Alex,
The real meaning of Arrow's theorem is that group choice is not *at
all* like individual choice. You are correct that the theorem states
that only a dictatorial choice function is consistent with Arrow's list
of assumptions such as IIA. But the point is that when you abandon
these assumptions groups can and will make choices that we would regard
as irrational if they were the choices of individuals. The reason that
dictatorship is the only choice function consistent with Arrow's other
assumptions is that a dictator is an individual!
On the point Dan made about there really only being two choices in
this election. Well sort of, but if you place the election in the
larger context of a two-stage process in which the parties choose
candidates and then the voters vote - then Arrow's theorem applies full
force.
It's true that the voters aren't really thinking about aggregation
issues but they do seem to have a sense that the "will of the voters" is
out "there" if only we could count ballots correctly. While in actual
fact any number of changes in the electoral system which would be
equally democratic (eg. Borda, Approval Voting, Cumulative Voting, etc.
etc.) could result in a *completely* different outcome. If voters
understood this then I think they would be more open to the idea that
what is important now is not that we count and double-count every last
ballot again and again but rather that there be a quick end to the
uncertainty.
Here is a quote from some notes of mine on Arrow's theorem:
"When an individual buys a quart of chocolate ice cream we have good
reasons for thinking that he prefers chocolate to vanilla or strawberry
ice cream. When a group of people buys a quart of chocolate ice cream we
cannot make similar claims. Most of us know that groups don't have
preferences and in this philosophical sense we know that it is
illegitimate to say that the group prefers chocolate to strawberry ice
cream. But the claim I am making is stronger. We might believe that
groups don't have preferences in the strict philosophical sense yet also
believe that group choice can be understood *as if* groups have rational
(individual like) preferences. If the latter claim were true it would be
a very useful fact to know. If we saw a group choosing apples rather
than bananas and bananas rather than coconuts and if groups acted *as
if* they had rational preferences we could predict that the group would
choose apples rather than coconuts. Similarly, suppose we saw a group
that has a choice of 33 flavors of ice cream choose chocolate ice cream.
If groups acted as if they had rational preferences we could conclude
that the group preferred chocolate to every other flavor of ice cream
and we could *predict* that if offered a choice of say chocolate,
vanilla, or stawberry the group would choose chocolate. Both of these
claims are false under several common voting schemes. Arrow's Theorem
shows that when choosing among three or more choices no voting system
can eliminate these paradoxes."
--
Dr. Alexander Tabarrok
Vice President and Director of Research
The Independent Institute
100 Swan Way
Oakland, CA, 94621-1428
Tel. 510-632-1366, FAX: 510-568-6040
Email: [EMAIL PROTECTED]
