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 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
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