is to treat all ballots equally, so the first round everyone gets one vote, second round 2 votes, etc. Any other interpretation would be something different. Any other interpretation denies the basis of voters to support a multiple vote option as 'fair'. But I don't have sources, or motive to be in an argument. I assume the issue comes out with Approval/Range voting advocates who are forever trying to make a case for multiple votes, and I've never found any resolution/compromise against their agenda. Tom Ruen (talk) 05:06, 20 May 2010 (UTC)" Markus Schulze 11:01, 20 May 2010 (UTC)

Tom Ruen is not particularly knowledgeable about Bucklin, though he knows more than many, and has previously said that he favors the method, as I recall. I can show RS, however, that original Bucklin generally allowed multiple votes in the third rank. I've seen no argument in the extensive justifications of Bucklin, written at the time by Mr. Bucklin and others, as to why overvoting was prohibited in the first two ranks, but the method does function to seek a majority if possible, and to do that it collapses the ranks so that voters are, in effect, voting for more than one, equally. And it is quite clear from the results of the first Bucklin election (and from stated Bucklin procedure) that ranks could be empty, for in the first election, in Grand Junction, Colorado, there were more votes in third rank than in second. The method is essentially ranked approval, counted in rounds, and from this perspective the requirement that voters only approve one candidate in first and second ranks has no clear justification, it simply requires voters to make a judgment that they may not have adequate preference strength to make. Majority Choice Approval, then, can be seen as a modified Bucklin with only two ranks. MCA with only one vote allowed in first preference is Bucklin with only two ranks, the middle rank being eliminated, that's all. --Abd (talk) 16:37, 20 May 2010 (UTC)

My position is that equal-ranking Bucklin-like systems clearly are forms of Bucklin. The Duluth system was called "Bucklin voting", among other names, at the time. While it only allowed equalities in the third rank, this clearly demonstrates that the term was (and thus is) broad enough to encompass various systems, including those which allow equal-ranking at all levels. Similarly, today, the same term "IRV" is used for systems with full ranking and those which only allow the top 3 ranks; although this distinction may have a significant impact on the mathematical properties of the system, it is regarded as minor for the purposes of terminology.Homunq (talk) 14:39, 20 May 2010 (UTC)

(copied from Talk:Voting system) Dear Homunq, what you label "Bucklin voting" is not Bucklin voting but Majority Choice Approval. It is clear that a Wikipedia article on Bucklin voting must be on Bucklin voting.

Furthermore, it is well known that Bucklin voting is not clone-proof. Example: Situation 1: 20:A>B>C, 17:B>C>A, 13:C>A>B. The Bucklin winner is B. Situation 2: A is cloned. 20:D>A>B>C, 17:B>C>A>D, 13:C>A>D>B. Now the Bucklin winner is A. Markus Schulze 16:42, 19 May 2010 (UTC)

(copied from Talk:Voting system)So, you finally come to understand that it's a difference of definition. But you're wrong, and your tautologies don't help matters. Majority choice approval is a form of Bucklin. In at least one US municipality (I'll check which), "Bucklin voting" (so-called at the time) allowed equal rankings.

Furthermore, your "furthermore" is just saying the same thing in different words. You can say it 5 times and you'll still be wrong. Homunq (talk) 22:16, 19 May 2010 (UTC)

Homunq, please stop. You are partly correct, Markus is partly correct, and the article doesn't depend on any one or two of us being correct, it depends on what's in sources. Markus, Homunq is correct that equal ranking was allowed in third rank. He's correct that Bucklin as it is being proposed today often allows equal ranking in all ranks, it's clearly superior. And he's correct that original Bucklin allowed equal ranking in third rank and allowed empty ranks. (I.e., you could skip second rank and vote in the third, which means that the ballot is a kind of Range ballot.) MCA is two-rank Bucklin. Any possible difference would be a difference in the overvoting technicalities. The specifics of those rules cause certain technical criteria failures. You are correct that "historical Bucklin" didn't allow multiple votes in first and second ranks. However, most Bucklin being proposed at this time is "Bucklin-ER," which is unrestricted approval in all ranks. Unfortunately, I'm not aware of any sources other than ubiquitous mention on the EM mailing list, including mention by experts.

