[EM] minmax is not a good public election method

James Green-Armytage jarmyta at antioch-college.edu
Tue May 31 19:30:06 PDT 2005

James replying to Kevin, on the subject of minmax(pairwise opposition),
a.k.a. MMPO...

>> 	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
>> ground at best.
>IRV has MMC (which doesn't really guarantee much), "Condorcet Loser"
>doesn't really guarantee much), and Clone Independence, which I agree is

	We seem to be looking at this in opposite ways. MMC and CL don't
guarantee a very good result ("good" with respect to expressed
preferences, of course), but failing them can mean a very bad result. In
other words, MMC and CL might be easy to pass, but if they are failed,
it's a rather heinous failure. For this reason, I consider them to be
important criteria.
	I don't consider absolute clone independence to be very important, but I
don't like methods that are very sensitive to cloning. Borda is of course
the worst example of this. Minmax's IC failure is less severe than
Borda's, but more severe than methods like SD and Smith//minmax.

>In return, one gets from MMPO FBC, monotonicity, and Woodall's 
>"Condorcet(gross)." In the three-candidate case, one also gets MMC,
>Defense, and Participation.

>> 	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.
>I suggest using CDTT,MMPO instead, then, so that MMC is satisfied. 

	If the electorate is ready for something as complicated as that, then
beatpath(wv), ranked pairs(wv), and river(wv) will be viable options.
Aren't these methods more elegant than CDTT,MMPO?

>I don't
>agree that even weak defeats need to be acknowledged, particularly if
>something else is gained by it, such as LNHarm.

	You mean non-majority defeats, right? Does CDTT,MMPO retain both FBC and
>> My
>> near-supermajority MMC failure example is an extreme one. Smaller mutual
>> majorities can be thwarted by cycles that are less improbable.
>That is barely true. Any example needs a majority-strength cycle.

	Yes it does, and bare majority strength cycles are more probable than
supermajority strength cycles. How likely are majority strength cycles,
occurring naturally? Not very likely, perhaps, but once again I think that
the liability is unnecessary.

>> 	So, in choosing MMPO instead of something like beatpath, you are
>> 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).
>> don't know if I can change your mind about this, but at least I can
>> my opinion that this is a very misguided trade.
>I wonder if you realize how related those five criteria are.

	I believe that Smith implies Condorcet, MMC, and CL. I don't think that
IC is as closely related to the other four.
>I'm not at all sure I would suggest MMPO rather than Schulze. I would base
>it on what the voters find more palatable.

	I'm glad to hear that at least MMPO isn't your strict favorite. 

>> 	Why do you think later-no-harm is so important?
>Because it gives voters the ability to safely rank all of their
>It reduces defection incentive (that is, defection by truncation). And as
>a result, it is more likely that MMC will be satisfied in practice.

	It is not always safe for voters to rank all preferences in MMPO. As in
WV, truncation (equal ranking) can still be useful (arguably necessary in
some cases) as a deterrent counterstrategy.
	If voters fail to use this strategy, they will sometimes be inviting a
burying strategy against their preferred candidate.

Example (sincere preferences)
46 A>B>C
44 B>A>C
5 C>A>B
5 C>A>B
	The A>B>C voters should vote A>B=C, and the B>A>C voters should vote
B>A=C. Otherwise it is possible for a burying strategy to undermine the
A-B comparison.
>> 	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.
>I'm not sure about this. What if you don't expect that your favorite
>will win? Then ranking him above or equal to your compromise choice can do
>little other than frustrate your compromise's ability to be elected.
	If your favorite candidate (F) really doesn't have enough support to be a
viable candidate, then s/he is unlikely to have a beat against your
compromise candidate (C), in which case C can't be harmed by your
expressing an F>C preference (in Smith-efficient methods). (Thus, your
preference won't cause the election of a greater evil (E).) 
	As for actually ranking C above F (compromising-reversal), this is only
necessary if there is already a big F>C defeat, a big E>F defeat, and a
smaller C>E defeat, and your group is trying to drastically cut down the
F>C defeat so that it becomes the weakest in the cycle. If enough of the
F>C voters get involved in this endeavor, then compromising-reversal can
always be made unnecessary (in ranked pairs/beatpath/river(wv), etc.).
	In cardinal pairwise, if a group of voters ranks F above C, and gives
both candidates a maximum rating, it seems especially unlikely that its
F>C preference will cause E to win instead of C. I argue that cardinal
pairwise has less of a compromising-compression incentive than WV or MMPO,
which means that voters in cardinal pairwise risk less in voting their
favorite *above* their compromise than they do in WV or MMPO.

my best,

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