>From a theoretical standpoint, this may look intractactable, but for any finite N,K the problem is solvable in polynomial time in a manner that depends only upon N, K, and the number of voters. From a practical standpoint, the calculation is not difficult for up to N,K=293 by demonstation (I do that daily in my report of records vs common opponents for division 1 american college baseball teams on a Dell laptop. It takes a few minutes to run only because it is also producing 294 web pages, and all that I/O slows it down).
_____ From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Simmons, Forest Sent: Monday, May 01, 2006 2:29 PM To: [email protected] Subject: Re: [EM] Proportional Condorcet Voting 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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