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

[Juho]

P.S. One way to use the concept of IAC would be to e.g. set a strict  
requirement of LNH-IAC to a method but only wish for reasonably good  
performance with full LNH.

Juho




On Apr 19, 2010, at 11:31 AM, Juho wrote:

> 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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>
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