Voting systems are usually classified according to general characteristics, not necessarily every specific detail. A Bucklin voting system is clearly recognizable by the addition of votes from a set of rounds or ranks or ratings, seeking a majority, rather than the substitution of votes from a ranked list as with IRV or examination of all pairwise contests as with your Condorcet method, Markus. Original Bucklin also included sequential elimination of the lowest vote-getter, a minor aspect of the method that was dropped in later implementations as unnecessary. --Abd (talk) 19:58, 20 May 2010 (UTC)

The above RFC covers this section (see initial question) as well as the following 2 sections. These are three related questions about Bucklin's compliance with mathematical criteria desirable for voting systems. Homunq (talk) 17:34, 20 May 2010 (UTC)

Well, Homunq, I wished you'd waited before putting up an RfC. We should only go to RfC if the editors involved here cannot come to agreement. RfC will bring in people with no understanding of the nature of the voting systems field and who will be likely to make decisions based on general Wikpedia principles, which often results in less than optimal decisions considering the particular needs of an article. That should only be done if those who know the field cannot find agreement. You could retract it, I certainly would not object. It could always be filed later. It's better, if possible, to have clear questions laid out with exact text in question. --Abd (talk) 18:22, 20 May 2010 (UTC)

I'm not going to withdraw the RFC, but I will concur with Abd in that I'm only seeking help in developing a consensus among the editors involved. I believe that it would be harmful to come in without understanding the issues involved and apply a strict, small-minded interpretation of Wikipedia policy. Much of this article lacks sufficient citation, and we're working on it; to denude it on that basis would be draconian. Please, RFC responders, don't be too bold in article space, just help us out here on Talk. Homunq (talk) 18:40, 20 May 2010 (UTC)

comment about RfC filing not necessary for content decisions. --Abd (talk) 19:46, 20 May 2010 (UTC)

That's unfortunate, Homunq. But I gave my advice, you chose not to follow it. For the sake of the encyclopedia, we can hope that the results help the article. *Before filing an RfC*, it would be better to have the arguments laid out, clearly, with all sides agreeing that these are the issues and the evidence, and then someone without prior knowledge can much better judge the situation. Doing this would often resolve the dispute, if editors are reasonable. Without that, we are likely to get a pile of well-meaning but uninformed comments, for the issues can be complex. Those who don't understand the issues will tend, naturally, to rely on what is clear in the most reliable sources, which largely don't exist or only exist in journals behind pay-walls, and which can provide misleading information in some cases, which anyone familiar with the field will recognize. We can still muddle through, perhaps, but it can get more difficult, not easier. The damage could extend through the entire family of voting systems articles, which are frequently very old articles that were based on common knowledge and that survived because of just that. Where the strict, wikilawyered interpretation of the rules has been brought in by people with an axe to grind, notable topics have been deleted, and good and informative text, not actually controversial, has been removed. We'll see. --Abd (talk)

Responses to question 1

• Yes, some forms of Bucklin as proposed allow equal ranking in all ranks, specifically Condorcet's proposal in 1793, and original Bucklin (Grand Junction method) allowed it in third rank, as did most Bucklin implementations. --Abd (talk) 18:10, 22 May 2010 (UTC)

I agree, but I would note that of course Condorcet lived before Bucklin, and thus never referred to "Bucklin". So: This proposal of Condorcet's is not covered in any other article, and Abd and I are arguing that this article is the natural place for similar systems. Many actual Bucklin implementations did allow some degree of equal ranking; that is the most relevant point. Homunq (talk) 12:58, 23 May 2010 (UTC)

Does equal rankings pass ICC, IIAC, and MC?

Issue 2: Do systems with equal and skipped rankings allowed in all ranks (called =Bucklin below, for short) satisfy (a) the ICC; (b) the IIAC; and (c) the MC?

If equal rankings and skipped rankings are allowed, Bucklin satisfies both IIA and clone independence. (You have to assume intrinsic rankings - but the IIA criterion makes no sense at all without this assumption, so it's justified.)

