On Apr 19, 2010, at 10:46 AM, Kristofer Munsterhjelm wrote:
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.
Your last sentence contains word "cycle". Were you thinking about IAC
in the sincere opinions only or also in the actual votes? (If needed
one can handle separately cases where IAC applies to sincere opinions
only vs. both sincere opinions and actual votes.)
Juho
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