[EM] Arrow's Theorem flawed?

Curt Siffert siffert at museworld.com
Thu May 12 17:58:34 PDT 2005

I recently posted this addendum to the Arrow's Theorem page on 
wikipedia:  It was immediately deleted for "bias".

"The theorem is criticized by many vote theorists, however, for 
depending on flawed requirements. [...] It is the final (IIAC) 
criterion that is most controversial. Some vote theorists believe there 
are scenarios of voting behavior where "failing" the IIAC is considered 
rational behavior by a voting society. One such example is where one 
candidate's supporters are far more loyal than another's, and the 
introduction of a third candidate would split the support of the third 
candidate. If failing IIAC is not always a "flaw", then the voting 
methods that fail only this criterion would not necessarily be 
considered flawed. In other words, some vote theorists believe Arrow's 
theorem improperly asserts that passing the IIAC is a requirement to be 
considered a satisfactory voting method. This would render follow-up 
theorems, such as the Gibbard-Satterthwaite theorem, flawed as well."

Was I out in left field for writing this?  I was under the impression 
that many vote theorists agreed with this characterization.  It seems 
to me that Arrow's theorem has a hidden assumption that every voter 
feels equally represented by their choice when they cast their ballot, 
which is a pretty silly assumption to make about an electorate.  If 
they don't feel equally jazzed about their choices, then failing IIAC 
could sometimes be desired behavior.

My favored example:
40 A
60 C

C wins.   Introduce B, and:
  40 A B C
  35 B C A
  25 C A B

If A's supporters felt dead-set on A, and C's supporters largely felt 
they were compromising and didn't object to A all that much, then this 
breakdown could make sense.  Almost all common voting systems 
(including most Condorcet tie-breakers) pick A as the winner.  It's 
pretty hard to make the case that that is a bad thing.  Arrow's theorem 
declares that any voting method that picks A is by definition a flawed 

-------------- next part --------------
A non-text attachment was scrubbed...
Name: not available
Type: text/enriched
Size: 2693 bytes
Desc: not available
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20050512/35a1718d/attachment-0002.bin>

More information about the Election-Methods mailing list