On Wed, May 28, 2003 at 04:33:05PM +1000, Anthony Towns wrote: > On Tue, May 27, 2003 at 10:33:31AM -0400, Andrew Pimlott wrote: > > > Which makes D win, rather than A, B or C. > > Unfortunately, that doesn't mean this is not the best strategy. > > Sure it does: if their sincere preferences were "A,B,C > D" in all cases, > (whatever their preferences amongst A, B and C) then they've all got > the worst possible result. > > > It could be that the best strategy, applied by everyone, tends to > > produce stalemate. :-/ > > If that's not what they want, then, by definition it's not the best > possible strategy.
I can't do a full analysis, but that's surely too simplistic. This is the whole prisoner's dilemma problem. You can definitely have situations where both players are "forced" into the worst result. > For example, [snip] Sorry, those numbers are entirely arbitrary. Change them a bit, and they point the other direction. > > However, throw in one more ADBC vote, and Concorcet+SSD will declare > > A the winner, whereas the proposed method will be stuck on D. > > Huh? Oops, my mind was on situations where Concorcet+SSD was more strategy resistant, and I got carried away. > Note that if your strategy is "keep rerunning the vote 'til everyone > agrees that A is the best", then your sincere preference really is "ADBC" > -- that is, you really do think further discussion is a better result > than B or C. That is a distinction worth appreciating, and I incorporated it into my last message. However, in the above I was assuming that D was sincerely ranked below the other options by everyone. Andrew
