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

[Kristofer Munsterhjelm]

Juho wrote:
> 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 absence of cyclic preferences, any and all Condorcet methods pass 
IIAC. Say X is the CW. Then eliminating a candidate other than X won't 
turn X from CW to not-CW.

The same is true of, for instance, LNHarm. If X is the CW, then if a 
subset of the voters add Y to the end of their ballots, that won't make 
X a non-CW. However, it's also possible to show that no matter how the 
Condorcet method behaves in the case of a cycle, one can construct an 
example where the method fails LNHarm.