[EM] How close can we get to the IIAC (=> "in the absence of cyclic preferences")

[Juho]

On Apr 16, 2010, at 1:23 AM, fsimmons at pcc.edu wrote:

> Since the IIAC is out of the question, how close can we get to the  
> IIAC?
> Independence from Pareto Dominated Alternatives (IPDA) is one tiny  
> step in that
> direction.  Another step might be independence from alternatives  
> that are not in
> the Smith set.

There is one well known and useful borderline, "in the absence of  
cyclic preferences". This condition is not really an answer to the  
question "how close can we get" but it is often a natural rough  
estimate, and applies to many common criteria. One could answer to a  
question "does method m meet criterion c" either YES, NO or IAC. For  
many Condorcet methods and criteria answer IAC would much more  
informative than plain NO.

In Condorcet methods it is typical that one can not meet all the  
criteria that one would like to meet, and therefore one must do some  
trading between different criteria. Often it is a good thing to fail  
numerous criteria slightly than to meet some of them fully and fail  
badly in some. (For example strategic voting often resembles security  
in the sense that the weakest link of the chain determines the  
strength of the whole system.)

I also note that sometimes one may even prefer answer IAC to YES. Some  
criteria that are very natural requirements when there are no cycles  
may not be what we want when there are cycles. (One should not rely  
too much on the logic of the "Newtonian" transitive model when the  
world is no more transitive. The rules may well be different in the  
new cyclic space.)

Textually term "IAC" gets very close to "IIAC" :-).

Juho