[EM] Arrow's Theorem - The Return (again)

[Eric Gorr]

At 1:17 PM -0700 8/2/03, Alex Small wrote:
>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.



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== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
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