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

[Chris Benham]

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.

>"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"?

"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. 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.

 >"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.   

"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".

"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.

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?

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


Chris Benham


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