Say B wins at rank N. Remove another candidate? B is still ranked the same, so still wins at rank N. Add another non-winning candidate? Same deal. IIA is satisfied. Add a bunch of clones of B? They all tie for a win at rank N. So clone independence is satisfied. Homunq (talk) 22:39, 15 May 2010 (UTC)

Thank you for responding, User:MarkusSchulze. It would be easier for third parties if you'd deign to post here on talk, rather than just edit comments, but I can repost it. You say: "Arrow's impossibility theorem applies to Bucklin voting." You are wrong. Most variants of Bucklin voting do not have an "unrestricted domain" in the sense of Arrow. Ballots cannot express full preferences if there are more candidates than ranking categories; and for a given preference ordering, there is more than one possible ballot if equalities and skipped ranks are allowed. Homunq (talk) 10:23, 16 May 2010 (UTC)

Hello, this is James Green-Armytage. Homunq asked me to have a look at this discussion. Unfortunately I'm finding it hard to figure out precisely what is at issue here. Is there a very specific piece of text that's at issue, or are there multiple disputed points? One of the first disputed pieces of text I found was this:

"If equal rankings are allowed and only the ballots are considered, it also passes the independence of irrelevant alternatives criterion and the independence of clones criterion, although in that case it may violate the majority criterion for the underlying voter preferences."

Homung, are there some proofs of this anywhere? How exactly does Bucklin work when equal rankings are allowed? I don't know if there is a good literature on this, so it might be considered original research, yes. My intuition is that Bucklin probably still fails at least ICC even if equal rankings are allowed. You should be aware that voters may prefer one 'clone' to another; the contrary idea is a common misconception about ICC. I also strongly doubt that Bucklin would satify IIA, even with equal rankings. I hope that this has been helpful. Hermitage (talk) 04:19, 20 May 2010 (UTC)

My position is yes to all three. This does, however, depend somewhat on the definition of the three criteria. For (a), it requires clones to be ranked equally; since this definition of the ICC is called a "misconception" by Hermitage above, this would clearly need to be clarified in the text somehow. For (c), although only I have questioned Bucklin's compliance with MC, this too depends on the definition of the MC, and should probably be clarified somewhere. If the MC is defined as "must elect X if a majority votes solely for X in the top rank", then =Bucklin trivially passes. If it's defined as "must elect X if a majority votes for X uniquely above all other candidates", then it does not.Homunq (talk) 14:39, 20 May 2010 (UTC)

What you have done, here, is to raise questions that are controversial among experts. Obviously. Both "Bucklin voting" and "IIA" and clone independence are not crisply defined in ways that are universally accepted. Bucklin was implemented in various ways, and has been proposed with an obvious extension of allowing equal ranking in all ranks. Normally equal ranking was allowed only in third rank. But nobody in the field would fail to recognize as Bucklin a voting system that worked like, say, Duluth Bucklin, but allowed equal ranking in all ranks. All Bucklin systems that I've seen allow skipping ranks, and it was clearly done in the 1909 Grand Junction election. The issue of whether or not full-equal-ranking Bucklin would pass the majority criterion depends on the precise definition, and I spent weeks on this issue (of the definition of the MC) with Terry Bouricius and others. It's clear that if only one candidate is allowed in first rank, Bucklin does satisfy the majority criterion, and it's also clear that with full-equal-ranking Bucklin, if a majority favorite fails to win, it is because the majority, uncoerced, also approved someone else and thus failed to express the exclusive preference that you might assume they have. What it boils down to is that if the voters have a preference, the voting system allows them to express it, and they don't express it, the voting system cannot respect the preference. No voting system could. Now, try to find this obvious argument in the literature. Good luck. The active voting systems experts mostly went to on-line discussion by the mid-1990s, and those who publish in journals are mostly out of touch with the general field, with blatant nonsense sometimes being published because the reviewers aren't experts on voting systems, per se. The Election Methods list isn't directly usable because it is, after all, just a mailing list and anyone can subscribe and write.

