Juho wrote:
On Apr 16, 2010, at 1:23 AM, [email protected] 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.
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