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<h1>[EM] Re: MMPO, Majority, Condorcet failures (Raynaud versions)</h1>
<!--htdig_noindex--> <b>Chris Benham</b> <a
href="mailto:election-methods-electorama.com%40electorama.com?Subject=%5BEM%5D%20%20Re%3A%20MMPO%2C%20Majority%2C%20Condorcet%20failures%20%20%20%28Raynaud%20versions%29&In-Reply-To="
title="[EM] Re: MMPO, Majority, Condorcet failures (Raynaud versions)">chrisbenham
at bigpond.com </a><br>
<i>Wed Dec 29 11:33:31 PST 2004</i>
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<pre> Gervase,
On Tues.Dec.21 you wrote:
><i>Monotonicity to me seems to be a very fundamental requirement for ranked
</i>><i>election methods. If I had to choose between Clone Independence and
</i>><i>Monotonicity, but not both, then I think I would go for Monotonicity.
</i>><i>
</i>Why? I live in Australia, where IRV's failure of Mono-raise
(lack of Monotonicity) goes virtually completely
unnoticed, much less worried about. Failure of Clone Independence on
the other hand, tends to have obvious
pernicious effects which begin with the nominations. (There is either a
split-vote problem, or a Rich Party problem).
Mono-raise has fallen off my list of "fundamental requirements", and
I now rate it as merely highly desirable.
It is somewhat hard to meet, and the best methods that meet it seem to
be much more vulnerable to Burying than the
best methods that don't (as evidenced by a lot of good examples from
James Green-Armytage).
Your remark was prompted by my opinion that Raynaud is better than
MinMax Pairwise Oppostion (MMPO).
MMPO meets Mono-raise and Later-no-harm. Raynaud loses those but
gains (Mutual) Majority, Condorcet, and
Clone Independence. Given that it seems to give similar results in the
3-candidate, lots of truncating, scenarios that
Kevin Venzke was concerned about, surely that is a great trade!
It seems to me that three versions of Raynaud are possible ( one that
meets Symmetric Completion and two that don't).
The obvious one that does is Raynaud (Margins). The other two could
be called Raynaud (Pairwise Opposition),
which eliminates the candidate which loses the pairwise comparison in
which the winner has the highest gross score
(explicit winning votes); and Raynaud (Gross Loser), which eliminates
the candidate with the lowest gross score in any
pairwise comparison.
In this example of Kevin Venzke's:
49: A
24: B
27: C>B
A>C 49-27 (m 22)
C>B 27-24 (m 3)
B>A 51-49 (m 2)
The three versions each give a different winner. PO eliminates A and
elects C, failing Plurality.
GL eliminates B and elects A, failing Minimal Defense. Margins
eliminates C and elects B.
Douglas Woodall gives this demonstration that Raynaud fails Mono-raise:
7 abc
7 bca
6 cab
"There are no trucated ballots, so the three methods are identical. I think
c has the most decisive defeat here, by b, and so c is eliminated and a
is elected. But if you replace two of the bca ballots by abc, then b has
the most decisive defeat, by a, and so b is eliminated and c is elected."
Chris Benham
><i>
</i>><i>
</i>
</pre>
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