[EM] Minmax ranked method

robert bristow-johnson rbj at audioimagination.com
Wed Nov 8 11:32:37 PST 2017

---------------------------- 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>


> On 11/07/2017 03:55 AM, robert bristow-johnson wrote:



>> ---------------------------- Original Message ----------------------------

>> Subject: Re: [EM] Minmax ranked method

>> From: "Kristofer Munsterhjelm" <km_elmet at t-online.de>

>> Date: Mon, November 6, 2017 7:36 am

>> To: rbj at audioimagination.com

>> "EM" <election-methods at lists.electorama.com>

>> --------------------------------------------------------------------------


>>> In the Minmax Condorcet method, what you're taking the minimum of the

>>> maximum of is the Condorcet matrix. The Minmax method chooses the

>>> candidate with the weakest (minimal) greatest (maximal) defeat, i.e. the

>>> candidate who loses the least one-on-one to the candidate he loses the

>>> most to.


>> and that is the same candidate who is chosen by RP (margins) and by

>> Schulze (margins).


> Only for three candidates. For instance, Schulze and RP are cloneproof,

> but Simpson is not; e.g.

> https://en.wikipedia.org/wiki/Independence_of_clones_criterion#Minimax


>>> When there's a Condorcet winner, that CW doesn't lose to

>>> anybody, and so he's the winner of the Minmax method since you can't do

>>> better than not losing at all.


>> i understand there is no issue (with any of those 3 methods: Minmax, RP,

>> Schulze) when there is a CW. my specific question was about the case

>> that there is no CW and a Smith set of 3 candidates, which i think is

>> the Rock-Paper-Scissors scenario.


> 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
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
that's the opinion of an armchair voting systems advocate.

r b-j                  rbj at audioimagination.com
"Imagination is more important than knowledge."
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