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. 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. This is because the Majority Criterion neglects preference strength, and thus a minor, practically inconsequential preference is given the same weight as a clear, stark preference. So if Preference Strength is considered in determining the winner, in the presence of expressed first-preference votes of a majority, it must be true that under some circumstances preference would alter the winner and thus the Majority Criterion would not be satisfied. (2) There is a serious semantic problem in how the Criterion is expressed and applied. It is commonly stated that the Majority Criterion is satisfied by Plurality and not by Approval. In order to state this about Approval, one must presume that there are unexpressed preferences on the part of voters. Approval, just like Plurality -- Approval *is* Plurality plus an additional freedom of the voter -- allows voters to express a preference between two candidates. Just vote for only one of them. If a majority express this preference for one candidate, then, under Approval as well as under Plurality, then that candidate cannot lose to the less-preferred candidate. (And if this preference is expressed over all other candidates, the candidate cannot lose the election.) Looks to me like Approval *does* satisfy the Majority Criterion. Range, generally, does not. However, Approval allows the voter to abstain from a pairwise election. The voter does so by giving both candidates the same vote. By voting for both candidates, the voter has expressed a preference for both of them over all other candidates not so marked, and has abstained from the pairwise election between them. Only by assuming that the voter has a preference between the two even though this preference has not been expressed, and then by using this unexpressed preference to determine if the method satisfies the Majority Criterion, do we come up with the answer that Approval does not satisfy it. The Majority Criterion has been crafted, though, to create a technical correctness of the common analysis: >The majority criterion is a ><http://en.wikipedia.org/wiki/Voting_system_criterion>voting system >criterion, used to objectively compare ><http://en.wikipedia.org/wiki/Voting_system>voting systems. The >criterion states that if a majority of voters strictly prefers a >given candidate to every other candidate (i.e. the given candidate >is the first preference of more than half the voters) and they vote >sincerely, then that candidate should win. No method can determine a winner based on unexpressed preferences. The definition glosses over this. Approval allows voters to express that they "strictly prefer a given candidate to every other candidate," in exactly the same manner as Plurality. If they choose not to do this, then, within the definition of preference as it can be expressed in the method, *they have not expressed a preference and we cannot claim that they have one.* The only difference between Approval and Plurality is that one may express preference for a group of candidates over all others, instead of just for one. But expressing preference for a group is outside the purview of the Majority Criterion, it is irrelevant to it. So we can only consider the expressed preferences, and Approval satisfies the Majority Criterion with respect to them. In Approval, one has expressed a preference for every candidate for whom one has voted, over all other candidates. If a candidate enjoys such an expression from a majority of voters, that candidate cannot lose unless a majority has *also* expressed that same preference for another candidate. There is more than one possible winner who satisfies the Majority Criterion, just as there can be more than one winner who satisfies the Condorcet Criterion. 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 came to write this from reading the following: http://www.reformthelp.org/issues/voting/glitch.php Thanks to Jan Kok for suggesting I look at this article. > ---- election-methods mailing list - see http://electorama.com/em for list info
