[EM] Minmax ranked method

Kristofer Munsterhjelm km_elmet at t-online.de
Wed Nov 8 13:52:28 PST 2017

On 11/08/2017 08:32 PM, robert bristow-johnson wrote:
> ---------------------------- Original Message ----------------------------
> Subject: Re: [EM] Minmax ranked method
> From: "Kristofer Munsterhjelm" <km_elmet at t-online.de>
> Date: Wed, November 8, 2017 1:40 pm
> To: rbj at audioimagination.com
> "EM" <election-methods at lists.electorama.com>
> --------------------------------------------------------------------------

>> When there are only three candidates, then RP and Schulze give the same
>> result as Simpson. When there are more candidates but a Smith set of
>> three, then RP and Schulze might give a different result from Simpson.
> the reason i want to be square on this point is only that of advocacy.
> i want to see a Condorcet method advocated for Ranked-Choice Voting
> instead of IRV.  i want to see RCV (Condorcet) adopted for use in
> governmental elections.
> i know that people, like me, that know only enough to be a little
> dangerous, will ask two questions (assuming their fine with the ranked
> ballot, but they are used to IRV).
> 1. they will ask questions about the complexity of the tallying
> algorithm (which, for some reason, they think IRV is simpler), and
> 2. they'll say something about Arrow and ask about what i consider is
> the only conceptual problem with Condorcet which is what happens with a
> cycle.
> because of those two issues i would probably always advocate that Ranked
> Pairs (margins) be the method adopted, even though i think that Schulze
> (margins) would be better (and you're confirming that Minmax would be
> worse) but they're all equivalent in outcome if there is a CW or if the
> Smith set is 3.
> i feel comfortable about that.  first of all, i think that in reality it
> will be very very rare that a cycle happens.  in Burlington 2009 we had
> 5 candidates out of which 4 were serious candidates (that they really
> campaigned) and 3 were all plausible winners.  of those three, one was
> the Plurality winner (of first choice votes), one was the Condorcet
> winner, and one was the IRV winner.  and the supporters of all three all
> said that they're guy deserved to win.  since the CW didn't win the IRV,
> the final round was between the Plurality and the ultimate IRV winner
> and the margin was only 252 votes out of 8900 total.  (the CW beats the
> IRV winner by 587 and beats the Plurality winner by 930.)
> but the Condorcet ordering was solid for *every* subset of candidates.
> we knew who was preferred pairwise over every other candidate.  then if
> you hypothetically remove the CW, then the IRV winner was clearly
> preferred pairwise over every remaining candidate.  if you remove both
> the CW and IRV winner, the remaining Plurality candidate was preferred
> over every other candidate remaining.  there was no doubt who was really
> preferred by the city and what the order of preference was.
> cycles are not gonna happen very often. almost never.
> now, perhaps, once in a blue moon a cycle happens, how often do you
> think the cycle will be any more complicated than a Smith set of 3?  i
> think it will *never* be any bigger than a Smith set of 3 because i
> think a Smith set of 3 will happen almost never.  and since Minmax and
> RP and Schulze pick the same candidate when the Smith set is 3 (and
> Minmax doesn't sound so good anyway), my advocacy is for RP, which in my
> opinion is much easier to explain to people than Schulze or Minmax.  and
> even though i saw Markus post some pretty compact legal language for
> Schulze, it seemed inpenetratable to me.

I can think of two situations where cycles could happen more often:

1. The political landscape changes. E.g. Condorcet breaks two-party rule 
and there's real competition along multiple political dimensions again.

2. The organized participants/parties try to exploit the system.

For the first reason, I prefer systems that generalize well (like Ranked 
Pairs or Schulze, contrasted with say Minmax/Simpson). Voting systems 
should last, because it's really hard to change them, that kind of thing.

For the second reason, I prefer systems that are robust to tactical 
nomination (usually clone independence).

But I wouldn't have a problem with someone proposing a Condorcet method 
that doesn't really pass number one, because as long as it's not 
something obviously flawed (like say "Condorcet if there's a CW, 
otherwise the IRV winner"), just lasting until the kind of political 
environment where there is real competition is a real improvement 
compared to Plurality two-party rule.

Of course, one has to be careful here. FairVote could say that IRV is an 
improvement upon Plurality too - but the problem with IRV is that it 
breaks down too quickly (as you know). Approval, IMHO, has the risk that 
miscalculation on the voters' behalf could produce some very 
counterintuitive results and thus also a backlash. Approval is more a 
"rather risky" thing, whereas IRV is a "definitely fails" thing.

However, I would want the system to have some reasonable resistance to 
point number two. I seem to value tactical nomination resistance higher 
than say, Mike, who values strategic voting resistance more highly.

There are degrees here as well. I'd consider Minmax's clone resistance 
problems to be less severe than Borda's, since Borda's are so serious 
that it's pretty much unusable.

In any event, I agree that Ranked Pairs is easier to explain than 
Schulze. Schulze is probably at least as easy if you're talking to a 
mathematician (since beatpaths can be defined quite elegantly in a 
recursive manner), but Ranked Pairs seem more procedurally clear (sort 
the pairs, lock in unless that causes a contradiction with what you've 
already seen).

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