The basic truncation dilemma is a familiar one on this list. There are two near-clones A and B who split a majority of the vote - say, with 35% and 25% honest-first-choice support - and one distinct candidate C who has a plurality of first-choice support - say, 40%. Since C voters don't care much which of A or B is elected, they are willing to truncate, even if A and B are the frontrunners. So in many voting systems, including both Approval-like and Condorcet-like systems, A and B voters are faced with a collective prisoners-dillemma like situation; they can cooperate and perhaps help elect their second preference, or truncate, giving the most possible relative support to their favorite but risking the worst-case winner.
Note that I am speaking of a true truncation dilemma, where A and B voters honestly see little a priori utility difference between the two (though the strategic need to truncate may lead to demonization and/or bad feelings over the course of the campaign). If they actually had strong preferences, truncation might simply be more honest than strategic. So, in all that follows, I'm assuming that A is the honest Condorcet, Range, and social utility winner, by clear margins. This is a true dilemma; it's no more an artifact of the voting system than an honest Condorcet cycle. And I believe that it would be much more common than such a cycle, to the point where the majority of apparent Condorcet cycles would actually be caused by truncation/burial strategy. So, what are the possible responses, from the point of view of voting system design? There really are only a few. 1. Embrace the dilemma. Either A and B voters manage to cooperate, or the system elects C; deal with it. This approach is perhaps best exemplified by Approval. 1a. Probabilistic dilemma. If truncation causes a cycle, then there is some probabilistic tiebreaker which always includes some chance of C winning. This can act as a goad to A and B voters to cooperate. I suspect that some system like this might be the theoretical optimum response if voters were pure rational agents; however, real people tend not to like probabilistic election systems. 2. Obfuscation; that is, hope that the voters don't really notice. I'd say that the best example of this is Bucklin. One hopes that the voters are satisfied by expressing a strong preference for their favorite, and they don't notice the strategic dilemma in adding lower preferences. This is not a vain hope. Between strategically naive voters and principled honest voters, there may well be enough to ensure A is elected. However, it's still obfuscation. 3. Elimination. IRV is the preeminent example of this response. If B is to be eliminated first, then there's no strategic reason for B voters to truncate. However, this can lead to other problems with the voting system - IRV's nonmonotonicity and center squeeze are directly related to this issue. Also, if it isn't clear which of A or B is the frontrunner, elimination might not help, because the best strategy is to loudly pronounce that your faction will truncate, and perhaps too many people will carry through with the threat. 3a. Quasi-elimination. I believe that winning-votes Condorcet methods, like Schulze, are an attempt to ensure that A wins even in the face of B's truncation. However, this only works if C voters truncate rather than splitting evenly between CBA and CAB. Other stronger quasi-elimination systems that I know of have IRV-like problems. 4. Runoff. Viewed in an outcome-oriented game-theoretic vacuum, this is just the same as elimination, and it suffers the same problems. However, if voters have some negative utility for the runoff itself, then a system can use the threat of one to motivate honest voting in the first round. Since the scenario assumes that there is a clear winner with no cycles under honest voting, that may be enough. I think that's it. Does anyone have any other possible responses? To me it's clear that option 4 is the best. Like options 1 and 1a, it's using the threat of something voters don't want to motivate honest voting. However, a runoff is a less extreme threat than N years of bad leadership, and so much more palatable if it actually comes to pass. This has clear implications for system design. If the main purpose of a runoff possibility is to motivate honest voting and thus never actually have a runoff, it's important to be as decisive as possible in the first round. In general, I think that at a minimum, if there's a first-round Condorcet winner evident from the ballots, there should be no need for a second round. This analysis suggests that, in response to this dilemma, two-round Condorcet systems deserve a closer look. I'd also suggest simpler systems which make a good approximation of that: for instance, 2-approved-rank Range, with a runoff if the winner's approval score doesn't beat all other Range scores. I think that two-round Condorcet systems have been neglected because the Condorcet matrix offers a seductive plethora of tiebreaking possibilities. Jameson Quinn
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