What we can do without specific and explicit reliable source is limited. How limited depends on how cooperative the editors involved in an article are. That's why revert warring and filing a 3RR complaint and losing patience with other editors is destructive. That's also why filing an RfC because agreement isn't appearing immediately is also a Bad Idea. We may get lucky and get some editors who understand the issues, but many won't. It would be better to first agree on what the issues are, collect whatever evidence is available, and then decide on the questions to be asked. Cooperate. Cooperation doesn't mean agreeing, except where agreement is ripe. --Abd (talk) 02:10, 21 May 2010 (UTC)

Responses to Question 2

• Yes and No Bucklin ER (=Bucklin) satisfies the majority criterion, but this is controversial; generally the arguments have raged over the question: if the majority chooses to equal rank in first rank when it has a choice (i.e., to exclusively rank), can a method fail the MC if the majority "really" prefers a candidate? In real Bucklin, though, multiple majorities were rare even when three ranks were completely collapsed, that a multiple majority, which is what this would require, would happen in first rank requires conditions that are essentially impossible except with artificially constructed "elections." (Where a majority chooses to add additional preferences, not only in lower ranks, but in first rank. I.e., the majority is quite ignorant and has no clue at all, otherwise, if their preference is significant, they would rank their second choice lower. Voters may be prohibited from adding multiple preferences in first rank. This would make MC compliance completely uncontroversial, but at the cost of tossing ballots that break the rule!) The substance is that Buckin ER satisfies MC, for sure. Technical failure depends on the exact definition, and some experts have tended to decide, first, if a method passes or fails (their "intuition") and then attempt to craft the definition to suit the conclusion, see the work of James Green-Armytage on Approval and the Majority Criterion. Bucklin ER satisfies IIA, but, again, someone can assert differently based on assumptions about voting strategy instead of actual ballots. (2 or 3-rank Bucklin without equal ranking allowed arguably fails IIA under the "additive" definition). As to ICC I'm not "voting" yet. Tideman says nothing about Bucklin ER, only that ordinary Bucklin, under his assumptions (which aren't the general case for Bucklin methods) fails IIA. "Clones" has a technical meaning that isn't the same as our ordinary word "clone." Which makes this truly confusing for the non-expert. --Abd (talk) 18:27, 22 May 2010 (UTC)

I'd just like to note that the Tideman reference now cited in the article, to say that Bucklin fails ICC, clearly refers to Bucklin without equal rankings allowed. Thus, depending on the answer to the prior question, its use may need to be qualified somehow. Homunq (talk) 12:53, 23 May 2010 (UTC)

Does the answer above constitute original research?

Issue 3: If we do resolve issue 2, does that constitute original research?

I would prefer it if this article were not held to standards that other similar articles are far from meeting. I suspect that well under a quarter of the standards (non)compliances asserted in Wikipedia are adequately referenced. I think that if we're being reasonable, a mathematical proof should suffice, even if it's not published in a strongly reliable source. I'd even be willing to provide such an unpublished proof, if we can agree that it would be adequate; or consider creating an computer-checked proof if necessary. However, if others insist on strict compliance with WP:RS, I will of course have to cede this point, and I won't make an asshole of myself by insisting on the same standard for other articles. In that case, I will of course insist that whatever the article does claim is, as well as being sourced, not positively misleading on the facts; that is, it must not give the impression that any specific system doesn't pass criteria which actually it provably does pass. This is the reason for the current {{refimprove}} tag on the section; I hope we can reach consensus on these 3 points ASAP so as to remove that unsightly tag.Homunq (talk) 14:39, 20 May 2010 (UTC)

I am involving myself here because I'm a bit of an expert on Bucklin voting, just as Mr. Schulze is an expert on a "rival system," a form of Condorcet voting, the "Schulze method," and I was asked by Homung to comment (though the article is on my watchlist). I'm going to suggest that we start by making the article reflect as high a degree of immediate consensus as possible, and if it means stripping out stuff we can't yet agree upon, so be it. Then we work on that, to improve the article, thinking of the readership and basic policy. So far, some of those involved here might be considered somewhat COI on the topic, but that would suggest only what we should already do: work toward consensus through discussion, rather than through revert warring. I am personally pleased to see the participation here of Mr. Schulze, whom I know has deep knowledge of voting systems, and, as well, James Green-Armytage, whose study of voting systems is widely-known. I really want to encourage and protect that. And I think Homung for pinging me. --Abd (talk) 16:24, 20 May 2010 (UTC)

(copied from Talk:Voting system)Not everything that is allowed in a mailing list is also allowed at Wikipedia. For example: Original research is strictly prohibited at Wikipedia. Biased articles are strictly prohibited at Wikipedia. By the way: The majority choice approval article has been deleted because it was original research. Markus Schulze 22:54, 19 May 2010 (UTC)

That may have been the stated reason, but, in fact, the proper reason would be lack of demonstrated reliable source. WP:OR really refers to research done here; if OR is published by a proper publisher, it can become reliable source, and a great deal of reliable source is that. The exact dividing line is not sharp.

