[EM] Proportional Condorcet Voting

[Simmons, Forest]

Antonio Oneala lamented that proportional Condorcet methods tend to be intractable.  This is because if there are N candidates from which to choose K winners, there are  C(N,K)=N!/(K!*(N-K)!) subsets to be compared pairwise, for a total of  C(C(N,K),2) pairwise comparisons of subsets.
 
However, suppose that instead of comparing all C(N,K) of the K candidate subsets, we just compare all submitted proposals, including those sets that would be elected by STV under various rules (Droop Quota, etc.).  There might be ten thousand such proposals. But that would only require  C(10000, 2) = 49995000 comparisons, a few seconds of CPU time on a second rate computer.
 
Forest
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