[EM] Re: To Chris, about Range Voting

[Chris Benham]

  Mike O.,
In response to my Fri.Jan.7 post, you wrote:

>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.
>
>  
>
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.  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.:

>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.
>
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".  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:

>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.
>
CB: If   the 99  voters  don't  "want to be heard", then why are they 
bothering to vote?   Take this example:

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:

>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)?
>
Those last two numbers are the wrong way round.




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