[EM] Re: Arrow's Theorem flawed?
siffert at museworld.com
Fri May 13 02:59:37 PDT 2005
On May 12, 2005, at 9:24 PM, Paul Kislanko wrote:
> Bart Ingles wrote in respone to
>> Paul Kislanko wrote:
>>> I would go a little farther. Since Arrow's was a PROOF in
>> which no one has
>>> found a flaw in over 50 years, I would say that anyone who
>> has found fault
>>> with it is not a "vote theorist."
>> But Arrow didn't prove that IIA compliance was necessary, or even
>> desirable (although the latter was probably assumed). He
>> merely proved
>> that IIA was incompatible with other criteria.
> We weren't talking about that. We were discussing "election theorists
> Arrow's proof flawed".
> See why the Wiki-poedists found the statement less than enlightening?
Well, I didn't include this in the original email, but part of what I
was reacting to
in the wiki entry is that the wiki page's treatment of Arrow's proof
very much represented
it as a collection of criteria that any society would reasonably
require of a voting method
for it to be considered a valid voting method, and that no voting
method meets all those
criteria, so therefore, no voting method is sufficient to meet a
requirements for a social choice function.
That's a pretty common understanding of Arrow's proof, so those are the
which it should be opposed. But, I do now have a better understanding
that that shouldn't
be phrased as claiming that Arrow's proof itself is invalid. It's more
that most people
think that Arrow's proof proves something that it doesn't prove.
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