In response to my Fri.Jan.7 post, you wrote:
CB: "Majority Favourite" refers to a candidate who is the favourite of the majority. It is about nothing else except makingYou continued: , Majority FavouriteI reply: Majority favorite is usually defined in terms of voting rather than sincere preference: Majority Favorite (as usually defined in terms of voting only): If a candidate is voted as favorite (voted over every other candidate) by a majority of the voters, that candidate should win. [end of Majority Favorite definition] For instance, Plurality is usually said to meet the Majority Criterion. Yes, I agree that it's better to define the criteria in terms of sincere preferences, and that it would be good to have a Majority Favorite version worded in terms of sincere preferences. But how would you word it? You could say: If a majority of all the voters prefer X to Y then X should win. that's no good, because no method meets it. How about: If a majority of the voters prefer X to Y, and vote sincerely, then X shouldn't win.
that candidate win, not just some other candidate lose. So then the short version would be:
"If a majority prefers candidate x to any other candidate, then x must win".
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."
Obviously if the method doesn't collect enough information to infer the voters' favourites, then it can't meet MF.
Without the part in parentheses, Approval could perhaps be smuggled in by having a ballot instruction "check only
your equal-favourite candidates". Voters whose biggest utility gap is below their second preference will have a
zero-information incentive to not comply.
Mike O.:
CB: Approval definitely fails Majority Favourite (and also ML), for the very simple reason that the ballot doesn'tYou continued: [If a method that fails Majority Favorite] , and Majority Loser qualifies as a "majority-rule method"; then can you tell us which methods don't? Yes: Plurality, Instant Runoff, Borda, Margins Condorecet, and nearly all methods other than CR (including Approval), Condorcet(wv), Bucklin, ERIRV, and very few others.
ask the voter "Who is your favourite?", but rather "Which candidates do you approve?" or "Rate the candidates on a
scale of 0,1". The ballots don't contain sufficient information to infer the favourites of all the voters who have one, only
those voters who approved a single candidate.
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.
Approval, Range Voting, Borda, and Plurality don't qualify.
In addition to the basic May's, CF, and CL; IRV meets (Mutual) Majority and Condorcet Loser. On top of that
Condorcet (Margins) meets Condorcet.
Mike O:
CB: If the 99 voters don't "want to be heard", then why are they bothering to vote? Take this example:Brian Olson wrote (Fri.Jan 4): >Of course, even a 1-100 scale can be so "abused". But if 99 people really >vote for their favorite with a "1", and the other guy with a "0", aren't >they effectively saying "I don't care (much)"? I reply: If the range is 0-100, then they're saying they care very little about the election. You (Brian) continued: Why should >we be listening to their votes more than they want to be heard? II reply: Agreed. They're only voting one point of difference in a 100 point range election.
2: A7, B6
1: B100, A0.
(Ralph Suter can multiply these numbers by 5 million, if that will make him happy.) The two A supporters are very
religious, and they have resolved to reserve the maximum possible rating of 100 for the second coming of Jesus Christ
and the lowest possible rating of 0 for the anti-Christ. Nevertheless they have gone to the trouble of doing their civic duty
by showing up to vote and express their clear preference for A over B. (If the method were Approval, there prefernce
for A could not be inferred from their ballots because they would not have approved either candidate.)
The B supporter doesn't share their religion, and is either a strategist or is in love with B, it doesn't matter which.
The A supporters did their duty and reported their sincere ratings of the candidates. It is complete nonsense to infer
that they have somehow volunteered to be over-ridden by the minority B supporter, and so therfore majority rule doesn't
matter.
Chris Benham
PS: I made a small mistake in my Friday post:
Those last two numbers are the wrong way round.CB: The question on the ballot paper is "How do you rate these candidates?", not "How much do want to be heard?". The voting system should do its best to protect sincere voters from being over-ruled by strategists. In your example 99* 1.0, 0.0 1* 0.0, 100000000.0 what if the single voter is insincere, and his sincere ratings are 1.0, 0.0 (or even 0.0, 98.99)?
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