Mike O. wrote (Sat.Jan.8):
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 otherwise? The Majority Favorite Criterion, as currently used, is as I stated it, and, as you said, refers to who wins, not who loses.
I thought you did:
Presumably the second "X" should read "Y", but you seem to be talking about a candidate losing .How about:
If a majority of the voters prefer X to Y, and vote sincerely, then X shouldn't win.
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.
CB: I meant "any other candidate" to mean "all other candidates" . I didn't mean "if some majority which may include
voters whose favourite is not x, pairise prefer x to some other candidate y, then x must win".
CB: This is just sophistry. The "usual definition" is only meant to apply to ranked-ballots. A voting methodYou 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.
can be thought of as a court of enquiry, and the voters as witnesses whose duty it is to truthfully answer the
questions asked by the court.
The voters show up, and more than half of them have candidate x as their sincere favourite.
Approval to each voter in turn: "Which of these candidates do you approve?", and asks no other questions.
Then the "court" (Approval) announces: candidate y is elected. The majority of voters, whose favourite is x,
appeal the decision to a higher court, on the grounds that the court violated Majority Favourite.
Judge Ossipoff turns them down, saying:
"You were all clearly asked 'which candidates do you approve?", and so you all had the chance to take the initiative
and lie by saying that you only approve your favourite, denying the lower court grounds for electing y or any other
non-x. Not enough of you did that, so you only have yourselves to blame. I dimiss the appeal. Let this be a lesson to
you."
Chris Benham
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