[EM] (no subject)

[Alex Small]

Bart Ingles said:
>
> I think there have been several incarnations of Arrow's theorum.  The
> original 1951 version used monotonicity, IIAC, non-imposition, and
> non-dictatorship.  I think Alex is describing the 1963 version.  Both
> are described in the 2nd edition of Arrow's "Social Choice and
> Individual Values".  It's still in print, I found it on amazon.com.


I found what Bart calls "the 1963 version" in a paper by a a U. Chicago
econ prof

(http://faculty-web.at.northwestern.edu/economics/chung/mr/Reny.pdf).

I'm pretty sure it's also in Saari's book.  Also, this link gives the 1963
version:

http://www.math.vanderbilt.edu/~bruff/voting/arrow.html

In my opinion, Arrow's theorem is more impressive when you have as few
assumptions as possible.  When the list of incompatible assumptions is
large, somebody can say "Well, duh!  If you pile on a whole bunch of
assumptions you're likely to make the task impossible."

But if you have just Pareto, non-dictatorship, and "Independence from
Irrelevant Alternative Candidates" (IIAC), it's a more impressive result. 
Non-dictatorship and Pareto efficiency (if everybody prefers A to B then B
never wins) are satisfied by just about any method ever seriously proposed
for public elections, so Arrow's Theorem then proves that this single
condition (IIAC) is impossible for any seriously proposed method.



Alex