It occurs to me that maybe Symmetrical IC-Beatpath(lv) and Symmetrical IC-Ranked-Pairs(lv) might meet FBC, and fail Smith. That would be a lot better the reverse.
I don't know if they meet FBC. But, at this time, I don't know that they don't meet FBC, CD, Condorcet, 0-info LNHe, MMC, and Clone-Independence. Of course neither do I know that they do. "Ranked-Pairs" is abbreviated "RP". I'll abbreviate "Beatpath" as "B". So it's Symmetrical IC-RP(lv) and Symmetrical IC-B(lv). Or, abbreviating more, SICRC(lv) and SICB(lv). Of course Beatpath and Ranked-Pairs are only for when everyone is beaten. Otherwise, a top-count should choose among the unbeaten candidates, as in Symmetrical ICT. Someone could object that, in SICRC(lv) and SICB(lv), a defeat of 2 to 1 counts for more than a defeat of a million to 2. But remember that Ranked-Pairs and Beatpath are only used when the defeats nonsensicially, paradoxically, contradict eachother. The electorate choose A over B, and B over C, and C over A. If people object to 2 to 1 being more than a million to 2, then might not they also object to defeats that can form nonsensical cycles? And, non-defeats don't do that. Only defeats do that. So wouldn't it make sense for non-defeats to have "default" status, and for the number of objectors to a defeat to matter more than te number of advocates of a defeat? The defeat-objectors are the ones who are voting against something potentially nonsensical. So maybe they should be listened to with higher priority. Isn't this an alternative definition of the Schwartz set?: A candidate is beatpath-trounced if there is an unreturned beatpath to him. The Schwarz set is the set of un-beatpath-trounced candidates. Well, how would Symmettical IC-Schwartz-Top do? If no one is unbeaten, by Symmetrical ICT, then choose, from the Schwartz set (based on Symmetrtcal IC), the candidate with highest top-count. Symmetrical IC-Schwartz-Top could be abbreviated "SICST" That has more recently occurred to me, and I haven't had the opportunity to evaluate it. I haven't had the opportunity to evaluate SICRC(lv) or SICB(lv) either. I have no idea if any of those 3 methods would be any good, or would even work. The only IC methods that I make any claims about are ICT and Symmetrical ICT. SICRC(lv), SICB(lv), and Symmetrical IC-Schwartz-Top (SICST) are pure speculation at this point, and I don't claim to know their properties, of if they'd be any good at all. SICST occurred to me as a possible way to avoid need for losing-votes. Maybe using the Schwartz-set is good enough, and it isn't necessary to use Ranked-Pairs or Beatpath. I don't know. In voting systems, speculation has its place. Mike Ossipoff ---- Election-Methods mailing list - see http://electorama.com/em for list info