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

Kevin Venzke stepjak at yahoo.fr
Mon Jun 20 20:18:52 PDT 2005


I was quite wrong about MMPO being unable to elect the Condorcet Loser unless
all candidates have a majority-strength loss. As an example,

48 A
2 B=A
2 B=C
48 C

MMPO elects B decisively. So MMPO fails Plurality even worse than I thought.
I don't know how I forgot this; two-slot MMPO was the first method I advocated
on this list, and I knew it had this problem then.

--- Russ Paielli <6049awj02 at sneakemail.com> a écrit :
> > 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. 

It doesn't matter why they abstain from the election. If I want to complain
that A should have beaten B, the preference of someone who didn't even bother
to vote isn't important.

> 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.

Because those voters have a right to be considered, but we don't know why they
abstained from a given contest. Maybe they did want other voters to decide.
Maybe they felt unable to participate in the contest for strategic reasons.
Maybe they wanted the method to behave exactly as it did. When the method is not
Condorcet, you can't use Condorcet to argue how abstaining voters should be
counted. You don't have their permission. Get them to vote for you next time.

> 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.)

If it is fundamentally wrong to have a convention on abstentions, why do you
propose a convention on abstentions?

Smith//Approval and DMC behave more like WV than margins, by the way, so
it doesn't seem to me that they have "dodged the issue." WV and Approval
both consider the literal number of voters in favor of some position.

> >>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 find that very strange. In my mind Condorcet is a means to an end, it isn't
the end itself. That is, satisfying Condorcet greatly reduces the amount of
strategy most voters need to use. But when Condorcet itself gets in the way of
this goal, I think it can be overruled.

> >>>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?

Well, I don't like to advocate so much. I wouldn't want you to think I'm
advocating MMPO so much as I am responding to arguments that I don't agree
with. But this method (ICA or tC//A) is currently my favorite method.

I don't think it has one single Achilles heel, but here are some downsides:
1. it has a LNHarm problem almost as bad as Approval.
2. unlike Approval, you can't even argue that ICA satisfies Clone-Winner.
3. you need two matrixes to count it.
4. I like 3-slot methods, but if you don't, and use a ranked ballot, voters might
get the mistaken impression that they can/should rank as low as they want.

Some noteworthy advantages:
1. it comes very close to satisfying Condorcet.
2. unlike Smith//Approval or plain Condorcet//Approval, FBC is preserved.
3. if you cause your compromise to fail to be the CW, you still have a very good
chance of electing him, since essentially your vote will just be counted again
with your favorite>compromise pairwise preference deleted.
4. there's practically no burial incentive. Any dummy candidate you elevate over 
your opponent, in attempt to keep him from being the CW, would then have to be 
"approved," just as strongly as the candidate you actually want to win.

It's a very intuitive procedure, I think. If you vote A>B, you are hoping that
A will be able to "win decisively" (as the CW). If he doesn't, and no one else
does, then you'd want to collapse that ranking in order to save B, since A is not 
as popular as you'd hoped. Further, if your last choice wins decisively, you couldn't 
have prevented it by collapsing your ranking.

Kevin Venzke


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