poly: re: Arrow's Social Choice Theorem / Borda count

From: Anton Sherwood <bronto@pobox.com>
Date: Mon May 08 2000 - 02:41:19 PDT

Saari's article <http://www.colorado.edu/education/DMP/voting_b.html>
contains this paragraph:

"This same argument explains Arrow's Theorem. Arrow's IIA assumption
requires procedures to concentrate only on pairs while totally ignoring
whether the pairs satisfy transitivity. As such, IIA admits only
procedure that are prefectly reasonable in an irrational society where
voters can only rank pairs. Thus IIA disqualifies any procedure, such as
the Borda Count, which monitors and requires the voters to have
transitive preferences. Consequently Arrow's result can be viewed as
seeking a procedure which satisfies his assumptions and which can serve
societies with irrational voters, ..."

On the contrary, I believe Arrow assumes that the input is like Borda
ballots, complete rankings by each voter. In theory an election *could*
be run by asking each voter N*(N-1)/2 pairwise questions, but it seems a
lot cheaper all around to ask for a ranking.

By "irrational voters" does Saari here mean the aggregate, where a
Condorcet cycle exists?

"...but which always has transitive outcomes in those special settings
when used by voters with transitive preferences. Namely, which methods
designed to handle irrationality become [shouldn't that be `remain'?]
reasonable when the voters are rational?"

Heh. Similarly, what laws, drafted on the assumption that the people
are all adolescents on Angel Dust, remain reasonable when the population
includes sober adults?

Anton Sherwood  *\\*  br0nt0@p0b0x.com  *\\*  http://ogre.nu
Received on Mon May 8 02:38:01 2000

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