Take a look at that AfD. The nominator is banned. The AfD closure was possibly improper, but few were left, by that time, to challenge these AfDs. I didn't do it because I was not aware of clear reliable source, and once the deletionist bulldogs bite onto a topic they consider fringe, they don't let go. But you never can tell. By the way, I'm not claiming those deletionists are wrong, and certainly not that they are always wrong. I can't say that MCA belongs in the project, but a merge of MCA with Bucklin voting might be in order, since it is clearly recognizable as a Bucklin method. --Abd (talk) 20:08, 20 May 2010 (UTC)

WP:NNC might support that line of argument. Homunq (talk) 21:16, 20 May 2010 (UTC)

(copied from Talk:Voting system)Right now, you are the one promoting your own original research in this article. If there are no sources on what gets called Bucklin or on whether it passes clone or IIA, then the relevant cells must be left blank. Homunq (talk) 23:01, 19 May 2010 (UTC)

The sources may not exist, even though criterion failure can be seen by doing some simple math. In this case, IIA, it depends on the details of the rules, and, as well, details of criteria definitions that aren't necessarily universally accepted. --Abd (talk) 20:08, 20 May 2010 (UTC)

(copied from Talk:Voting system)Try to get majority choice approval adopted or published somewhere and then write a Wikipedia article about it. Markus Schulze 23:19, 19 May 2010 (UTC)

(copied from Talk:Voting system)This is not about MCA, this is about Bucklin. Which has been used in major US cities, and so is clearly a more notable inclusion in the table than Schulze voting.

Where are your sources which say Bucklin does not meet clone independence and IIA? Until you find them, you are pushing original research. Homunq (talk) 23:22, 19 May 2010 (UTC)

Please stop with the accusations, like "you are the one who," and arguments that avoid the immediate issue, which would be the definition of Bucklin voting, first, and then its apparent characteristics. Homunq is correct that we might have some flexibility in that, and it is possible to note that a method passes, say, IIA, under one set of specific rules and not another. It is clear, though not widely known, that original Bucklin did allow skipped ranks, and most of the implementations I've looked at allowed unlimited approval in the third rank. However, this has become so much of a catfight that I'm retiring for the night. --Abd (talk) 02:16, 21 May 2010 (UTC)

Abd, those comments were from right after my "no sources" proposal (in two cells of the Voting systems table) were reverted with the comment "removing original research". I copied the comments here because they were relevant, but they came long before this section was created; the discussion has actually cooled down since then, and I feel that we're actually making progress now. Homunq (talk) 03:33, 21 May 2010 (UTC)

Responses to Question 3

• Who wants to know? Seriously. Wrong question. The answer depends on conditions and the way in which we base our conclusions, and an answer here might be, for example, "Yes," implying that we cannot use the conclusion (which is the real question), but that could then change if, say, a single reasonably reliable source pops up, or consensus finds that some text is obvious from the sources and simple math, and does not violate WP:OR. Who decides what text is allowable? Not even ArbComm! The decisions are made by ad hoc editorial consensus. Sometimes what one person might think is original research is, in practice, allowed, and other times what might be more considered WP:SYNTH violations are disallowed. There is no rigid rule applicable under all conditions, not yet, at least. It is often pointed out that editorial consensus doesn't trump policy, but that's a misunderstanding. Policy is subject to editorial consensus and is generally interpreted by editorial consensus. The real issue is whether or not a small group of editors can toss out policy because of their local consensus, and the fact is that they can, but can't maintain it if a larger group becomes involved, if the matter escalates, and there isn't some clear and accepted reason to set aside the general rule, i.e., policy. And however we answer this question now, it does not bind us in the future. The most basic policy is Rule Number One. But be careful. Rule Number One does not allow or excuse disruptive disregard for consensus. --Abd (talk) 18:40, 22 May 2010 (UTC)

