Hallo, to demonstrate that a given election method violates a given criterion it is sufficient to find a single example where this election method violates this criterion. When in this very special example each voter casts a complete ranking of all candidates then this does not mean that you have to presume that each voter always casts a complete ranking of all candidates.
In other words: To prove Arrow's Theorem it is not necessary to presume that each voter always casts a complete ranking of all candidates. Actually, it is not even necessary to presume that each voter casts transitive (= non-cyclic) preferences. It is sufficient to presume that each voter can cast a complete ranking when he wants to do this. [Of course, when you allow cyclic preferences then the Pareto criterion has to be modified in such a manner that it says that _when each voter casts transitive preferences_ and no voter strictly prefers candidate B to candidate A and at least one voter strictly prefers candidate A to candidate B then candidate B must be elected with zero probability.] ********* To prove Arrow's Theorem it is also not necessary to presume that the used election method is deterministic. A very good paper is "Distribution of Power Under Stochastic Social Choice Rules" (Econometrica, vol. 54, p. 909-921, 1986) by Prasanta K. Pattanaik and Bezalel Peleg. They prove that no paretian non-dictatorial rank method can satisfy the following criterion ("regularity"): Adding candidate Z must not increase the probability that candidate A (with A <> Z) is elected. Markus Schulze ---- Election-methods mailing list - see http://electorama.com/em for list info