I have posted the following on http://en.wikipedia.org/wiki/Talk:Majority_criterion#How_does_the_majority_criterion_apply_to_non-ranked_methods.3F . I'd welcome responses either there or here. I feel that posting this here is not a violation of wikipedia's anti-canvassing rules because this list includes people who will be on all sides of this issue.
I see the following possibilities for defining the criterion in the context > of absolutely-rated methods: (I'm not noting whether Plurality passes, > because it always does.) > X must win if...: > 1. ...A majority gives candidate X the maximum support, and does not give > any other candidate Y the maximum support. Approval and MJ pass; Range does > not. > 2. ...A majority gives candidate X the maximum support, and prefers X over > all others, and gives a non-insincere maximally-expressive vote (Note that > the "maximally expressive" part is necessary so that equal-ranking-allowed > Condorcet methods do not suddenly fail this criterion). MJ passes; Approval > and Range do not. > 3. ...A majority does whatever it can to ensure that X will win. MJ, > Approval, and Range all pass. Borda does not pass, because all potential > opponents cannot be simultaneously buried. Still, the fact that Borda even > comes close to passing makes this possibility seem impossibly wrong to me. > 4. ...A majority prefers X over all others, and gives a non-insincere > maximally-expressive vote. Neither MJ, Approval, nor Range pass (although > 3-level medians with a Condorcet tiebreaker would.) > 5. ...A majority expresses a preference for X over all others. Approval > passes; MJ and Range do not. > 6. ...It is possible to say, looking at the ballots, that any expressive > honest majority preferred X to all others. Approval neither passes nor > fails, the criterion simply doesn't apply; MJ and Range fail. > I think that 3 is pretty indefensible, so I won't say any more about it, > except that it should probably be removed from the NB's on the [[voting > system]] table. 6 is even worse. > Clearly, a pedant would choose 5; it is the most-direct extension of > Arrow's verbal definition to rated systems. > Personally, I find definition 2 to be the most in line with the "spirit" of > the criterion. However, I see that 1, 4, and 5 are all strictly simpler than > 2, so I can't defend using 2 here without at least a reliable source. 4 is > also unnecessarily complex, and moreover will have opposition from both > Approval and MJ supporters. Therefore, I think that 5 and 1 are the best > options. Of these two, I support 1, as being closest to what I feel the > "spirit" of the criterion is. Verbally, it's more complex than 5; but > mathematically, it's actually simpler. > If we're going to find some kind of compromise which "teaches the > controversy", then I would support 1 and 4 as being defensible "poles of the > debate". In this case, 5 is clearly dominated by 1, because I don't know > anyone who really feels that 5 is the "right" definition; anyone who likes 5 > will prefer 1. (That is, 5 is only possibly-viable as a pedantic > compromise). > Actually, I think that "teaching the controversy" by including both 1 and 4 > is the best solution. But probably explicit support for this position from > reliable sources will be slim to none, so it's only viable if we have > consensus (which also presumes nobody decides to be a pedantic #$@#$ to make > a [[WP:POINT]]). JQ ps. Please, if you respond on Wikipedia, use my wikipedia name; do not refer to me by my real name.
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