To continue what I was saying about Ranked Pairs (RP), I like SSD, CSSD, & RP because they only drop (or decline to keep) a defeat if it's the weakest defeat in a cycle, and that gives them compliance with GSFC & SDSC. PC at least meets SFC. For PC & SSD, the problem with cycles is that there might not be any unbeaten candidate. So these methods drop weakest defeats till they undefeat someone. Of course for RP it's also a problem if no one is undefeated, but RP looks at cycles more critically, and RP regards defeats in a cycle as being contradicted, nullified. As judged by RP, we can't really name the unbeaten candidates till we get rid of all the cycles, by judging which defeats most deserve to be kept. Whereas RP gets rid of all the cycles, CSSD gets rid of all the cycles in the Schwartz set, drops weakest Schwartz set defeats till the current Schwartz set has no cycles--that happens when that set has no defeats among its members. So--two differences: Only dropping defeats in the current Schwartz set; and dropping weakest instead of keeping strongest. I don't have an opinion about which sounds fairer or more right. The example that I posted is one in which both methods only drop one defeat, and all the candidates are in the Schwartz set. So there, the 2 methods only differ in keep-strongest vs drop weakest. I guess the question is whether or not a defeat is nulified by a beatpath in the opposite direction, as opposed to honoring all defeats except for the weakest, even if they're in cycles, contradicted by return beatpaths. The question is, how important is a beatpath, in disagreeing with a defeat. Of course one could just simultaneously drop every cycle's weakest defeat, but that often undefeats unnecessarily many candidates. Repetition of that procedure to narrow down the winner-set has been shown to be nonmonotonic. By starting at the top, RP minimizes the number of defeats that need to be not kept, when making a transitive ordering, by sequentially keeping the strongest defeats if they aren't contradicted by already-kept defeats. Of course most would like the tendency for RP's winner to pairbeat the winners of other monotonic Condorcet versions, including SSD & CSSD, where those winners differ. Speaking of monotonic, though, I don't know if RP(wv) or RP(m) has been shown to be monotonic. CSSD & PC have been demonstrated to be monotonic. Though RP's procedure for equal defeats isn't important in public elections, because equal defeats are vanishingly rare in public elections, the electoral law still must include a provision for equal defeats. But it still isn't something that need be brought up to complicate public RP proposals. Most likely it's something that no one needs to bother with till the electoral law is written. The public electoral law provision for equal defeats in the middle of an RP count could be something like "If the defeats are even, then treat as stronger the ones whose defeating candidate is alphabetized earlier. If they're odd, treat as stronger the ones whose defeating candidtate is alphabetized later." That's no worse than the drawing of lots specified for ties in Plurality elections. I bring all this up because 1) Someone asked about RP; and 2) Now that IRV has been adopted in SF, there's more interest in public proposals, because it's obvious that Approvalists & Condorcetists have been letting themselves be left-behind promotionally. Mike Ossipoff _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com
