small correction: On Sat, Oct 11, 2008 at 6:37 PM, Greg Nisbet <[EMAIL PROTECTED]>wrote:
> So far some nice ideas have been proposed for measuring how effective a > multiwinner method is. > All of the ones proposed are based on n, let n be a list of utility scores > for the candidates. > 1. ln(2*sum(n)+a) we don't know what a is. It's probably pretty close to a > constant, let's just call it 1. > > Note: > values for the ln(2*sum(n)+a) can be computed exactly if you have time on > your hands > f(1) = 1 > f(2) = 1 + 1/2 => 1.5 > f(3) = 1 + 1/2 + 1/3 => 1.83 > > 2. this iterative procedure: > def sortpav(n): > n.sort() > n.reverse() > ret = 0 > for y,x in enumerate(n): > ret += x/float(y+1) > return ret > Of course these three procedures can be used for Range Voting, but it is > not necessary to accept the validity and perfection of Range Voting to use > these as metrics. > > Range Voting resembles utility summation with two fundamental differences > 1) people vote strategically and 2) a ceiling > > So, now we move onto the multiwinner bayesian versions. > Unlike single winner, the methods for measuring regret so far proposed have > a floor, specifically 0. See, the ln of negative numbers includes pi*i. I do > not know how to handle imaginary numbers with regard to voting methods, so I > am going to outlaw negative numbers as the lazy solution to the problem. > > If anyone has a multiwinner method to suggest, a criticism to the metric or > anything else before I run the simulation please let me know. I know better > than to call a vote on which metric to use, so if you have an opinion on one > of them please tell me. >
---- Election-Methods mailing list - see http://electorama.com/em for list info
