[EM] electing a variable number of seats

[fsimmons at pcc.edu]

Yes, I do think the non-sequential version of RRV for sufficiently large numbers of winners (with repeated wins allowed) is equivalent to the Ultimate Lottery.The Ultimate Lottery is the lottery that maximizes the product of ballot expectations, or equivalently the one that maximizes the sum of the logs of the ballot expectations. The non-sequential version of RRV basically picks the subset of candidates that maximizes the sum (over the ballots) of the logs of the sums (plus epsilon to avoid the log of zero)) of the ballot ratings of the candidates in the subset.Since  log(epsilon+N)/log(N) approaches 1 as N approaches infinity, the methods are equivalent in the limit.----- Original Message -----From: Kristofer Munsterhjelm Date: Tuesday, May 17, 2011 11:24 pmSubject: Re: [EM] electing a variable number of seatsTo: fsimmons at pcc.eduCc: Andy Jennings , election-methods at lists.electorama.com> fsimmons at pcc.edu wrote:> > Andy,> > > > I like the idea of iterating RRV to infinity to find the > weights for a weighted voting system.  > > > > And of course,interpreted stochastically. it also gives > another solution to Jobst's consensus challenge.> > > > I doubt that it is always the same as the Ultimate Lottery.  > Probably an example where sequential PAV > > differs from PAV would show that.> > Do you think the non-sequential version would be equivalent to > the > Ultimate Lottery?> > And since I don't recall, how do you measure the quality of a > given lottery?> > > I suspect that, unlike sequential PAV and RRV, both ordinary > PAV and the Ultimate Lottery may be > > computationally NP-complete.> > If you're lucky, the NP-complete problem may still be feasible > in > practice. For instance, I implement both Kemeny and Young's > method in > Quadelect, and in the vast majority of the time, the linear > programming > relaxation is already optimal. In the other few cases (unless > you're > dealing with extreme numbers of candidates and voters), branch-> and-bound > finds a solution in reasonable time.> > 
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