On Wed, Dec 11, 2002 at 06:48:58PM -0500, Buddha Buck wrote: > A->b->c->A > where A is a supermajority option, and b, c are normal options and the > b->c defeat was the weakest. > (late-dropping): c won, because we discounted the votes of the people > that preferred b over c, but counted the votes of the people that > preferred A over b, even though B couldn't have won. This is unfair and > counterintutive. > > (early-dropping): b won, but only because A was a supermajority option. > If A had been a normal option, c would have won. Why is it that > making A harder to win shifted the result from one winner to another? > This is unfair and counterintuitive. Having a cycle is counterintuitive; relying on intuition to determine a "fair" result doesn't seem entirely reasonable. I'm still failing to see anything unfair about dropping options we _know_ can't win. Consider a normal Condorcet vote, no cycles. A beats B, B beats C, C beats N. We see everything beats N, so we decide it can't win, so we drop it. Everything else stays the same, A still wins, everything's stable, and just as fair. We know N can't win, because every other option is preferred to it. Likewise, we know that A can't win. Further, dropping it actually simplifies the problem so that we can get an unambiguous result from what remains, using expressed preferences, rather than guesswork. Actually, I'd say letting c win is unfair in that it specifically ignores the express preferences amongst the plausible options; while letting b win when it wouldn't if some other option were handled differently is simply surprising and mildly disappointing. I can't see any reason why it's "unfair". If you make the vote be: 40 abNc 50 bcNa 60 caNb then you have: c defeats a 110:40 a defeats b 100:50 b defeats c 90:60 c defeats N 110:40 a defeats N 100:50 b defeats N 90:60 which gives you a different result if you make any of a, b or c require a 3:1 supermajority and drop it early; if you don't, c wins unless it requires a supermajority, in which case a wins. In the example above, if a required the supermajority, and you let c win, then you're adopting the _last_ preference of most of the people who preferred a, and adopted the second preference of the people who preferred the other plausible option. How does that make any sense at all? Why should "stability in the face of adding the supermajority requirement" be a more important criterion than "the result's independence from the addition of options that have no chance of winning" ? (Where "chance of winning" is defined as passing supermajority, passing quorum and ending up in the Schwartz set -- options that don't do all those things won't win, by def'n) What benefits does the former buy us? The latter makes the vote easier to analyse (there's no recursion, marginally smaller chance of cycles, etc), and reduces the chance of strategic nominations at least. 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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