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Mike O.,<br>
In response to my Fri.Jan.7 post, you wrote:<br>
<blockquote type="cite">
<pre>You continued:
, Majority
Favourite
I 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.
</pre>
</blockquote>
CB: "Majority Favourite" refers to a candidate who is the favourite of
the majority. It is about nothing else except making<br>
that candidate win, not just some other candidate lose. So then the
short version would be:<br>
<br>
"If a majority prefers candidate x to any other candidate, then x must
win".<br>
<br>
A long, votes-related version might say:<br>
<br>
"If the voting method asks or requires the voters to specify one candidate
as favourite, or to provide sufficient information<br>
so that the unique favourites of all those voters who have one can be
inferred from the ballots (and not give the voters<br>
any zero-information incentive to do anything else); then if a majority
of voters prefer candidate x to any other candidate<br>
and vote sincerely then x must win."<br>
<br>
Obviously if the method doesn't collect enough information to infer the voters'
favourites, then it can't meet MF. <br>
Without the part in parentheses, Approval could perhaps be smuggled in by
having a ballot instruction "check only<br>
your equal-favourite candidates". Voters whose biggest utility gap is below
their second preference will have a<br>
zero-information incentive to not comply.<br>
<br>
Mike O.:<br>
<blockquote type="cite">
<pre>You 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.</pre>
</blockquote>
CB: Approval definitely fails Majority Favourite (and also ML), for the
very simple reason that the ballot doesn't<br>
ask the voter "Who is your favourite?", but rather "Which candidates do
you approve?" or "Rate the candidates on a<br>
scale of 0,1". The ballots don't contain sufficient information to infer
the favourites of all the voters who have one, only<br>
those voters who approved a single candidate.<br>
<br>
It is perhaps debatable where the line between "majority-rule methods" and
others should be drawn, but complying with<br>
May's criterion, Majority Favourite and Majority Loser are certainly bare
minimum requirements.<br>
Approval, Range Voting, Borda, and Plurality don't qualify. <br>
In addition to the basic May's, CF, and CL; IRV meets (Mutual) Majority
and Condorcet Loser. On top of that <br>
Condorcet (Margins) meets Condorcet.<br>
<br>
Mike O:<br>
<blockquote type="cite">
<pre>Brian Olson wrote (Fri.Jan 4):
><i>Of course, even a 1-100 scale can be so "abused". But if 99 people really
</i>><i>vote for their favorite with a "1", and the other guy with a "0", aren't
</i>><i>they effectively saying "I don't care (much)"?
</i>
I reply:
If the range is 0-100, then they're saying they care very little about the
election.
You (Brian) continued:
Why should
><i>we be listening to their votes more than they want to be heard?
</i>
II reply:
Agreed. They're only voting one point of difference in a 100 point range
election.</pre>
</blockquote>
CB: If the 99 voters don't "want to be heard", then why are they bothering
to vote? Take this example:<br>
<br>
2: A7, B6<br>
1: B100, A0.<br>
<br>
(Ralph Suter can multiply these numbers by 5 million, if that will make him
happy.) The two A supporters are very<br>
religious, and they have resolved to reserve the maximum possible rating
of 100 for the second coming of Jesus Christ<br>
and the lowest possible rating of 0 for the anti-Christ. Nevertheless they
have gone to the trouble of doing their civic duty<br>
by showing up to vote and express their clear preference for A over B. (If
the method were Approval, there prefernce<br>
for A could not be inferred from their ballots because they would not have
approved either candidate.)<br>
The B supporter doesn't share their religion, and is either a strategist
or is in love with B, it doesn't matter which.<br>
The A supporters did their duty and reported their sincere ratings of the
candidates. It is complete nonsense to infer<br>
that they have somehow volunteered to be over-ridden by the minority B supporter,
and so therfore majority rule doesn't<br>
matter.<br>
<br>
<br>
Chris Benham<br>
<br>
PS: I made a small mistake in my Friday post:<br>
<blockquote type="cite">
<pre>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)?</pre>
</blockquote>
Those last two numbers are the wrong way round.<br>
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