Talk:Burr dilemma

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This page doesn't explain what the Burr dilemma is. [posted from 65.57.245.11, this note added by Abd 22:04, 3 December 2007 (UTC)]

Indeed. One would have to follow the external links. There is an explanation of the Dilemma, I think it was taken from Nagel, on the RangeVoting.org web site:

Statement of the Burr Dilemma: When three or more candidates compete for an office that only one can win, and voters (V) may support two (or more) of them by casting equal (approval) votes, candidates (C1 and C2) seeking support from the same group (G) of voters will maximize their respective votes if all members of G vote for both C1 and C2. Both candidates thus have an incentive to appeal for shared support. However, if such appeals succeed completely and neither candidate receives votes from members of V-G, the outcome will be at best a tie in which neither C1 nor C2 is assured of victory. Each candidate therefore has an incentive to encourage some members of G to vote only for himself or herself. If both C1 and C2 successfully follow such a strategy, either or both may receive fewer votes than some other candidate C3 supported by members of V-G. The risk that both C1 and C2 will lose is exacerbated if a retaliatory spiral increases the number of single votes cast by members of G. At the limit, such retribution reduces approval voting to conventional single-vote balloting among the members of G or, if the problem is endemic, among all voters. The nearer that limit is approached, the lower the probability that advantages claimed for approval voting will be realized.

Nagel calls this a problem with Approval Voting, though the election involved wasn't Approval, exactly, it was vote-for-two plurality, sort of, with single votes being valid (but because there were two winners, it would be normal for most voters -- electors -- to vote for two).

However, the "problem" is simply that Approval Voting, if voters go for only their favorite, reduces to Plurality. Which is blatantly obvious and not even a problem in the real world, or at least such could be alleged.

The article itself, peer-reviewed and all, is blatant opinion, often unsupported. Why is the Burr Dilemma irrelevant in real politics?

Well, let's start with a two-party system. Introducing Approval Voting into such a system is going to have little effect, at least at first, on most voters. They will continue to vote for their favorite; by definition -- it's a two party system! -- this will be one of the major party candidates. What is affected by the ability to vote for more than one is that small body of voters who prefer other, minor party candidates. So we would see a few percent of such votes. Enough to whack the spoiler effect upside the head, having incurred practically no cost in the process. The Burr dilemma is completely irrelevant to this.

Now, let's look at an election with three viable candidates. This can happen with primaries under the present system. What the Burr Dilemma implies is that one candidate is going to try to influence supporters of another candidate to vote for him also, while at the same time trying to encourage a significant number of his own supporters to vote only for him. Certainly it's possible, but it might also be political suicide. To influence significant numbers of voters, the action must be public. And how would the supporters of the other candidate respond? Quite simply, they would act as predicted by Nagel, they would not vote for the first candidate. So? Frankly, were I a supporter of that first candidate, and before the "recommendation" came out I preferred him, I'd seriously reconsider that support, I think I would be likely to withdraw it. Why? Well, I happen to think that cooperation is more important, especially in a party primary, than competition, and the candidate seems to be putting himself and his personal victory above what is best for the party. What is best for the party is for the candidate with the broadest support to be elected. Encouraging voters to vote any way other than sincerely, in my view, disqualifies the candidate.

What about three independent candidates, say in a nonpartisan election? Well, this normally happens in small towns or other places where people are pretty well-known to each other. The strategy Nagel proposes involves negative campaigning, attempting people to not vote for another candidate who is, in fact, similar to oneself. (Otherwise this is not the Burr Dilemma, the voters aren't going to vote for both candidates, period). That can seriously backfire.

No actual example of the Burr Dilemma having a real world effect has been shown. As Warren Smith points out in the link in the article [1]:

But actually, Burr's dilemma did not result in any pathology in 1800, in the sense that the two "clones" Burr and Jefferson did not enter into a retaliatory spiral causing them both to lose – they actually both won. But Burr's dilemma plausibly would genuinely have resulted in a pathology in Portugal 1986. Therefore, "vote splitting" effects can still occur in approval voting – contrary to advertising.

Nagel simply imagines that there was a dilemma, that one of these candidates *could* have won by encouraging electors to drop one of their votes. Risky, it would have been. They both won, as it is, and thus the decision of who was to be elected went to the House of Representatives, which runs under different rules.

Smith claims that it might have happened in Portugal. But not that it did. Portugal was not using Approval Voting.

Nagel's article was a hit piece, designed to imply that Approval Voting is defective as an election system. The voting system was not Approval, as Nagel claims, it was two-winner majority vote, with each elector having two votes. If it had been Approval, more than two votes would have been allowed if there were two winners; plus multiwinner Approval isn't seriously proposed by election methods experts without extensive modifications. Approval Voting, basic and simple, is a single-winner method.

