[EM] Arrow's Theorem; I comment on Arrow's e-mail
Craig Carey
research at ijs.co.nz
Tue Jul 15 00:01:01 PDT 2003
What bilgewater: I am unfamiliar with the concept of Kenneth Arrow
producing a theorem.
At 2003-07-14 13:47 -0400 Monday, Eric Gorr wrote:
>At 10:20 AM -0400 7/14/03, Eric Gorr wrote:
>>At 10:18 PM -0700 7/13/03, Alex Small wrote:
>>>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."
>
>Mystery Solved.
>
>I decided to write to Dr. Arrow concerning this and got the following
>message back:
>
>
>--
>Dear Mr. Gorr,
>
>Both statements are correct. The "monotonicity" condition together
>with Independence of Irrelevant Alternatives, implies the Pareto
>condition, which is the sufficient condition used in the "Vanderbilt"
>version. Actually, the monotonicity condition is used in the first
>statement of the theorem (first edition of my book, SOCIAL CHOICE AND
>INDIVIDUAL VALUES, 1951), while I used the Pareto condition in the
>second edition (1963). If one looks at the proof of the theorem in
The bottom fell out with the Handbook of Sen and others.
Presumably it takes an awful lot of work to get something as
neglectable as that out.
>the first edition, I showed that the monotonicity condition implied
>the Pareto condition and then, in effect, derived the theorem from
>the Pareto condition. The difference is, therefore, not very large.
>--
>
>So, it would appear that in all cases monotonicity is there even if
>it is not mentioned explicitly.
>
Monotonicity can't safely be in the collection of ideas argued to be
inconsistent (i.e. the bits for the imposs pseudo-theorem). Surely
we don't actually which of the principles it is more in.
Instead of Arrovianism (a word of the handbook) it might be
named Incrementalism: an acquisition of memories of earlier books
and published papers.
Arrow might be much in dispute with my last message here since
seeming to know what monotonicity is, yet at the Soc Choice journal,
there is not that mathematician's view that symbols alone hold the
meaning. If proper to strip off understandings, rewrite the
symbols in a backwards compatible way, and then restore meaning,
we MUST know it right o strip off Arrow's writings.
No principle there saying that there is a right to a 0..1 powerful
vote.
All of these next are pointless and fit to be ignored: IIA,
dictatorial, Pareto.
To Mr witless I retain my private messages idea that interest in
Arrow's Imposs fake Thrm makes this mailing list be dumb and do
tell me about the knowledge of your trolls or troll. How much do
they know ?.
Craig Carey
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