[EM] Proportional Condorcet Voting

[Antonio Oneala]

"Simmons, Forest" <simmonfo at up.edu> wrote: 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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After reading up on the CPO-STV method, the mehtod I've just come up with actually seems to be simpler.  CPO-STV involves a complicated comparison of outcomes and the transferring of all votes to certain areas in each of these outcomes; mine only involves a complicated comparison of outcomes, giving a score to each outcome based on how many candidates are preferred more than the other outcome in the score according to the D'Hondt or Webster quotas, adding all of these up, declaring a pairwise winner, and then comparing all pairwise competitions to see which outcome won the most pairwise proportional competitions.  Wait.  That's more steps.  Oh well.  It is, at least, monotonic, and the direct application of the quota seems better than the use of the transferrable vote as a quota.

As for the other reply to my thread, I'm not a fan of asset either.  I have a feeling it will enforce party structures, as a candidate inside of a party is far more likely to give it to another candidate in the party than to and independent.  It also has the problem that a lot of systems do; it doesn't increase the amount of voting power per each voter to accomodate more candidates.  Therefore, it will lead probably lead to factionalization, or at least cannot handle more parties than there are seats.  I've come up with a formula, where V is the amount of voting power per a voter, and C is the amount of candidates.  The formula is, easily enough, C = V.  If the voting system keeps V stable as C increases, then vote-splitting will result.  If it adds more C then V as C increases, then teaming will result.  For instance, Plurality keeps V stable as C increases (as you always have only one vote), approval and Condercet increase V in proportion to C, and Borda increases V at a
 faster rate than C.  Asset seems to fall into the plurality situation, although it is a bit less vulnerable.  However, a moderate who has 20 votes as compared to the polar candidate thirty votes doesn't have much leeway to convince the other guys to send votes to him, his only choice would probably be to send his votes to the lesser of two evils.



		
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