[EM] Re: Arrow's Theorem flawed?

[Curt Siffert]

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 
> found
> 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 
society's reasonable
requirements for a social choice function.

That's a pretty common understanding of Arrow's proof, so those are the 
grounds on
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.

Curt