I just had a minor realization. As I said to Abd, his Bucklin-ER (as I understand it) has slightly less resistance to the chicken dilemma than GMJ, because the Bucklin-ER tiebreaker effectively ends up focusing slightly below the median in the grade distribution, while GMJ focuses on a region balanced around the median. Well, why not take that in the other direction? Consider the following Bucklin system, tentativlely named: uı|ʞɔnq-ᴚƎ:
Count the votes at the highest grade for each candidate. If any one candidate has a majority, they win. If not, add in lower grades, one at a time, until some candidate or candidates get a majority. If two candidates would reach a majority at the same grade level, then whichever has the most votes above that level wins. If there are no votes above that level, the highest votes at or above that level wins. Now consider a chicken dilemma where Y and Z must cooperate to defeat X. If a Y voter rates Z at the second-to-bottom grade, then further strategy simply will not help unless Z's median falls to 0 — which would mean risking an X win if Z's voters are similarly strategic. This is a stronger, and more-simply-argued, bulwark against the chicken dilemma's slippery slope than GMJ's. GMJ still has certain advantages. Because it's cleaner and more symmetrical in an abstract sense, its criterion compliances are slightly better; and uı|ʞɔnq-ᴚƎ does not allow reporting via 1 number per candidate. But these are minor, technical points. While I still have a father's affection for GMJ, I think that uı|ʞɔnq-ᴚƎ is now my favorite system. Obviously the name needs fixing; I've left it with a deliberately unusable one for now. I'd be happy to call it IRAV, or APV, or whatever other people support in this thread.
---- Election-Methods mailing list - see http://electorama.com/em for list info
