[EM] WP Talk:Majority_criterion

[Jameson Quinn]

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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