From: Juho <[EMAIL PROTECTED]>
> On Mar 29, 2008, at 23:35 , Michael Rouse wrote: > > has > > someone proposed a method to convert Range votes to maximal strategy > > Approval votes? I was just wondering what the properties of such a > > system might be (including cool-looking graphs, if available), and any > > paradoxes or problems that might arise. > > > > For example, would it be possible to convert Range ballots into the > > equivalent of Approval ballots where every voter has the equivalent of > > perfectly accurate polling data? > > It may be possible to create some interesting algorithms. The first > problem to solve is that the optimal strategy is not stable since the > best strategy of one voter depends on the decisions of other voters. > That means that you maybe need to force the voters to use some > strategy that is equally good for all but not optimal. There was a suggestion to use the standard approval strategy "Approve your favourite of the top 2 and everyone you prefer to that candidate" It doesn't converge if there is a condorcet loop. E.g. Voter 1 (A>B>C>D) A: 10 B: 7 C: 3 D: 0 Voter 2 (B>C>D>A) A: 0 B: 10 C: 7 D: 3 Voter 3 (C>D>A>B) A: 3 B: 0 C: 10 D: 7 Voter 4 (D>A>B>C) A: 7 B: 3 C: 0 D: 10 Assume, top 2 is A,B. Voter 1 approves A Voter 2 approves B Voter 3 approves A, C, D Voter 4 approves A, D A: 3 B: 1 C: 1 D: 2 New top 2 is A,D Voter 1 approves A Voter 2 approves B, C, D Voter 3 approves D, C Voter 4 approves D A: 1 B: 1 C: 2 D: 3 New top 2 is C,D If you repeat the process it goes A,B D,A C,D B,C A,B and loops (following the condorcet loop) This also happens (I assume) with the strategy "approve your favourite of the top 2 and everyone you prefer to the expected winner" or "approve everyone who you rate higher than the expected utility of the election" In the above example, it is a perfect tie, but there might be a way to get it to converge. Also, it doesn't use ratings at all and only considers the rankings. The last strategy would use ratings though. Raphfrk -------------------- Interesting site "what if anyone could modify the laws" www.wikocracy.com ________________________________________________________________________ AOL's new homepage has launched. Take a tour at http://info.aol.co.uk/homepage/ now.
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