[EM] minmax is not a good public election method

James Green-Armytage jarmyta at antioch-college.edu
Tue May 31 06:04:53 PDT 2005

James here, replying to Kevin...

>> 	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
>> Condorcet loser, and independence of clones criteria.
>Despite those criteria, I consider IRV to be less majoritarian than MM(wv)
>or MMPO, since IRV can't even respect majority preferences with three
>candidates. That is a bigger failing than MMPO failing mutual majority.

	Maybe MMPO is better than IRV; I'm not sure. But IRV does pass a number
of significant criteria that MMPO fails, which means that MMPO is on shaky
ground at best.
	My point is that as long as you are in a political climate that will
welcome a pairwise count method, you should choose a good pairwise count
method, one that at least passes Condorcet, Smith, MMC and CL. These
failures of MMPO are an absolutely unnecessary liability.
	If A beats B, and B has absolutely no beatpath to A, then in my opinion
no good pairwise count method will elect B.

>This is very pessimistic. If minority voters have enough coordination to
>vote insincerely *in a cycle*, surely the majority voters have enough 
>coordination to simply not rank those candidates strictly!

	I grant you that. However, such counterstrategy would of course distort
voter preferences. Also, it is possible that an MMC failure in MMPO could
occur as a result of simple bad luck. Is this likely? Probably not. But
again, my point is that the liability is clearly unnecessary. My
near-supermajority MMC failure example is an extreme one. Smaller mutual
majorities can be thwarted by cycles that are less improbable.
>> 	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,
>> 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
>> to greatly embarrass pairwise count methods in general.
>On the other hand, I'm not sure that a ranked ballot method which fails
>Later-no-harm would be publicly acceptable.
	So, in choosing MMPO instead of something like beatpath, you are willing
to trade Condorcet, Smith, MMC, CL, and IC for later-no-harm and what I
call elimination of compromising-reversal incentive (and you call FBC). I
don't know if I can change your mind about this, but at least I can voice
my opinion that this is a very misguided trade.
	Why do you think later-no-harm is so important? If it guaranteed immunity
to the burying strategy, I would agree that it was very important, but it
doesn't guarantee that at all. MMPO is still vulnerable to the burying
strategy... in practice, probably just about as vulnerable as WV methods. 
	I am aware of the Minnesota decision about Bucklin that seems to use
LNHarm as a supporting argument, but Bucklin's later-no-harm failure is
much worse than any Condorcet method. Plus, as Markus pointed out, the
wording of the Minnesota decisions suggests that later-no-harm failure
might be more acceptable if coupled with later-no-help failure. Also,
there is no particular reason to assume that the LNH fetish of that
particular court would be shared by other high courts.
	As for getting rid of compromising-reversal incentive I think that it's
enough to reduce it to an acceptable level while satisfying other
important criteria like Smith. For example, compromising-reversal
incentives in beatpath(WV) and beatpath(CWP) are extremely minor and
occasional. Eliminating this minor and occasional incentive is not worth
throwing over these important criteria.
	You mention public acceptability. I think that MMC is likely to have much
more public acceptability impact than LNHarm. MMC can be explained as
follows: "Imagine that an electorate is comprised of 55% solid Democrats
and 45% solid Republicans. The Democratic and Republican parties each run
3 candidates. All Democrats rank all 3 Democratic candidates above all
Republican candidates. In ranked pairs, beatpath, SD, IRV, etc., a
Democrat will certainly win. In minmax and Borda, a Republican could
possibly win." I think that many citizens will see this as a major
disadvantage of minmax.

my best,
James Green-Armytage

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