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

[Kevin Venzke]

Hi Chris,

--- En date de : Dim 11.1.09, Chris Benham <cbenhamau at yahoo.com.au> a écrit :
> Kevin,
> 
> You wrote (10 Jan 2009):
> 
> 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}."
> 
> Oops!  (I knew that!)  Sorry for falsely contradicting
> you.

I guessed you must have known that.

> >"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."
> 
> Well I don't. If none of the election criteria were
> incompatible with each
> other, wouldn't we say that nearly all of them are
> "important"?

I don't think so. There are reasons for criteria to be "important"
other than how easy they are to satisfy. Otherwise why would we ever
bother to satisfy the difficult criteria?

> "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."
> 
> No. With mono-add-top and Participation, the
> quasi-intelligent device in
> reviewing its decision to elect X gets (possibly
> relevant) information about
> other candidates besides X.

How can it be relevant? X was winning and X is the preferred candidate
on the new ballots.

> With mono-add-plump it gets
> nothing but information
> about and purely in favour of X, so it has no excuse at all
> for changing its "mind"
> about electing X.

I don't think the information is purely "about" X. The method also learns
about indecision between Y and Z.

>  >"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?"
> 
> It's absurd that ballots that plump for X should in any
> way be considered relevant
> to the "strength" of the pairwise comparison
> between two other candidates.
> This absurdity only arises from the
> algorithm specifically using (and relying on) a
> majority threshold.

Instead of "strength" you could view it as "decisiveness."

This is moot anyway, isn't it? We have Mutual Majority and beatpath GMC
displaying the same phenomenon. Clearly there's no problem since neither
criterion requires failures of mono-add-plump.

> "It would be better, as in less arbitrary, if you
> simply criticized that beatpath GMC is 
> incompatible with ratings summation."
> 
> So is Condorcet. I don't think it's particularly
> "arbitrary"  to value electing a voted
> Shwartz winner. I'm still a bit confused as to why
> anyone would be interested in
> "beatpath GMC".

Well, it's a majority-rule criterion that is compatible with clone
independence and monotonicity. In the three-candidate case it's also
compatible with LNHarm. By adding a vote for your second choice, you
can't inadvertently remove your first preference from the CDTT.

> "So essentially, Schwartz//Approval is preferable to
> any method that satisfies SMD, 
> Schwartz, and beatpath GMC."
> 
> Yes, much preferable to any method that satisfies
> "beatpath GMC" period
> 
> "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."
> 
> And why is that a negative?  I value LNHarm as an absolute
> guarantee, but in inherently- 
> vulnerable-to-Burial  Condocet methods, I think it is
> better if they have a "watch who you rank
> because you could help elect them" Approval flavour.

This is a negative because it suggests that your positional criterion
will be self-defeating. If you want to write a criterion about burial,
that would probably be better.

> From your earlier post:
> "In the three-candidate case, at least, I think
> it's a problem to elect a candidate who isn't in the
> CDTT."
> 
> Why?

Because in the three-candidate case this is likely to be a failure
of MD or SFC, or close to it.

> 25: A>B
> 26: B>C
> 23: C>A
> 26: C
> 
> In this "situation 2" election from my
> demonstration, can you seriously contend (with a straight
> face)
> that electing C is "a problem"?

It's not ideal. You have to use the B>C votes contrary to the wishes of
those voters, and for little purpose that isn't self-defeating 
considering that voters will just truncate, accomplishing the same result 
as if you had just guaranteed in the first place that the C preference 
wouldn't unnecessarily hurt B.

I can see justifying the election of C using burial-related arguments,
or FBC. But that doesn't mean it's not a problem.

> Refresh my
> memory: who first suggested  "Max. Approval
> Opposition" 
> as a way of measuring a candidate's strength?

Probably me, in 2003.

Kevin Venzke