[EM] The issue of comments about Arrow's theorem
siffert at museworld.com
Sun May 15 03:06:50 PDT 2005
On May 14, 2005, at 9:07 PM, Russ Paielli wrote:
> The importance of IIAC is a matter of individual preference, of
> course, but it is a perfectly reasonable criterion. If I offer a group
> the choice of chocolate or vanilla ice cream, and they choose
> chocolate, why should the additional choice of strawberry cause them
> to switch their choice from chocolate to vanilla?
I think that's an overly simplistic definition of IIAC, and a very good
example of how the definition of IIAC is abused to convince people that
Arrow's Theorem has more destructive power than it does.
Imagine this group of people:
1) Slightly less than half is crazy about chocolate, likes strawberry
okay, and hates vanilla.
2) The rest like vanilla slightly more than chocolate, but likes both.
However, some of them love strawberry (first choice), and some hate
strawberry (last choice).
In the choice between chocolate and vanilla, vanilla wins. Introduce
strawberry, and the lukewarm edge of vanilla is exposed - the greater
utility of chocolate ends up winning.
Do you see? That's the secret flaw of IIAC right there: Sometimes a
Condorcet Winner is not the candidate with the greatest utility.
"Failing" IIAC can make a greater utility candidate win. In this
example, that's actually a good thing. And if in some cases, failing
IIAC is a good thing, then it isn't exactly a reliable criterion.
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