Markus Schulze wrote: >>Arrow proved that there is no single-winner election method with >>the following four properties:
>> 1) It is a rank method (= a ranked-preference method). >> 2) It satisfies Pareto. >> 3) It is non-dictatorial. >> 4) It satisfies IIA. Ken Johnson wrote: > But why did Arrow stipulate #1? Because it was necessary for his method of proof. Arrow demonstrated that, given assumptions 1, 2, and 4, there was no method of resolving disagreements between ballots, except to give one ballot priority over all others (i.e. to be dictatorial.) If you allow cardinal methods, then you can use the strength of preferences to resolve such disagreements without letting the system become dictatorial. (This isn't to say that cardinal methods don't suffer from their own problems -- just that they don't suffer from the particular problems Arrow highlighted.) Here's a rather straightforward graphical proof that might make it more clear why restriction #1 plays such a crucial role: http://www.indiana.edu/~econed/pdffiles/summer02/phansen.pdf > (By the way, shouldn't the criteria also include transitivity, or does > that follow from the other criteria?) It follows from Pareto. -Bill Clark -- Ralph Nader for US President in 2004 http://votenader.org/ ---- Election-methods mailing list - see http://electorama.com/em for list info