Just an idea... "BANKS//APPROVAL": Take the Banks set (that is, find the top elements of all maximal chains (= acyclic complete subgraphs) of the graph of strict defeats), find the element(s) with largest approval, break remaining ties by random choice.
This is pretty easy, seems to fulfil Condorcet, monotonicity, cloneproofness and so on, and resolves at least the examples of strategic voting James cited (at least I think so). As the Banks set is a subset of the Schwartz set, the method is "in the spirit" of Condorcet although it doesn't consider strengths of defeats. Unfortunately, I can't remember whether the Banks set tends to be large or small in case of many candidates... When A wins in Banks//Approval, each argument "B is better than A" with majority support can be shown to be ridiculous by pointing out a chain of similar arguments leading back to A (since A is in the Schwartz set). However, the latter defeats might of course be smaller. Thus, another interesting variant could be the following: "BANKS//WEAKLY IMMUNE//APPROVAL": Find those elements A of the Banks set such that for all B defeating A there is C defeating B by at least the same magnitude. Proceed with approval. Perhaps we focused on cycle breaking methods a bit too much? Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info
