Reweighted Range Voting http://rangevoting.org/RRV.html does not check every possible combination of candidates. However there may be a way to determine the optimal candidate quickly.
Set X and set Y are adjacent if it is possible to create one group by changing a single candidate in the other. …in other words, all the members are identical but one. Set X is a local maximum if the utility of every adjacent set is less than Set X’s utility. The utility function is rather simple. for each voter, the utility is ln(1+score_sum/max) with score_sum being the score they gave each candidate individually and max being the maximum rating allowable for a single candidate. This is taken from the D'hondt divisors 1+1/2+1/3..., but integrated rather than summed. presumably ln(1+2*score_sum/max) would work as well. >From a few tests I’ve run, it seems as if there’s never more than one local maximum. Naturally, this single local maximum would be the optimal candidate set. This suggests that a simple iterative procedure will determine the optimal candidate set without examining all of them. (Perhaps using Reweighted Range Voting or Naive Multiwinner Range as a starting point) I, however, lack the expertise to prove whether it is possible for multiple local maxima to occur. I was wondering if anyone could. This method is called Proportional Range Voting due to its resemblance to Proportional Approval Voting http://www.knowledgerush.com/kr/encyclopedia/Proportional_approval_voting/
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