[EM] Re: minmax is not a good public election method

[Russ Paielli]

Kevin Venzke stepjak-at-yahoo.fr |EMlist| wrote:

>>>Well, it seems to me that when the CW loses in MMPO, it is never very ugly.
>>>The MMPO winner would not have any majority-strength loss, for instance.
>>
>>That depends on how you define "majority." If you define it in terms of 
>>the number of voters who voted a preference in that particular pairwise 
>>race, then *every* pairwise loss is a "majority-strength" loss. We've 
>>been over this before, of course. You could also define a "majority" in 
>>terms of all registered or all eligible voters, but why? What is the 
>>fundamental difference between someone abstaining from the entire 
>>election or from one particilar pairwise race? And why should one be 
>>counted and not the other in your definition of "majority"? (That's 
>>intended as a rhetorical question, by the way.)
> 
> 
> Why, because you assume it can't be answered?

No, because I already know the answer and I disagree with it.

> Someone who abstains from the election evidently doesn't care very much
> about the outcome. Someone who abstains from one pairwise contest does so
> for reasons we can't know. When these latter voters cause there to be an
> absence of a majority-strength win, I don't consider the winner of this
> contest to be "cheated" somehow; he could have won, he just needed more votes.
> We don't know if he's *really* the majority's preference in the contest.

First off, I don't necessarily agree with your assumption as to why some 
  eligible voters "abstain" from the election. I've heard many people 
claim that they don't vote because they dislike both major parties and 
the entire process. Yes, that may be an excuse for some, but certainly 
not all. And as for why voters "abstain" from a particular pairwise 
contest, I don't see why it should matter in the tally procedure any 
more than it matters why some eligible voters abstained from the entire 
election.

By the way, one of the great features of Smith/Approval and DMC is that 
the entire "margins vs. winning votes" debate is completely irrelevant 
-- as it should be. The notion that the winner should depend on some 
convention about counting abstentions strikes me as fundamentally wrong. 
(If we count them as equal ratings, why not give each candidate 1/2 
vote? Then margins = winning votes.)

>>>>As most of you realize, we have a dilemma here. You can design an 
>>>>election method that counts sincere votes in a reasonable way, or you 
>>>>can design one that provides little or no incentive to vote insincerely, 
>>>>but you can't do both at once. You want FBC and/or LNH? Then you can't 
>>>>satisfy Condorcet.
>>>
>>>Well, I've suggested a method or two now which satisfy FBC and come so close
>>>to satisfying Condorcet as to make no difference.
>>
>>You've proposed some very innovative ideas, and you are obviously a very 
>>skilled analyst. However, I don't agree that you can "come so close to 
>>satisfying Condorcet as to make no difference."
> 
> 
> Really? Note, I was not talking about MMPO when I said that.

Nor was I. I just don't think that coming "close" to satisfying 
Condorcet is good enough. To me, it's like saying that we can come close 
to determining the winner of a footrace. The goal should be to determine 
the winner, not to just come close. I realize that errors are 
inevitable, but that doesn't mean we should intentionally let a loser 
win because he was "close enough."

>>>I prefer Condorcet//Approval with the special tie rule. Maybe I should give
>>>it an actual name: "Improved Condorcet Approval." It satisfies FBC, and only
>>>fails Condorcet by letting people vote to create pairwise ties. When the CW
>>>loses an "ICA" election, he doesn't have a good claim over the ICA winner.
>>
>>I don't know how ICA works, but it sounds interesting. Do you mind 
>>explaining it or pointing me to its definition? Thanks.
> 
> 
> Sure: Assume the use of a ranked ballot, on which all ranked candidates are
> considered approved. Find the set S containing every candidate X such that for
> any other candidate Y, the number of voters ranking X over Y, plus the number
> of voters ranking X and Y tied at the top, is greater than or equal to the number
> of voters ranking Y over X. If this means that S is empty, then let S contain all
> the candidates. Elect the most-approved candidate in S.
> 
> Suppose the winner is A, but the CW is B. If the B supporters argue that B
> should have won and not A, the ready response is that the voters ranking A and
> B tied at the top intended that A and B have a pairwise tie (and they had the
> numbers to make it happen). Also, A must have had higher approval than B.

That's interesting. At first glance, that appeals to me more than MMPO. 
I'd be interested in knowing why you don't seem to be advocating it very 
strongly. What do you think is its Achilles heel?

--Russ