On Wed, Dec 11, 2002 at 11:51:27AM -0500, Raul Miller wrote: > A defeats b 8:3 > c defeats A 8:3 > b defeats c 6:5 > eliminate 6:5 Sorry, I don't buy this. You're looking to choose amongst A, b, c and N to work out what should be done. A can't win, since it doesn't have supermajority support, leaving b, c and N. Amongst just b, and c, the majority of the voters prefer b. There are also majorities that prefer both b to N and c to N. That seems to me to be a *perfectly* reasonable chain of logic to declare b the winner. Which is to say, rather than telling the people who voted b>c, "sorry, there weren't very many of you, so your vote doesn't count", I'd be happier telling the people who voted A>b, "sorry, your option didn't make its supermajority so could never have won, so your vote doesn't count". Alternately. Suppose you select A as the winner. Who can complain? Everyone who voted N>A, since it didn't make supermajority, and everyone who voted c>A. So you can't do that. Suppose you select c as the winner? Then the people who voted for b can complain, which is more than half the people who voted. If you select b as the winner, only the people who voted for A can complain -- but you can tell them "sorry, but your option had no chance anyway because of the supermajority requirement". There's no need to work out the smallest majority to offend, because you've got an actual _justification_ to answer the A voters objections: that they failed supermajority. > > Define "like Condorcet". > Same outcome as Condorcet for the same votes. Heh. Condorcet doesn't produce a winner for the case you give; it only does so when there is a single option that defeats every other option. That the winner should be a member of the Smith or Schwartz sets is also satisfied. The only thing that isn't is whether or not ties are broken in the same way. Cheers, aj -- Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/> I don't speak for anyone save myself. GPG signed mail preferred. ``If you don't do it now, you'll be one year older when you do.''
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