The question isn't who's asking, but who's answering. Unlike the two other questions above, there isn't even a ghost of a "right" answer to this one; it's just a matter of what answer we can agree on here. If we can all agree something's reasonable, well, then, it is. On the other hand, if somebody insists on a more conswervative view of WP:OR and WP:RS, then that's the answer. My preference is for being reasonable, but I'm just one person here. Homunq (talk) 12:14, 23 May 2010 (UTC)

Bucklin election with multiple majority

[5] Actually, this was the original Bucklin ballot, the first time it was used. The rules provided for "majority" to mean more than half of the ballots, so if a voter left a race blank, the ballot still counted. This can be seen in the canvass report shown: majority is shown for all of the races as 924 votes. For the Commissioner of Highways, there were 5 candidates. The winner led in all three ranks, no majority was obtained until the third rank votes were included, and then the winner had 1175 votes and the runner-up had 976 votes. So this is an example of a multiple majority. The worries about Bucklin not satisfying the Condorcet criterion are based on either a plurality win or a multiple majority. But it's not true that no examples are known; I removed that text from the article. --Abd (talk) 16:11, 22 May 2010 (UTC)

Multiple majorities appear to have been rare. Much criticism of Bucklin appears to have been the reverse: no majority was found in some environments. --Abd (talk) 14:35, 28 May 2010 (UTC)

Independence of irrelevant alternatives criterion

This criterion can be stated in various ways, apparently. Our article on IIA has this:

If A is preferred to B out of the choice set {A,B}, then introducing a third alternative X, thus expanding the choice set to {A,B,X}, must not make B preferable to A.

Generally, with voting systems (as distinct from the social ordering process of concern to Arrow), we are concerned if a result changes as the result of an irrelevant alternative. There is a general problem with the application of voting systems criteria that are based on "preferences," as distinct from actual votes. No method can extract preferences from the mind of the voter unless the voter chooses to express the preference. So there are two general approaches: use only actual ballot changes to see how they affect the result, or use internal preferences, with, then, some presumption about how voters vote. But this latter choice can become quite complex and even subjective.

Then there is this definition, about "voting rules," also from our article on IIA:

If A is selected over B out of the choice set {A,B} by a voting rule for given voter preferences of A, B, and an unavailable third alternative X, then B must not be selected over A by the voting rule if only preferences for X change.

The criterion is sometimes stated as : If all the votes for a candidate who does not win under an election rule are removed, the result of the election will not change. But what it means when "votes are removed" can be unclear. I find it simplest to consider that, literally, the name is there, but the candidate is, say, illegible, or the space is now blank. Nothing else is changed. In Plurality, all that changes is the vote for that candidate, thus Plurality satisfies IIA under this approach. But we have:

Independence_of_irrelevant_alternatives#Plurality_voting_system with Plurality failing, because it is assumed that the voters "rank" candidates. Which they don't do with Plurality. Whether or not the result changes depends on whether or not the voters vote "sincerely" or vote "strategically." This cannot be judged from the actual plurality ballots.

This is the issue with Bucklin. Suppose a voter ranks A>X>C, and X is irrelevant, i.e., X does not win. If we remove X, does the result change? Some may assume that the voter will vote A>C, which could change the outcome, but A>.>C was a legitimate (and even strategically optimal) vote. (Bucklin is closer to Range voting than to ranked voting systems, it is ranked approval voting).

If we look at it from the other direction, suppose X is introduced to an election, a voter has voted A>C, but prefers X to C. If the system prohibits voting for more than one candidate in a rank, we can see that the voter might vote differently for C than without X, if X is included. (Voting systems theorists have generally neglected write-in votes, i.e., that all candidates are within the range of possible choices, which consideration requires us to realize that (almost) all voting is strategic, unless the voter happens to truly and absolutely prefer a frontrunner.) With equal ranking allowed, however, we can keep the votes the same and simply add X, and the result does not change.

