[EM] Minmax ranked method

[robert bristow-johnson]

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

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> On 11/06/2017 08:02 AM, robert bristow-johnson wrote:

>>

>>

>>

>>

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

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

>>

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

>> Date: Sun, November 5, 2017 3:39 pm

>> To: rbj at audioimagination.com

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

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

>>>

>>> For each potential council, there's a voter that's most displeased with

>>> having that council elected. A minmax method minimizes how displeased

>>> this most displeased voter is (which may be a different voter for

>>> different proposals).

>>>

>>> In veto situations, if a minority can say "nope", it's more important

>>> that no such minority can be annoyed enough that they do so than just

>>> how annoyed the rest of the voters get.

>>>

>>

>> and, for a Smith set of size 3, Minmax picks the same candidate as does

>> Ranked-Pairs (margins) as does Schulze (margins), right? i just wanna

>> make sure i got that right.

>>

>> so how is the rule worded differently for these three methods in this

>> context of 3 candidates?

>

> That's because the word "minmax" is used in two different contexts.



i understand that now.  but i mean in the ranked-ballot context.  (sorry to poke in this question out of context.)



> 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).
> 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.




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