[EM] "Beatpath GMC" compliance a mistaken standard?

[Kevin Venzke]

Hi Chris,

--- En date de : Sam 10.1.09, Chris Benham <cbenhamau at yahoo.com.au> a écrit :
> De: Chris Benham <cbenhamau at yahoo.com.au>
> Objet: [EM] "Beatpath GMC" compliance a mistaken standard?
> À: "EM" <election-methods at lists.electorama.com>, "Kevin Venzke" <stepjak at yahoo.fr>
> Cc: "Markus Schulze" <markus.schulze at alumni.tu-berlin.de>
> Date: Samedi 10 Janvier 2009, 0h31
> Kevin,
> 
> You wrote (9 Jan 2009):
> 
> "Well, with "Mutual Majority," when X may
> win, it's possible that by
> adding bullet votes for X, then every other candidate
> becomes able to
> win."
> 
> No it isn't. (Can you give an example?) 

26 A>B
25 B>A
49 C

Mutual Majority elects {A,B}

Now add 5 A bullet votes:

26 A>B
25 B>A
49 C
5 A

Now Mutual Majority elects {A,B,C}.

By the way, it's very easy to define a single-winner method that
satisfies Mutual Majority and which elects A in the first scenario and
C in the second.

> "Is there any way to explain, why it isn't
> completely absurd, that adding
> bullet votes for X should cause other candidates to become
> eligible to 
> win?"
> 
> No.

Ok.

> "Why is mono-add-plump important?"
> 
> Because as an election method algorithm that fails it
> simply can't have any
> credibility as a quasi-intelligent device (which is what it
> is supposed to be)
> and because satisfying it should be (and is) very cheap.

I feel that cheapness isn't relevant to whether a criterion is important,
and certainly not to whether failing it is absurd. I save the term 
"absurd" for ideas that are bad regardless of what else is available.

Regarding your first reason: Why is it acceptable to fail mono-add-top
or Participation, but not acceptable to fail mono-add-plump? I guess
that you based this distinction almost entirely on the relative cheapness
of the criteria.

> "If we view CDTT somehow as an election method, then
> when it fails
> mono-add-plump, the bullet votes for X are not simply
> "strengthening"
> X, they are also *weakening* some pairwise victory of Y
> over Z, which X
> had relied upon in order to have a majority beatpath to
> Z."
> 
> That just testifies to the absurdity of an algorithm
> specifically putting some
> special significance on "majority beatpaths"
> versus other beatpaths.

You're saying it's absurd, but what is absurd about it? The only reason
X is allowed to win in the first place is due to a decisive Y>Z win
providing a path from X to Z. Why is it clear that X should be entitled 
to remain a possible winner irrespective of the status of this win?

I agree it would be better if this were possible, but I don't see anything
essential about it.

> "Of course, you can always use the mechanics of the
> method to explain why
> something has happened. But it seems to me that the bullet
> voters aren't
> purely "strengthening" X, they are also weakening
> Y and thereby also X".
> 
> This contention that "bullet voters for X aren't
> purely strengthening X" but are
> in some way "also weakening X" is completely
> absurd.

The strengthening and weakening are in two different senses. The
strengthening is in terms of bullet votes. The weakening is in terms
of losing a majority beatpath to a candidate that the voters decisively
prefer.

> "This is an oddity inherent to beatpaths, really"
> 
> I think only to beatpaths that measure "defeat
> strengths" in a silly way.

I don't agree. Just because the use of beatpaths doesn't naturally
cause problems with mono-add-plump, doesn't mean there aren't other
oddities. Why should a candidate's ability to win, ever depend on the
strength of a contest between two other candidates?

> >But I contend that here in my "situation 2"
> >election Beatpath GMC does exclude
> >the clearly strongest candidate C. 
>  
> "You're attacking a lot more than just beatpath
> GMC with this scenario.
> Excluding C is required by SFC (the 51 B voters are
> basically assured
> LNHarm when voting for C, since B might be the sincere CW)
> and also
> basically any WV method."
> 
> Yes, you catch on quick.

It's just a bit puzzling that this thread is phrased as an attack on
beatpath GMC, if the bottom line is that beatpath GMC isn't compatible
with the positional criterion.

> >In other words the CDTT set can fail to include the
> >candidate that on overwhelming 
> >common-sense (mostly positional) grounds is the
> strongest
> >candidate (e.g. C in "Situation # 2").
> 
> "Having read that archive post the motivation behind
> the criteria 
> (especially the Smith-compatible one) is unclear to me.
> ...The only reason you gave for adding a beatpath
> requirement is that 
> you're "still interested" in Condorcet
> methods."
> 
> Sorry, do I need a better reason? 

If you want to be persuasive, then yes. Otherwise when you use this
criterion to attack beatpath GMC, this is no better than explaining that
when you wrote this criterion you weren't interested in beatpath GMC.
Because if you had been interested in it, you could have made it
compatible, as you did for Schwartz.

It would be better, as in less arbitrary, if you simply criticized that
beatpath GMC is incompatible with ratings summation.

>>So given a method that meets what I've been recently calling "Strong 
>>Minimal Defense" (and so Minimal Defense and Plurality) and Schwartz 
>>(and so fails LNHarm and meets Majority for Solid Coalitions), I 
>>consider the addition of compliance with "beatpath GMC" a negative if 
>>without it the method can meet "Smith- Comprehensive 3-slot Ratings 
>>Winner" (which should be very very easy).
> 
> "It should be very easy? What methods are there other
> than Schwartz//Approval?"
> 
> That will do to be going along with.

So essentially, Schwartz//Approval is preferable to any method that
satisfies SMD, Schwartz, and beatpath GMC.

I'd rather describe the benefits of approval completion as 1. simplicity
and 2. better burial resistance. I don't feel there's an advantage to
tending to elect candidates with more approval, because in turn
this should just make voters approve fewer candidates when they doubt
how the method will use their vote. I think it's regrettable that approval
completion can't at least satisfy SFC.

Kevin