Dear election methods fans,
In response to recent talk about minmax(pairwise opposition), I'd like
to
briefly argue that minmax methods in general are very significantly
inferior to methods that pass the Smith criterion, e.g. beatpath, ranked
pairs, river... even sequential dropping (despite its monotonicity
failure), and Smith,minmax (despite its inelegance).
For public elections, I think that it would make more sense to use IRV
than any minmax version, because at least IRV passes the mutual majority,
Condorcet loser, and independence of clones criteria.
I consider this to be a fatal "failure example" for minmax:
100 voters, strict rankings as follows:
22 RSTZ
21 STRZ
21 TRSZ
12 ZRST
12 ZSTR
12 ZTRS
Pairwise comparisons as follows:
R>S 67-33
S>T 67-33
T>R 66-34
S>Z 64-36
R>Z 64-36
T>Z 64-36
The set {R, S, T} is supported by a 64% mutual majority, and yet Z (the
Condorcet loser) wins.
Any mutual majority up to a 2/3 supermajority can potentially be
thwarted
by a three candidate cycle in minmax. Note that voters who oppose the
mutual majority can contribute to its downfall, which opens up extra
possibilities for strategic manipulation.
I argue that minimax makes no sense as a public election proposal. If
we're going to try to implement pairwise count methods on a big scale, we
should choose good ones. In my opinion, that absolutely cuts out minmax
methods (because of MMC failure, CL failure, etc.) and margins methods
(because of lack of strategic stability). These methods have the potential
to greatly embarrass pairwise count methods in general.
Sincerely,
James Green-Armytage
http://fc.antioch.edu/~james_green-armytage/voting.htm
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