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Steve Eppley wrote:
<blockquote cite="mid414AF08D.17148.33B0C1BB@localhost" type="cite"><!---->
<pre wrap="">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.
</pre>
</blockquote>
Both of these are true ties -- I don't know of a method that would
consistently choose one winner with either profile. <br>
<br>
<blockquote cite="mid414AF08D.17148.33B0C1BB@localhost" type="cite">
<pre wrap=""><!---->
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. </pre>
</blockquote>
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. :)<br>
<br>
<blockquote cite="mid414AF08D.17148.33B0C1BB@localhost" type="cite">
<pre wrap="">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. </pre>
</blockquote>
No, this would be an advantage of MAM. <br>
<br>
<blockquote cite="mid414AF08D.17148.33B0C1BB@localhost" type="cite">
<pre wrap="">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.
</pre>
</blockquote>
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.<br>
<br>
<blockquote cite="mid414AF08D.17148.33B0C1BB@localhost" type="cite">
<pre wrap="">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.
</pre>
</blockquote>
I cheated and grabbed the term from this page: <br>
<a class="moz-txt-link-freetext"
href="http://www.univ-pau.fr/%7Efleurbae/papiers/Social%20Choice%20and%20Just%20Institutions5.rtf">http://www.univ-pau.fr/~fleurbae/papiers/Social%20Choice%20and%20Just%20Institutions5.rtf</a><br>
<br>
The relevent part is:<br>
<br>
"<font face="Times New Roman" size="3">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."</font><br>
<br>
<br>
As a counter-argument, you might check out <br>
<a class="moz-txt-link-freetext"
href="http://citeseer.ist.psu.edu/cache/papers/cs/16845/http:zSzzSzwww.math.nwu.eduzSz%7Ed_saarizSzvotezSzkem-new1.pdf/saari97geometric.pdf">http://citeseer.ist.psu.edu/cache/papers/cs/16845/http:zSzzSzwww.math.nwu.eduzSz~d_saarizSzvotezSzkem-new1.pdf/saari97geometric.pdf</a><br>
<br>
Here Donald Saari has some harsh words about Kemeny -- things like<br>
<br>
"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."<br>
<br>
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. :)<br>
<br>
<br>
Mike<br>
<br>
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.<br>
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