James, Comparing Approval Margins (AM) with Approval-Weighted Pairwise (AWP), I'd written: In all your excellent examples given to demonstrate AWP's resistance to Burying, AM also frustrates the Buriers; except in one where AWP "cheated" by electing a "strongly defeated" candidate (pairwise beaten by a candidate with a higher approval score).
You responded: "I'm sorry, but I don't think that this definition of "strongly defeated" is especially useful. Nor do I think that it is "cheating" to drop such a defeat in the event of a majority rule cycle." CB: Well, its not supposed to be especially "useful" so much as *normative*. Recently I wrote strongly in favour of the Plurality criterion, which says that if candidate y has more first-preferences than candidate x has above-last-preferences,then x can't win. Electing x gives those voters who prefer y (to x) a very strong, virtually unanswerable complaint. When an otherwise reasonable method fails Plurality,it is usually caused by a lot of the y supporters truncating. So I suppose an available (but not very strong) retort to the complainers might be: "Well, you shouldn't have truncated!". That said, one of my current favourite plain ranked-ballot methods (CDTT,IRV) does fail Plurality, but gives the voters incentive to fully rank so that failure is very unlikely to occur in practice. Compared with failing the Plurality criterion, electing a candidate that is pairwise beaten by a more approved candidate can give more voters an even stronger,irresistible complaint. There isn't available the comeback: "This method encourages full ranking and so sometimes seems unfair to truncators. The winner's supporters didn't truncate, and you shouldn't have", because in AWP (as in your two examples) the failure can occur when all the voters fully rank and use their cutoffs. Comparing AWP with DMC, AM and Condorcet completed by Approval; AWP needs to collect more information. The other three are all happy with just the pairwise matrix and the approval scores (of each candidate). I think it would be difficult to justify collecting that extra information (and explaining what you want to do with it) to not particularly sophisticated, but fair-minded and not stupid people. Suppose we have the pairwise rankings matrix and the candidates' approval tallies in front of us, and the three candidates in a cycle. The supporters of the different methods make their suggestions: (1) Approval. Lets elect the most approved candidate. (2) DMC. Lets just eliminate the least approved candidate, and then elect the pairwise winner of the two remaining. (3) AM. Lets elect the most approved candidate, unless the second-most approved candidate both pairwise beats the most approved candidate and has an approval score that is closer to the most approved's than to the least approved's; in which case we elect the second-most approved. (4) AWP. I need more information, so that I can...[insert mumbo-jumbo]. I might want to elect the *least* approved candidate, partly because in cases like this I tend to assume that some of the voters are falsifying their preferences. That just won't fly. You can't say to voters: "Ok, we're looking for a pairwise beats-all candidate. We're asking you for rankings information, and in case there is no such candidate, also your approval cutoffs"; and then try to tell them the right winner is pairwise beaten and also the *least* approved. AM doesn't do that, and yet I still can't see that it is significantly worse than AWP at resisting Burying. (And it would have to be a lot worse for me to accept that the extra resistance gained by AWP is worth the cost.) Chris Benham Find local movie times and trailers on Yahoo! Movies. http://au.movies.yahoo.com ---- Election-methods mailing list - see http://electorama.com/em for list info
