Juho wrote:
On Apr 19, 2010, at 10:46 AM, Kristofer Munsterhjelm wrote:
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.)
No, that was a brief departure from IAC. The point was to show that even
though Condorcet methods pass LNHarm in the "non-cycle" case, the
Condorcet compliance itself introduces a discontinuity of sorts, which
means that the method as a whole (with ballots that may be cyclic or
not) cannot pass LNHarm.
In other words, I was answering, in advance, a possible reply of "but if
a Condorcet method can pass LNHarm inside the acyclical domain, then all
we have to do is to align the cyclical domain propely, and we'll have a
LNHarm Condorcet method, no?".
----
Election-Methods mailing list - see http://electorama.com/em for list info
