[EM] Addenda: Who is wronged in MMPO bad-example? MCA protection of top-rated from middle-rated. 3-slot SFC. The 100, 15, 0 example.

[Kristofer Munsterhjelm]

MIKE OSSIPOFF wrote:
> Kristofer:
> 
> I'd said:
> 
>> MIKE OSSIPOFF wrote:
>>> Who is wronged in Kevin's MMPO bad-example? 
>>> -------------------------------------------
>>> 
>>> Yesterday I asked how bad C can be, in that example, if nearly all 
>>> the A voters are indifferent between B and C, and the only one not 
>>> indifferent prefers C to B.
>>> 
>>> I'd like to additionally ask who is wronged in that example.
>>> Someone who is indifferent between the winner and the other top
>>> candidate? Hardly.
>>> 
>>> Surely the "wrongness" of a result must be judged by whether or not
>>>  someone is wronged by it.
>>> 
>>> Kevin's MMPO bad-example, MDDTR's Mono-Add-Plump failure, are 
>>> Plurality-prejudice aesthetic matters.
> 
> You replied:
> 
>> If some candidate gets more first place votes than another candidate
>>  gets any place votes, it seems only reasonable to not elect the
>> latter. Call it aesthetic if you want

> Yes.

> You continued:
> 
>> , but anything that breaks it that flagrantly will seem really
>> unintuitive to the voters.
> 
> [endquote]
> 
> Perhaps, but, as I've pointed out, every rank method is going to act
> counterintuitively or unaesthetically sometimes. We don't choose a
> rank method for all-the-time aesthetics. We choose one for the
> _practical_ guarantees that it can offer. Ways that it can ease
> voters' strategy dilemmas.

Not only strategy dilemmas. It's also important to know how the method 
behaves under honesty. A monotonicity failure like IRV's might be hard 
to wilfully exploit, but I still think that when it happens - when the 
actual ballot set is one of a pair that exhibits monotonicity failure - 
the method got the answer wrong.

As an extreme, although not in a criteria compliance fashion, Random 
Candidate is strategy-proof (with exception of strategic nomination), 
but in practice returns bad results.

> As tell you what I told Chris Benham: I'm not saying that you're
> wrong about the criteria that you judge by. That's an individual
> matter. There's no reason why we should all have the same goals and
> purposes with voting systems.
> 
> I'm more interested in practical guarantees for the voter, to
> alleviate or avoid defensive strategy dilemma. But I can't, and
> don't, criticize others for not sharing those same goals.
> 
> You continued:
> 
>> So you ask who's wronged in the example. I would say that the
>> combined group of the A-first and B-first voters are wronged
> 
> [endquote]

> But you know that won't do. You can't say that the A voters are
> wronged. They're nearly all indifferent between B and C (except for
> the one who prefers C to B). For the same reason, you can't say that
> the B voters are wronged.

Sure it will. Many criteria deal with coalitions of voters. The clone 
independence criterion ensures all the clone voters - who many not be 
ranking the clones in the same order - that the presence of those clones 
won't affect the outcome. The mutual majority criterion similarity gives 
guarantees to a majority voting the same set of candidates first (not 
necessarily in the same order), and the Condorcet and Smith criteria 
tell voters of different groups that if a majority - not necessarily the 
same majority in every case - ranks X ahead of some other candidate Y, 
and all other candidates take the place of Y, then X wins.

> ...by electing someone they like no less than the other candidate?
> 
> If the A voters aren't wronged, and the B voters aren't wronged, then
> certainly the A and B voters are not wronged.

I don't agree. To use an analogy, say you have some cake. There are two 
groups. The first group, A, wants to have the cake, but doesn't want 
anyone else to have it. The same goes for the second group, B. So you go 
over to a random person and give him the cake instead (this person 
represents the 2 preference for C-top-equal preferences).

Now A says "hey, you could have given it to us instead", and B says 
"hey, you could have given it to *us* instead". By giving the cake to 
the random person instead of letting one of the groups have it, you have 
made both groups unhappy.

You could of course argue that "if I gave it to B, A would have been 
just as unhappy, and if I gave it to A, B would have been just as 
unhappy, so I dare you to show me the particular group that has been 
wronged by this". I still think that you can say that you wronged the 
two groups as a whole - hence my statement of "how you traded off 9999 
voters to please two".

> You wrote:
> 
>> Pleasing the two A=C and B=C voters is not worth 9999 votes.
> 
> [endquote]
> 
> I've emphasized that I don't justify MMPO's result by saying that
> it's for those two voters. MMPO's rule's purpose is to meet FBC, SFC
> or SFC3, Later-No-Harm, CD, and Mono-Add-Plump.
> 
> And the cost of those big advantages is...what? The election of
> someone that over whom no one prefers anyone other than their
> favorite?

So to be more precise, you're pleasing the two voters at the cost of the 
9999 others so that you can pass the criteria above. If you highly value 
the FBC, I can see that the criteria could outweigh the bizarre result. 
In my particular case, I don't consider FBC very important. Sure, high 
levels of FBC failure is bad, but these tend to show up as failures of 
other criteria too.

But even if you like the FBC, couldn't you use one of the other methods 
that pass FBC? I don't think any of these have such serious instances of 
getting it wrong as Kevin's example shows MMPO does.

(Though if you consider it important that a method should pass all the 
criteria above, and do so more than you think MMPO gets it wrong in 
Kevin's scenario, then sure.)