MIKE OSSIPOFF wrote: > > 1. No one, that I'm aware of, says that Plurality passes CC. > > 2. Blake Cretney says that his CC applies only to rank methods. > He does that in order to keep Plurality from passing. I don't > claim that anyone other than Blake uses that way of preventing > Plurality from passing CC. I didn't say > that there's an article that does that. I don't claim that there's > an article that does that. I said that Blake, in his website, > does that. > The Condorcet Criterion is most naturally expressed with regard to ranked ballots. Plurality is most naturally expressed with regard to lone-mark ballots. If you want to talk about whether Plurality passes CC, you either have to define Plurality so that it applies to ranked ballots, or define CC in such a way that it refers to Plurality ballots.
Its pretty easy to define CC to apply to plurality ballots, because you can think of the voted for candidate as ranked above all the others, and all the others as being ranked equally. Defined this way, plurality passes CC. However, we have a sense that it has cheated, that it has passed only by greatly limiting the expressivity of the ballot. Another way out is to redefine plurality so that it applies to ranked ballots. The winner is the candidate who gets the most first-place votes. Now, plurality fails. I suspect that this is the approach most academics would take. However, it clearly involves a redefinition of plurality. For my web site, I avoid the problem by using a definition of CC that only applies to ranked ballots, and a definition of plurality that only applies to lone-mark. So, CC doesn't apply to plurality. In other words, I avoid the question. Personally, I think that it is obvious that the goals of the Condorcet advocates are not achieved by plurality. But I am not interested in redefining plurality because then someone could legitimately question what my plurality has to do with the traditional kind. I think I could answer this question, but the defense would be complicated and perhaps subjective. Another solution to the problem would be to redefine CC to involve the idea of voting sincerely. Presumably, sincere votes in a Condorcet completion method should result in the sincere Condorcet winner winning. But they would not in plurality. So, if we define CC on sincere votes, perhaps this would be the best solution. In fact, as this list has proven, that solution is far more complicated that one might naively imagine. Remember that the previously suggested approaches only considered ballots, with methods and criteria based on them. The sincerity-based CC involves a theory involving voters having mental states that correspond to particular ballots. But it isn't always clear in what sense these mental states exist, and how they correspond to "sincere" votes is not obvious either. I am amazed by all the competing interpretations of sincere votes. Mike believes that a voter implies acceptance of any candidates she ranks. I, for one, believe no such acceptance is implied. Some people believe that they "approve" only of a fixed number of candidates, and that a sincere approval vote is for exactly these candidates. So for them, a particular approval ballot corresponds to a particular judgment about the candidates, a particular mental state. Personally, I do not normally make this kind of judgment about the candidates in an election. So although the purpose of the sincerity-based CC was to make it easier to explain why a Condorcet advocate would reject plurality. In fact, it makes the explanation much more complicated. Having said all that, I'll get to how I interpret P&P. P&P talk about ballots, and criteria and methods based on those ballots. By ballots I could just as easily say preference orders. I don't think P&P intend to propose a theory in which the preference orders are mental states, but the method works on actual ballots, so the ballots must be "sincere", whatever that might mean. They ignore the sincerity issue. They just have methods and criteria that refer to preference orders. But where those preference orders come from isn't their concern. For you, preference order implies sincere preferences, and you recognize that a real-world method can only work on cast votes. But for P&P, a method is just a function from a hypothetical set of preference orders to a set of winners. Of course, the current dispute is not really over this issue. It is about who was wrong countless emails ago. I honestly don't know the answer, and since I have no interest in the question, I suspect I'll never know. ------ Blake Cretney See my Election Method Resource http://www.fortunecity.com/meltingpot/harrow/124/
