>Date: Fri, 07 Jan 2005 08:31:30 -0800 >From: Mike <[EMAIL PROTECTED]> >Subject: [EM] Thanks to a couple of list members (Condorcet/Range > completion method) >I'd like to thank Chris Benham for providing me the links to James >Green-Armytage's site, which answered a lot of my questions. > >I might as well ask another question, since this one went so well: Has >anyone tried replacing Borda with Range voting in methods like Borda >elimination or Nanson to see what the properties and paradoxes were? >
Mike, sequential elimination always introduces the same basic strategy problem that IRV has: you attempt to help a compromise candidate survive to the last round at the expense of candidates that you prefer, because you have reason to fear that your favorite(s) would not fare as well in the last round as your compromise. To counter this problem the idea of "Runoff Without Elimination" has been proposed independently by various people (even Donald, of all people). RWE requires that in the final stage, all of the candidates who have been eliminated are put back into the pool. The runoff stages are just for gathering information about relative probable success of the candidates. For example, you could do the runoff that you suggest, and then (after your final stage) put all of the candidates back in the pool, and calculate an approval cutoff on each ballot based on a weighted average of the candidate ratings on that ballot. The weights (for example) could be proportional to the square (for example) of the number of stages survived by the respective candidates. There is no particular incentive to have your favorite survive too many rounds, since the one who survives the most rounds is squarely in the cross hairs of the other candidates. Another RWE method would be to use Random Ballot Dutta to get the weights: Temporarily cross off all candidates except the members of the Banks set or Dutta set. Do a symmetric completion of these ballots so that each revised ballot has exactly one Dutta candidate in first place. Use the first place counts on these revised ballots as weights (for approval cutoff calculation) on the original ballots. What if there is only one member of the Dutta set? That's a nice problem. I think it would be hard to improve on the performance of this method, but it would probably be a harder sell than a simpler version of RWE. Check out Kevin's "Gradual Information Approval" for a simple, appealing method. In the k_th stage the top n-k approval getters from the previous stage are given equal positive weight for an approval vote. In the last (n-2) stage, only two candidates have positive weight for the cutoff calculation (so on each ballot the cutoff is halfway between them) but the other candidates are still in the action. "Where there's life, there is hope." Forest ---- Election-methods mailing list - see http://electorama.com/em for list info