At 11:29 AM 11/6/2006, Michael Poole wrote: > By the majority criterion, a candidate X should win if a majority of > voters answers affirmatively to the question 'Do you prefer X to > every other candidate?'. > >A voter who cannot honestly or easily answer "yes" to some candidate >is not a problem for this formulation of the majority criterion.
Note that Approval Voting provides a means of the voter expressing this preference. The claims that Approval does not satisfy the Criterion are based on a simultaneous assumption that voters "answer affirmatively to the question," but do not vote to express that answer. This is a contradiction. No voting method can use preferences that are not expressed. Linguistically, the Criterion contains a lost performative -- or something like that. *How* do the voters answer affirmatively. It could only mean that they so answer on the ballot. Which in Approval *requires* that they vote for X and not for any other candidate. And if a majority of voters do this, that candidate cannot lose. So why is it said that Approval fails the Majority Criterion? > The >existence of such a voter is an argument in favor of some other >criterion, but does not make the MC subjective. If you want to change >the "prefer" to "strongly prefer", pick a new name for your modified >criterion. > > > Further, it is alleged that Approval does not satisfy the Majority > > Criterion. It seems to me that this requires a few assumptions that > > have not been made explicit. > >It does not require any additional assumptions. Approval can only >capture preferences between members of the approved set and the >not-approved set. That's correct. However, voters are not required to approve more than one (indeed, they are not required to approve any at all, but that's another matter.) The ballot gives voters a means to do what the Criterion describes. If a majority of voters do that, their favorite cannot fail to win. Approval satisfies the Majority Criterion. Range does not, because Range does allow the expression of a weak preference. Approval does not allow that. I've been arguing, it might be noted, that this very fact makes Range a superior method. That Range does not satisfy the Majority Criterion is not a defect. But that is another matter. Here, the question is Approval. Does it satisfy the Majority Criterion *as stated?* >When there are only two viable parties, Range Voting's use of strength >of preference apparently encourages the factions to be strongly (even >bitterly) divided: that will maximize the difference in scores between >the two candidates among supporters of each party. That claim is made. It's only true if the factions are already bitterly divided, have a strong preference for winning over maximizing the value of the election to the society. In other words, if the use of maximum range ratings is *real*. The effect is here asserted as the cause. We don't really know how Range will behave in actual elections. The only evidence we have comes from Warren's poll, and I consider that relatively weak. So confident assertions about how Range will behave are, quite often, premature. I don't see how Range *creates* the use of maximum scores in any pathological way. Range reduces to Plurality in the two-candidate case, unless voters follow non-standard strategy, that is, weaken their votes. It's possible in Range to cast a weak vote, a vote that does not have full effect in determining the outcome. In the pizza case, this would be like someone voting for Pepperoni, 90, for Mushroom, 80. That person does not have a strong preference, and so their vote is discounted, effectively. Generally, the advice has been given to normalize your Range votes. That is, you would vote the maximum for your favorite, the minimum for the worst candidate, and then place the others either with these or in between. If there are only two candidates, this reduces to plurality. It is when there are more than two that it gets interesting. (Condorcet methods, of course, also reduce to plurality when there are only two candidates.) But it is true that voters may decide to weaken their votes, in which case, we have something different than plurality. Call it a "half-abstention." I have an opinion, and I'm going to express it, but it is not strong, so I accept that it will not have full power in determining the winner. It will merely have a lesser influence. > I am not sure that >more parties will necessarily resolve that; as Kevin Venzke showed, a >voter is most likely to affect a Range Voting election by giving only >extreme ratings. Sure. "Most likely to affect by giving only extreme ratings" means that if you care, vote the extremes. So? If you don't care, you are not required in Range to vote the extremes. It is absolutely true, it is not at all in controversy, that "a voter is most likely to affect a Range Voting election by giving only extreme ratings." And the decision of whether or not to do this is entirely up to the voter. It is not correct that therefore most voters will only give extreme ratings; there is some evidence, from Warren's poll, that they will not. But, I hasten to add, I consider that poll as interesting, because it is about all we have, but hardly conclusive. I'll say it again. Range does not satisfy the Majority Criterion because it allows the expression of a weak preference, a preference that does not have full strength in determining the outcome. Approval does not have this trait, which is why, in my opinion, it does satisfy the Majority Criterion. It does allow the expression of preference as described in the Criterion, and if the voter so expresses the preference, and a Majority of voters do this for a candidate, that Candidate must win. QED. ---- election-methods mailing list - see http://electorama.com/em for list info
