CB: "Majority Favourite" refers to a candidate who is the favourite of the majority. It is about nothing else except making that candidate win, not just some other candidate lose.
I reply:
Excuse me, but did I say otherwilse? The Majority Favorite Criterion, as currently used, is as I stated it, and, as you said, refers to who wins, not who loses.
You continued:
So then the short version would be:
"If a majority prefers candidate x to any other candidate, then x must win".
I reply:
Yes, and I pointed out to you that no method meets it.
You continued:
A long, votes-related version might say:
"If the voting method asks or requires the voters to specify one candidate as favourite, or to provide sufficient information so that the unique favourites of all those voters who have one can be inferred from the ballots (and not give the voters any zero-information incentive to do anything else); then if a majority of voters prefer candidate x to any other candidate and vote sincerely then x must win."
I reply:
I doubt that that will catch on. In any case, it isn't the Majority Favorite Criterion. But you could offer it as an alternative version. As I said, Approval meets the Majorityl Favorite Criterion as usually defined.
YOu continued:
Obviously if the method doesn't collect enough information to infer the voters' favourites, then it can't meet MF.
I reply:
No, if a method didn't allow us to indicate a favorite, then it would pass, because you couldn't write a failure example.
In any case, Approval _does_ let you vote X over everyone else, by voting only for X.
CB: Approval definitely fails Majority Favourite (and also ML), for the very simple reason that the ballot doesn't ask the voter "Who is your favourite?", but rather "Which candidates do you approve?" or "Rate the candidates on a scale of 0,1".
I reply:
No, Chris, that doesn't make Approval fail that criterion. Whether asked or not, you can vote X over everyone byv voting only for X. In any case, the criterion requires only that if a majority do so (whether or not the method allows it) that candidate must win. Approval passes that criterion as usually defined.
You continued:
It is perhaps debatable where the line between "majority-rule methods" and others should be drawn, but complying with May's criterion, Majority Favourite and Majority Loser are certainly bare minimum requirements.
I Reply:
You're certainly entitled to define majority rule methods as you wish.
Don't worry so much about 2-candidate elections. That isn't really the problem, you know.
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