OK, I stand corrected on the assertion that Arrow's Theorem assumes strict preferences.
However, this whole discussion began over the question "Does Approval Voting satisfy Arrow's assumptions?" Approval Voting certain satisfies non-dictatorship and Pareto. Does it satisfy the assumption that the winner is uniquely determined from the voters' preference orders?
I can see no reason, based on the original work, that it would not satisfy this assumption.
Arrow seems to be perfectly content with allowing equal rankings.
Approval voting merely requires the user to divide the options into two different groups, but doing do does not violate Arrow's Axioms or definitions regarding voter choice.
Again, from his book:
"However, it may be as well to give sketches of the proofs, both to show that Axiom I and II really imply all that we wish to imply about the nature of orderings of alternatives and to illustrate the type of reasoning to be used subsequently." (page 14)
Anyway, because the outcome of an Approval Voting election is not uniquely determined from the set of individual preferences, Approval Voting does not satisfy one of Arrow's assumptions.
Again, individual preferences do not have to be strict orderings.
As such, the voting system that Approval uses is fully accounted for by Arrow's Theorem.
I would strongly recommend that you pick up a copy of his book (I assume you don't have it) so we can discuss in more detail how Arrow has developed his theorem.
-- == Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 === "Therefore the considerations of the intelligent always include both benefit and harm." - Sun Tzu == Insults, like violence, are the last refuge of the incompetent... === ---- Election-methods mailing list - see http://electorama.com/em for list info
