Some, including me, after listing to others, have criticized RP for small committees by saying that it can need tiebreaking during the middle of the count, when it encounters 2 or more equally strongest defeats. But that seems to not be so. Let me write a definition of RP, and then add a provision for equal defeats: In order of stronger defeats first, consider each defeat in turn as follows: Keep it if it doesn't contradict already-kept defeats (by being in a cycle with them--i.e. by being in a cycle consisting only of it and some already-kept defeats). When all defeats have been so considered, a candidate wins if s/he has no kept defeats. But when 2 or more defeats are equally the strongest ones not yet considered, then, in any order, consider each of them by keeping them if they don't cycle with _stronger_ kept defeats. Then, when all of those equal defeats have been so considered (I'll call that the 1st consideration), unkeep any of those equal defeats that cycle with defeats that were kept at the completion of the 1st consideration. Then resume considering next-strongest defeats as described in the main instuctions before this paragraph. [end of definition] Fortunately that last paragraph isn't need in public proposals, where equal defeats are very unlikely. Sure, some provision must be made, as a formality, but it could be about drawing lots. It could be the above paragraph too, but the important thing is that there'd be no need to bother the man-in-the-street about equal defeats procedures, since it's practically certain that there won't be any. That certainly isn't simpler than randomly choosing consideration order, but it avoids tiebreaking during the middle of the count. I don't claim to have a good public-proposal name for RP, but a good descriptive name is: Sequentially-Keep-Un-Nullified-Defeats. Of course, "Ranked-Pairs" is no descriptive name at all. It seems to me that the difference between SKUND (RP) and BeatpathWinner/NIN/CSSD is that SKUND considers a nullified defeat to be unqualified to nullify another defeat. Obviously my way of dealing with equal defeats in SKUND in small committees still spoils SKUND's simplicity under those conditions. That's why I'd be more likely to recommend NIN for small committees. In public elections, if single-winner reform advocates want a rank-method, and if they don't like SKUND, I'd next offer NIN. And if they don't like that either, I'd next offer SD. If they don't like that either, I'd then offer PC. If they don't like that, I'd ask them to reconsider their requirement for rank balloting, and to consider Approval, which wouldn't lead to a count-rule debate. As much as I like the advantages of the best rank methods such as SKUND & NIN, I'd probably, in a place where there wasn't already a desire for rank-balloting, just propose Approval, to avoid the debate between the rank-counts, if there's any likelihood that people would insist on comparing a wide range of rank-count proposals, and debating which is best. Mike Ossipoff _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
