[EM] The issue of comments about Arrow's theorem

[Curt Siffert]

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.

Curt