Arrow's Theorem (was Re: Re: Re: Bill Joy interviewed in Salon)

Date: Wed Apr 12 2000 - 22:23:14 MDT

I wrote:

>>Arrow did make it pretty hard for reasonable
>>folks to claim that they can generate group preferences out of individual
>>preferences. Collectivists note: You cannot get there from here.

Damien commented:

>Marketeers note: hence the same must apply to the `votes' cast in the market.

Not so fast. Arrow's Impossibility Theorem would not hold if, in deciding
what was socially preferred, we could accurately compare degrees of
preference. Suppose, for instance, that we could say not only that Able
prefers apples to oranges to bananas, but that he prefers them by three and
two utiles, respectively, whereas Baker prefers oranges to bananas to apples
by five and two utiles respectively. Clearly, that small society's utility
function is maximized by choosing oranges.

That's just utilitarianism, and as such suffers the usual objections, most
relevantly that we cannot make interpersonal comparisons of utility. You
could (per Alfred Marshall) simply treat as equal each person's utility from
having one more dollar. That's clearly false, but it may still prove useful
for purposes of approximation.

The short of it is that both votes and dollars fail to overcome Arrow's
impossibility theorem, but that votes almost certainly fail in a more
spectacular fashion.

T.0. Morrow

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