Folks,
Kevin has pointed out some interesting properties of MMPO. Although it
fails CC, apparently it passes FBC and LNH, which Kevin argues are more
important than CC. That may be debatable, but for the sake of this
discussion, let's say he's right.
MMPO is an ordinal-only method, and I still think that cardinal
information in the form of an Approval cutoff is indispensible. Why?
Call it intuition at this point, or refer back to my earlier post on the
topic at
http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015216.html
I have been amusing myself trying to think of a way to combine MMPO with
Approval. Here's what I've come up with.
Start with ranked ballots and Approval cutoffs as usual. Then arrange
the pairwise matrix so the Approval scores are decreasing (or
non-increasing) along the main diagonal, as in DMC. Now select two
candidates as follows for a pairwise "runoff." The first candidate is
the Approval winner. The second candidate is selected using the
following variation of the MMPO procedure. In finding the candidate with
the minimum number of maximum votes against, only consider the other
candidates who are more approved than the candidate in question. In
other words, consider only the upper-triangular portion of the pairwise
matrix. That means the least-approved candidate has the most (n-1) other
candidates over which to find the maximum votes against (hence his max
votes against are more likely to be higher as a "penalty" for being
least approved).
Anyway, I am just "brainstorming" at this point. I haven't analysed this
method, but I think it may still pass FBC and LNH because it combines
two methods that both pass those criteria if I am not mistaken.
Admittedly, it *is* more complicated than MMPO but not a lot more, and
the addition of cardinal information may add significant value. I am
making no claims at this point, however.
--Russ
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