But the introduction of a new candidate may cause a voter to change their votes with any voting system. The introduction does not change the internal preferences, but may change the expression. No voting system uses internal preferences, they only use expressed preferences. So, if we look carefully enough, we can see that all voting systems fail IIA, strictly. Which would make it useless. Rather, to apply IIA, we must have a clear definition that is not manipulable, and it appears that such definitions are not necessarily at hand. We must also have an algorithm for determining how to apply the criterion to a particular method. Equal ranking in general upsets the criterion applecart. When these criteria were formulated, the assumptions were all strict ranking, with no consideration at all of preference strength or that a voter who had difficulty ranking two candidates might simply rank them equally.

I would argue that introducing a candidate requires consideration of how voters would change their votes, which would vary with the strategies being used by the voter. Many voters, if an obviously irrelevant candidate is introduced, wouldn't change their votes at all, and I'm pointing out that write-in voting implies that this is always true if a voter actually does prefer a possible eligible (or even not eligible) candidate not on the ballot. Some methods allow the addition of an "irrelevant candidate" without harm, others don't. Range allows it, Approval allows it, and Bucklin allows it, in original Bucklin, if the addition is in third rank. If the method is Bucklin-ER, it would be allowed in any rank, and Bucklin clearly becomes "instant runoff approval voting," i.e., a simulation of a series of approval elections with lowered approval cutoff at each round, specifiable by the voter. Condorcet's version, as I recall, was that each voter submitted lists of candidates for first preference, second preference, and so on. This was clearly Bucklin with equal ranking allowed in all ranks. Since Condorcet is quite notable, eh?, and since there is ample reliable source that Condorcet first proposed Bucklin, we have to, at least, note that the equal-ranking version of Bucklin satisfies IIA. A new candidate can, as with Range and Approval, be added or taken away from the ballot without affecting the other votes. --Abd (talk) 18:06, 22 May 2010 (UTC)

Is it true that "Although Majority Judgment does not use the Bucklin procedure, it can be considered as a Bucklin system with a rated ballot, that is, one which allows equal or skipped rankings."

Is this true? Even when equal or skipped rankings are allowed in a Bucklin procedure, it seems to me that the Bucklin procedure and the Majority Judgement procedure have different tie breakers. The former awards the win to the candidate with the most votes, counting from the best ranking down to and including the median ranking. Depending on the exact numbers, the latter may instead award the win to the candidate with the most votes, counting from the best ranking down to but excluding the median ranking. Thanks —Quantling (talk | contribs) 15:19, 27 October 2011 (UTC)

You are correct in your explanation of the tiebreakers (although you leave out the case where no candidate has an above-bottom majority, in which even plain-vanilla ordinal Bucklin uses the tiebreaker you gave for MJ). It's a matter of semantics whether those are close enough to categorize MJ as a Bucklin system. Given the extreme variety of Progressive-era "Bucklin" rulesets – for instance, some of them even included Borda-like fractional votes – I think it's reasonable to do so. Homunq (talk) 13:23, 16 May 2012 (UTC)

Bucklin voting is not a cardinal voting system

Bucklin voting should not be in the cardinal voting category. It is a preferential voting system and thus, strictly ordinal. Especially, since Majority Judgment can be considered as a cardinal enhancement of Bucklin voting, we should not mix up the categories. Thx, --Arno Nymus (talk) 12:53, 16 May 2012 (UTC)

Bucklin voting isn't, in fact, a single voting system at all. There were many versions of Bucklin that were used historically (in around 2 dozen US cities). Some were strictly ordinal; others, such as the one in Grand Junction, had at least some cardinal aspects (ie, exactly 3 grades plus unapproved; equal-ranking allowed in at least one grade; skipping any grade permitted, meaningful, and in fact quite common). Some even had Borda-like aspects. It would be a serious research project to find if any of them were strictly cardinal, but I believe that even given just what we know, we can say that "Bucklin voting" is a diverse category which straddles the ordinal/cardinal distinction. Homunq (talk) 13:20, 16 May 2012 (UTC)

Do you have adequate sources to advance the "variants" section with some example of the variants? I think, that would be very interesting to have the "standard" procedure described in the "process" section and some concrete (and historically used) variants in the variant section - best with info, where it was used. I would not object, if you reinsert the category, but I would appreciate if you advance the variant section as described. --Arno Nymus (talk) 23:22, 16 May 2012 (UTC)

Good idea. I'll see what I can dig up... Homunq (talk) 00:30, 17 May 2012 (UTC)

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