Mike, you wrote: > >In many or most cases, there's some vaguness about Pareto's definition. >Is >it about preference or voting? If it's about preference, then no method >meets it, or at least it isn't complete till someone adds stipulation >about >how people vote. If Pareto is about voting, then it says that a candidate >shouldn't win if another candidate is voted over him/her by everyone. No, >they don't say it that way, and so I'm just trying to guess what they >might >mean. >And if they do say "voted over", then it would be necessary to supply a >definition of that too. Sometimes the academics don't seem to have their >act >together very well. I'd supply my definition. >Anyway, if Pareto is about voting, then of course Approval passes. I've >read >in academic publications that Plurality, Borda, IRV, Copeland, etc. meet >Pareto. (Copeland is or was usually the only pairwise count method >mentioned >in academic articles, though occasionally Condorcet (meaning PC) or >Dodgson >is mentioned). Sequential Pairwise, the familiar parliamentary procedure, > >is mentioned as the method that notably doesn't meet Pareto. So, most >likely, for most authors at least, Pareto is intended to be about voting, >though vaguely defined. > I believe that Pareto is a criterion taken from the literature of welfare economics. It deals primarily with preference. The basic idea is that if there is some outcome A that everyone concerned prefers to another outcome B, then B should not be selected. It's a very weak criterion. The application of Pareto to ranked ballot voting methods seems fairly straightforward. Assume that voters vote sincerely, and then ask whether the method can ever choose a candidate who is Pareto-dominated. How to apply Pareto to approval? I suggest that we start by trying to take the same approach as before: assume that voters vote sincerely. But what is sincere voting in approval? It's not as easy to define as in a ranked ballot method. Perhaps the most we can assume is that no voter will approve a less-preferred candidate while not approving a more-preferred candidate. Given that restriction, is it possible that a Pareto-dominated candidate will be elected by approval voting? I think so. Consider this example:
Sincere preferences and approval cutoffs: 60: A>B>>C 40: C>>A>B A and B are tied with 60 points each. Hence, assuming that the method resolves ties randomly, B wins with 50% probability, in which case Pareto is violated. Sincerely, James ---- Election-methods mailing list - see http://electorama.com/em for list info