I do not agree these two things are equivalent, although they are related. If a method exhibits "favorite betrayal" but only rarely then third parties might be able to flourish. For example Coombs' IRV-like method exhibits favorite betrayal. Would it lead to 2-party domination?
Really 2-party domination is an experimental question and may not be answerable with mathematics alone, although one can often use math to become fairly confident of the answer. If rational voters acting in realistic scenarios with imperfect information often find it wisest to do favorite betrayal (especially in 3-candidate scenarios with 2 major-party candidates) then I think we get 2-party domination. The key muddy words here are "realistic scenarios with imperfect information" and "often" and another problem is voters are humans rather than rational beings. wds PS. Although approval voting does not involve favorite betrayal, there is some reason to suspect it will lead to 2-party domination. See http://math.temple.edu/~wds/crv/NurseryEffect.html and note that range voting seems a lot less likely than AV to lead to 2-party domination. This is quite a subtle effect, and I certainly was not smart enough to predict it with mathematics alone - it required an experiment to make me see the light. ---- Election-methods mailing list - see http://electorama.com/em for list info
