I recently posted this addendum to the Arrow's Theorem page on wikipedia: It was immediately deleted for "bias".
<x-tad-bigger>"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 </x-tad-bigger><x-tad-bigger>Gibbard-Satterthwaite theorem</x-tad-bigger><x-tad-bigger>, flawed as well."
</x-tad-bigger>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:
<x-tad-bigger>40 A</x-tad-bigger><x-tad-bigger>
</x-tad-bigger><x-tad-bigger>60 C
</x-tad-bigger>
C wins. Introduce B, and:
<x-tad-bigger> 40 A B C</x-tad-bigger><x-tad-bigger>
</x-tad-bigger><x-tad-bigger> 35 B C A</x-tad-bigger><x-tad-bigger>
</x-tad-bigger><x-tad-bigger> 25 C A B
</x-tad-bigger>
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 method.
Curt
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