On Apr 19, 2010, at 11:11 AM, Kristofer Munsterhjelm wrote:
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?".
Right. As you can guess from my comments I tend to see the cyclic
opinions as forming a new kind of opinion space when compared to the
simple models of individual voters and transitive preferences. It is
reasonable to assume that the sincere opinions of individual voters
are transitive. But we know that the opinions of groups don't follow
the same laws. In the same way I want to reconsider whether or not
those rules that apply in the simper models should apply also in the
world of cyclic preferences. For example I don't like very much terms
like "cycle breaking" because that seems to indicate that we want to
change the rules of the cyclic opinion space to rules of the
transitive opinion space, and I consider that to be more like a
violent act that may distort the true laws of nature of the cyclic
space. We should thus not break cycles but just identify the best
winner despite of the (natural) existence of cycles.
Juho
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