[EM] How close can we get to the IIAC (=> "in the absence of cyclic preferences")

[Kristofer Munsterhjelm]

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?".