[EM] Advocacy of Kemeny's method

[mrouse1 at mrouse.com]

Steve Eppley wrote:

>that two or more social orderings are Kemeny-best.
>Here are two examples:
>
>   50:  A>B
>   50:  B>A
>
>   33:  A>B>C
>   33:  B>C>A
>   33:  C>A>B
>
>I'll assume for the moment that Mike merely meant 
>that Kemeny socially orders the alternatives, since 
>orderings are acyclic by definition.  MAM socially 
>orders the alternatives too.
>
>  
>
Both of these are true ties -- I don't know of a method that would 
consistently choose one winner with either profile.

>
>Other than saying NP-hardness is desirable (which would
>be a controversial claim, beyond this narrow context) 
>this voting strategy "resistance" still hasn't been defined 
>rigorously enough for me to evaluate whether MAM satisfies 
>it.  
>
Not really desirable, but kind of the opposite of a mixed blessing 
(mixed curse?). It'd be better if the method were easy to calculate, but 
on the other hand you have to admit it makes strategic voting more 
difficult. :)

>MAM is not NP-hard to tally, so if Mike is really 
>looking for NP-hard methods--the rest of his writing 
>suggests otherwise--then MAM would be slightly 
>disappointing.  
>
No, this would be an advantage of MAM.

>On the other hand, MAM satisfies
>some defensive strategy criteria promoted by some
>members of this list, originated by Mike Ossipoff:
>SDSC (nearly equivalent to Minimal Defense, described
>at my website), WDSC (nearly equivalent to Non-Drastic 
>Defense) and Truncation Resistance.
>  
>
MAM does appear to have many attractive features and it would be a much 
better system than what we have now. It would get my vote above IRV and 
Borda, too.

>I don't understand what Mike means about Kemeny 
>disregarding "outlandish" votes.  I would say Kemeny
>does not disregard any votes.  Perhaps he meant 
>that "outlandish" votes won't be consistent with
>the Kemeny social ordering.  But that would seem
>to be just a definition of outlandish, and hence 
>tautological, so I'm sure I'm missing something.
>
>  
>
I cheated and grabbed the term from this page:
http://www.univ-pau.fr/~fleurbae/papiers/Social%20Choice%20and%20Just%20Institutions5.rtf

The relevent part is:

"Another important rule is the Kemeny-Young rule, which looks for a 
complete preorder which minimizes the total number of disagreements with 
the majority rule on pairwise comparisons. It has been axiomatically 
justified by Peyton Young, and has recently received a vigorous 
philosophical defense by Mathias Risse. This rule violates IIA because 
it discounts individual preferences which are outlandish, in the sense 
that they too often contradict the majority verdict in pairwise 
contests. It then often requires an extensive information about all 
majority comparisons before judging on two particular options."


As a counter-argument, you might check out
http://citeseer.ist.psu.edu/cache/papers/cs/16845/http:zSzzSzwww.math.nwu.eduzSz~d_saarizSzvotezSzkem-new1.pdf/saari97geometric.pdf

Here Donald Saari has some harsh words about Kemeny -- things like

"Indeed, KR treats certain preferences as though they come from 
non-existent voters with cyclic preferences. As a consequence, arguments 
promoting KR need to justify why we should ignore the erosion of the 
crucial 'rational voter' assumption to the extent of accepting outcomes 
that are signicantly influenced by non-existent voters with irrational 
beliefs."

Of course, he likes Borda the best, so you may take his conclusions with 
a grain of salt (grin). It's interesting to read, though, and it often 
seems to me he's praising it with faint damns. :)


Mike

PS Sorry I sent the first one to you directly instead of the list, 
Steve. I made a mistake when I hit reply without fixing the return address.
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