Nagel's argument boils down to the fact that, under Approval, you can hurt your favorite by voting also for someone else. So normal strategy is not not add another vote unless (1) you really don't have a strong preference or (2) you believe your favorite is not close to winning. For candidates to attempt to manipulate this process could be, as I note above, political suicide. The strategy would be irrelevant for voters with a strong preference, and could flip the vote of voters with weak preferences against the candidate that tries it.

When there is a majority election requirement, definitely, for voters to bullet vote can lead to a need for a runoff or other further process. This is actually desirable from the point of view of getting the best result, under some conditions. Remember, Robert's Rules recommends repeated balloting as the best election method, repeating until a majority vote for a candidate. It also recommends against using top-two runoff; but top-two runoff under Approval would behave much better, I suspect, than under Plurality.

My opinion is that the American electorate is largely going to want to be able to express exclusive preference, though there may be some exceptions. (In particular, third parties with no chance of winning now may realize that Approval is a quick fix at no cost, allowing them to build vote strength without spoiling elections, so we might indeed see pure Approval in some places.) The answer, of course, is Bucklin voting, which was quite popular for a time in the U.S., and which seems to have been killed because it was working, not for the spurious reasons advanced by FairVote. (In such systems, we can expect most voters, in fact, in partisan elections, to vote for only one; that only a few voters add additional preferences is harmless: the method still stops the spoiler effect though that small percentage. In some elections, not partisan, I've seen significant numbers of additional votes, including the famous election (of a judge) involved in Brown v. Smallwood.) Bucklin is "instant runoff Approval." The form in Duluth was a three-rank ballot. Only one vote was allowed in first and second ranks, but any number of votes could be added in third rank. (but, of course, only one vote per candidate!). The counting proceeded in rounds. If there was a majority in the first round, counting only the first rank votes, the winner was declared. If not, the second rank votes were added in. And if still no majority, the third round votes were added in. Thus Bucklin satisfies the Majority criterion, and I don't think there is any incentive to vote first preference for other than your favorite.

I would, however, *allow* additional preferences in the first and second rounds, for voters who want to show that they don't have a strong preference. Technically this causes the method to violate the Majority Criterion (under some strict interpretations), but that is harmless; for if voters really do have an exclusive preference that is significant, they will , I'd expect, vote that way.... They can still add preferences in lower ranks.

The whole matter of the Burr Dilemma, Nagel's invention, shows signs of having been manipulated for political effect.

It seems to me that in a situation with real-world uncertainty, for each of a set of candidates with identical constituencies, the optimal strategy is to slightly change platform(or emphasize any differences that exist). You end up with something more like corporate branding, where there's value in not being suit, which (amusingly) should mitigate the complaint about approval promoting identical candidates.

Also, the "To quote Nagel" form suggests that the quoted statements are true. Are there any citable sources that comment on his article, so we could get a less-biased view? (And if there are no citable comments on it, it's probably non-notable.) In any case, I'm adding a POV tag to warn people. Darekun (talk) 01:53, 24 February 2008 (UTC)

The proper protocol for initiating a NPOV debate was not followed, so I have removed the tag. Progressnerd (talk) 01:30, 14 April 2008 (UTC)

Abd, you're right that the article should contain a definition of the Burr dilemma. But the rest of your comments are largely irrelevant to the quality of the article.

In the paper, Nagel coins the term "Burr dilemma" and makes an argument as to why this would play a factor in real Approval Voting elections. You are free to disagree with the argument, but it is a published, peer-reviewed, academic paper by a Professor of Political Science at UPenn. There are also Wikipedia articles on Christian beliefs, for example, but the mere inclusion of those articles on Wikipedia does not make any statement as to the truth of the beliefs. The only relevant fact is whether it is true that people hold those beliefs, and it is. That Christian beliefs may not be true does not by itself subject them to NPOV debates. Similarly, here, whether or not the Burr dilemma would occur in real elections, does not change the fact that Nagel believes it may, and his argument carries serious academic imprimatur.

You point to Professor Smith's website, but he has no peer-reviewed, published work in political science or social choice theory. Let alone anything published that disputes the Burr dilemma. Wikipedia has a strict prohibition on original research.

Darekun, you said that including the phrase "To quote Nagel" suggests the statements are true. That is simply not the case. The only thing "To quote Nagel" suggests is that Nagel said it. And he did. Progressnerd (talk) 01:53, 14 April 2008 (UTC)