sorry, you are right that the first STV winner need not be the same as the IRV winner.
Re NP-hardness & polytime, all such results take place in an asymptotic limit as some parameter or parameters describing nput size tend to infinity. Say the input size is N bits; then an algorithm is polytime if its runtime is <P(N) steps where P is a polynomial. For the question of spotting IRV nonmonotonicty, the question of determining your strtaegic-best IRV vote, etc, if V (#voters) is large and C (#canddts) is fixed then the runtime is polynomial(V). However, no known method is polynomial(V,C) and these papers give NP-hard scenarios where both V and C are made large, e.g. V=2C and make C large, for example. I consider these regimes to be unrealistic and the regime V=large, C=fixed to be realistic. In the "realistic" setting, few or none of the NP-hardness results are valid and there are easy polynomial-time algorithms. This whole area of "research" is largely a "crock." If they were, for example, to make a semi-realisitc setting where, say, C=log(V) and V-->infinity, and prove NP-hardness there, then I would start to get impressed that their results had some relevance to reality. I do not mind these results, I just mind that a lot of people get the wrong impression that they matter, and I mind that the authors of these results do not take care to dispel that wrong impression. wds ---- election-methods mailing list - see http://electorama.com/em for list info
