At 11:06 AM 11/2/2006, Kevin Venzke wrote: >--- Abd ul-Rahman Lomax <[EMAIL PROTECTED]> a écrit : > > I've been realizing just how defective the Majority Criterion is. > > People tend to assume that the Majority Criterion is an important > > characteristic of any proper democratic election system. > >I suspect that many people would insist on a majority favorite being >elected at least if the method collects enough information to >determine who this candidate is.
Most methods do collect that information. But if a Majority preferred candidate fails to win under Range, it is necessarily that they, on average, also rated the Range winner quite high. Sure, people will insist on this. Because they have confused the Majority Criterion with Majority Rule. But elections are defective when they attempt to choose between more than two choices. Consider this: an election is held in two phases. The first phase is Range. The second phase, to take it to the extreme, is a ratification phase, in which the question is presented, "Shall the Range winner be elected to the office?" Would this election satisfy Majority rule? Yes, necessarily it would. Let me tell you, I've seen voting in actual situations where there was a status quo A. And objections to A were raised. And people, long-time members of the organization, and A had been the status quote for perhaps fifty years, literally said, "Over my dead body." After discussion, a poll was taken that was essentially an Approval polls. A variety of proposed alternatives to A, plus A itself, were presented and the members were asked to vote as to which of these were acceptable to them. I think it was perhaps 80% for A. But there was another option, B, where the vote was, in think unanimous approval, or maybe unanimous minus one. Then the question was asked, "shall we change to B?" The vote for this motion was unanimous in favor. You cannot predict what people will actually prefer until they have good information about what everyone else prefers. In the organization in question, unity was valued. They did not want to needlessly neglect the strong preferences of a minority. And they have been a strong organization for many years largely because of this. > > Yet the > > Criterion itself suffers from a number of serious problems. > > > > (1) It is clear that any method which satisfies the Majority > > Criterion cannot maximize the expected value of the election. Range > > is the method which directly does the latter, and this is directly > > connected with its non-satisfaction of the Majority Criterion. > >However, it is possible that there is no real method that can "maximize >the expected value of the election," unless you just mean to maximize >the value among all possible methods. No, Range does this. If we assume that voters express their expected value for the various candidates, the expected value for the voters, collectively, is the sum of the individual expectations. Objections to Range are often based on the assumption that voters will distort their expression for strategic purpose. However, I've shown, I believe, that this is an oxymoron. The alleged distortion is an alleged strategic rating of a serious competitor to the favorite at zero, even though, in the scenarios proposed, they actually only mildly prefer their favorite to the competitor. Yet, the scenario assumes, they are willing to lie about their preferences in order to gain the election of their favorite. I claim that this would be evidence that they are either mentally ill or they actually strongly prefer the favorite. It might be because their favorite is from their party, rather than because of the individual characteristics of the candidate. But preference strength and Range ratings include such considerations as party affiliation, at least for some.... >I don't think it is fair to say that Range "directly" "maximizes the >expected value of the elections." I would grant that Range is equipped >to do this better than other methods due to the ballot format, though. Range is designed to do exactly this. Note that a Range ballot can be analyzed and used for other methods. It collects the most information of any ballots I've seen proposed. >[...] > > Looks to me like Approval *does* satisfy the Majority Criterion. > >I can see nothing at all wrong with that interpretation, but personally >I don't like to imagine that the Approval voter is only submitting >first preferences. Neither do I. But the point is that if they have a preference, they are able to express it. They can also do something else, which is to prefer a block of candidates rather than just one. This is an additional freedom. In standard Approval, they cannot both prefer a block and express a preference within a block, but, of course, they can't do this with Plurality either. And, as I've noted, it is commonly stated that Plurality satisfies the criterion. We can say that Plurality satisfies the criterion if we assume that the voters have expressed their preference, without any strategic considerations at all. I.e., they vote for their favorite, and not for their favorite among the top-two. Which, of course, is seriously harmful behavior, in at least some ways. > > This is important because many writers assume that the Majority > > Criterion is some kind of gold standard for elections, and when it is > > asserted that Approval fails to satisfy it, this can be and is > > considered a fatal argument, or at least a serious defect of Approval. > >I don't feel that Majority needs to be satisfied under Approval, in >order to be publicly acceptable. My argument for Approval is simple: tossing overvotes is unjust, it has historically done a great deal of harm in suppressing actual voter intentions. Sure, some overvotes, maybe even most, are errors, and we can't tell which of the two candidates, if it is two, were intended. But we can be pretty sure that it was one of them! By tossing the vote, the method has made the voter abstain from all pairwise elections. By using it, the only pairwise election from which the voter abstains is the one between the two votes. Much less harm is done by not discarding the vote. It has also been argued that prohibiting overvoting helps prevent election fraud. All I can say is that it seems to me that it opens the door to election fraud more than it closes it.... The argument for prohibiting it seems to be that voters should make a clear choice. The reasoning behind this escapes me. Once again, it gives value to a slight preference, equating it with a clear one. Implementing Approval is trivial, just strike out the few lines in the election code that prohibit overvoting. Everything else stays the same. Approval is already standard in some states where there are two conflicting initiatives on the ballot. If they both pass, the one with the most votes wins. Really, it shouldn't be all that difficult. The arguments against it will really be that it will make it easier for third parties, but probably it will mostly serve to prevent the spoiler effect from being as common a danger as it presently is. And it will open the door to Range, being an obvious next step. Which might be Range 3 or Range 10 rather than Range 100. ---- election-methods mailing list - see http://electorama.com/em for list info
