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-------- Original Message --------
<br>
<blockquote cite="mid414AF8F4.9030708@mrouse.com" type="cite">Subject:
Re: [EM] Advocacy of Kemeny's method <br>
Date: Thu, 16 Sep 2004 21:05:52 -0700 <br>
From: Steve Eppley <a class="moz-txt-link-rfc2396E"
href="mailto:seppley@alumni.caltech.edu"><seppley@alumni.caltech.edu></a>
<br>
Reply-To: <a class="moz-txt-link-abbreviated"
href="mailto:seppley@alumni.caltech.edu">seppley@alumni.caltech.edu</a>
<br>
To: <a class="moz-txt-link-abbreviated"
href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>
<br>
References: <41472C37.120.24F9866E@localhost> <br>
<br>
<br>
I'm not sure what Mike means by some of those terms. <br>
(Extended Condorcet? Cycle "removal"? Voting manipulation
"resistance"?) I wonder if he can tell <br>
me if MAM, described at <a class="moz-txt-link-abbreviated"
href="http://www.alumni.caltech.edu/%7Eseppley">www.alumni.caltech.edu/~seppley</a>,
<br>
meets those criteria. MAM does satisfy the above <br>
criteria that I do understand: It chooses within <br>
the top cycle, hence is Condorcet-consistent, and it socially orders
all the candidates. (Like Kemeny, <br>
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 <br>
tallied in a time that's a small polynomial <br>
function of the number of voters and the <br>
number of candidates. <br>
<br>
</blockquote>
Michel Truchon gives the following description of XCC (the Extended
Condorcet Criterion):<br>
<br>
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.<br>
<br>
He goes into a bit more detail in his paper <span class="m"><span
class="l"><i>Figure Skating And The Theory Of Social Choice</i><b> </b></span></span>at
<a class="moz-txt-link-freetext"
href="http://citeseer.ist.psu.edu/cache/papers/cs/11707/http:zSzzSzwww.ecn.ulaval.cazSzw3zSzrecherchezSzcahierszSz1998zSz9814.pdf/truchon98figure.pdf">http://citeseer.ist.psu.edu/cache/papers/cs/11707/http:zSzzSzwww.ecn.ulaval.cazSzw3zSzrecherchezSzcahierszSz1998zSz9814.pdf/truchon98figure.pdf</a><br>
<br>
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.<br>
<br>
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.<br>
<br>
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.<br>
<br>
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 :)<br>
<br>
Mike<br>
<br>
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