Forest W Simmons wrote: > Here's the question to focus on: is there one method (that uses > approval information) that is uniformly best in the three candidate case? > The answer to that I think is affected by whether the balloting rules allow voters to rank among unapproved candidates or not. If not I think ASM is the best. If yes, then DMC is a bit more resistant to Burial than ASM, having the property that if there are three candidates X,Y,Z and X is exclusively approved on more than a third of the ballots and wins then altering some ballots from Y>X (and I hope Y=X) to Y>Z can't change the winner to Y.
But this IRV-like virtue definitely comes at some expense of monotonicity. DMC technically scrapes in to compliance with mono-raise and doubtless fails some other monotonicity property that ASM meets. 31: a|b 32: b|c 37: c|a I am a bit perturbed by anything that doesn't elect C here. C has the most approval, the most FPs, the highest Bucklin score and the highest Borda score. ASM elects C but DMC and James Green-Armytage's Approval-Weighted Pairwise elect B. Chris Benham http://wiki.electorama.com/wiki/Approval_Sorted_Margins http://lists.electorama.com/pipermail/election-methods-electorama.com/2002-April/008013.html > Chris, > > I'll have to ponder Adam's critique of three candidate Smith Approval > before I can fully respond. > > The main advantage of UncAAO over Smith Approval, ASM, DMC, etc. is > that it always picks from the uncovered set (no matter how many > candidates there are). And esthetically, the geometry of Unc(whatever > starting point)AO is very appealing to me. > > If I end up agreeing with you that ASM and DMC are uniformly better > than Smith Approval in the three candidate case, then I will explore > Unc(ASM)AO and Unc(DMC)AO. But I'm not sure that the loss of > simplicity would be worth it. > > Here's the question to focus on: is there one method (that uses > approval information) that is uniformly best in the three candidate case? > > If so, then that's the method that I would like to try to generalize > to an "Unc" method for any number of candidates. > > Forest > > > > > > ---- election-methods mailing list - see http://electorama.com/em for list info
