[EM] Advocacy of Kemeny's method

[mrouse1 at mrouse.com]

-------- Original Message --------

> Subject:     Re: [EM] Advocacy of Kemeny's method
> Date:     Thu, 16 Sep 2004 21:05:52 -0700
> From:     Steve Eppley <seppley at alumni.caltech.edu>
> Reply-To:     seppley at alumni.caltech.edu
> To:     election-methods at electorama.com
> References:     <41472C37.120.24F9866E at localhost>
>
>
> I'm not sure what Mike means by some of those terms.
> (Extended Condorcet?  Cycle "removal"?  Voting manipulation 
> "resistance"?)  I wonder if he can tell
> me if MAM, described at www.alumni.caltech.edu/~seppley,
> meets those criteria.  MAM does satisfy the above
> criteria that I do understand: It chooses within
> the top cycle, hence is Condorcet-consistent, and it socially orders 
> all the candidates. (Like Kemeny,
> MAM's ordering satisfies local independence of irrelevant 
> alternatives, and, unlike Kemeny, MAM satisfies a stronger criterion, 
> immunity from majority complaints.)  Also, MAM can be
> tallied in a time that's a small polynomial
> function of the number of voters and the
> number of candidates.
>
Michel Truchon gives the following description of XCC (the Extended 
Condorcet Criterion):

The usual Condorcet Criterion says that if an alternative is ranked 
ahead of all other alternatives by an absolute majority of voters, it 
should be declared the winner. The following partial extension of this 
criterion to other ranks is proposed: If an alternative is consistently 
ranked ahead of another alternative by an absolute majority of voters, 
it should be ahead in the final ranking. The term "consistently" refers 
to the absence of cycles in the majority relation involving these two 
alternatives.

He goes into a bit more detail in his paper /Figure Skating And The 
Theory Of Social Choice/* *at 
http://citeseer.ist.psu.edu/cache/papers/cs/11707/http:zSzzSzwww.ecn.ulaval.cazSzw3zSzrecherchezSzcahierszSz1998zSz9814.pdf/truchon98figure.pdf

Cycle removal just means that when you have a circular tie with regular 
Condorcet voting -- Candidate A is preferred to B, Candidate B is 
preferred to C, and Candidate C is preferred to A -- the Kemeny order 
will unwind the cycle and put the candidates in a specific order without 
the need for a tie-breaker method. Tie-breakers are fine, I just find is 
more aesthetically pleasing this way.

By "voting manipulation resistance," I mean it is difficult for a voter 
to come up with a way to improve his outcome over voting sincerely. 
Partly this is because it's a NP-hard problem to solve and requires 
complete knowledge of voting preferences, partly because it disregards 
orders it considers outlandish compared to majority preferences (the 
people who actually do prefer Nader>Bush>Kerry lose out, but hey...). Of 
course, like any non-dictatorial method it's still theoretically 
possible to manipulate.

I've heard of MAM, even read a bit about it, and it appears to be a 
fairly attractive system --especially  the ease of calculation compared 
to Kemeny. I haven't read it in depth enough to compare it to 
Kemeny-Young, though (and to be honest, a lot of the math involved in 
Kemeny is beyond me to begin with), but I'll check it out some more this 
weekend and see if I can get a better feel for it.

I'll check out the rest of the email in a bit -- I'm doing this between 
tech calls, and they frown on me if I do this too much :)

Mike

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