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

Russ Paielli 6049awj02 at sneakemail.com
Mon Jun 20 21:29:37 PDT 2005

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

My calculation shows

A: 51 against
B: 48 against
C: 51 against

If that's correct, I wouldn't call it "decisive." Nevertheless, the fact 
that B wins at all is certainly an embarrassment, considering that only 
4 of 100 voters ranked B above last place.

I commend you on your objectivity and integrity in evaluating your own 
method. MMPO just didn't seem right to me, but it would have taken me 
quite a while to find an example like that.

Please correct me if I am wrong, but I assume this means you no longer 
advocate MMPO.


>>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 
> 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.

Actually, I think the most likely reason for a voter to "abstain" from a 
pairwise race is also the most likely reason for a voter to abstain from 
the entire election: apathy. Why should a voter spend his time ranking 
the candidates all the way down if he doesn't care about all of them?

Therefore, I still don't think it makes sense to count one and not the 
other in the definition of "majority."

>>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?

I don't recall proposing any such thing. All I said is that whichever 
convention is used is merely a convention. If a voter leaves two or more 
candidates unranked, then one perfectly reasonable interpretation is 
that he considers them all exactly equal. That's what his vote says. If 
he didn't consider them exactly equal, he could have specified a 
preference by ranking them. Given that fact, I don't see why it is not 
perfectly reasonable to split the vote half and half for each pair of 
unranked candidates. You may think the voter did not intend to make them 
exactly equal, but the simple fact is that he did just that.

> 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.

I don't know how it "behaves," but the fact is that Smith/Approval does 
not need to determine margins or winning votes. It simply doesn't come 
up. Each pairwise race is essentially binary (ternary if you count the 
possibility of a tie).

>>>>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.

Thanks for the information. It sounds reasonable. I'll give it some thought.


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