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

Chris Benham cbenhamau at yahoo.com.au
Sun Jan 11 23:03:55 PST 2009


You wrote (11 Jan 2009):

"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?"

Well, if  as I said "none of the criteria were incompatible with each other" then
presumably none of the criteria would be "difficult".

>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."

You know that Condorcet is incompatible with mono-add-top (and so of course
Participation), so if we value compliance with the Condorcet criterion information
about candidates ranked below X must sometimes be relevant. But even if  the 
quasi-intelligent device is mistaken in treating them as relevant, then that is a much
more understandable  and much less serious a blunder than the mono-add-plump

>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.
"We have Mutual Majority and beatpath GMC displaying the same phenomenon."
No. I don't accept that 'being tossed out of the favoured (not excluded from winning)
set' is exactly "the same phenomenon" as 'being joined by others in the favoured set'.
The latter is obviously far less serious.

>"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."
How can it possibly be "self-defeating"?  What is there to defeat?

>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."

"Because in the three-candidate case this is likely to be a failure of MD or SFC, 
or close to it."
I'm happy to have MD, and I don't care about SFC or "close failures" of  MD.
> 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."
Other "majority-rule" criteria with those same properties will suffice. 

"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."
Well since Condorcet is incompatible with LNHarm, that doesn't explain why Condorcet
fans should like it.  Also I think this is mainly just putting a positive spin on gross unfairness
to truncators and the related silly random-fill incentive.
25: A>B
26: B>C
23: C>A
26: C
100 ballots (majority threshold = 51)

B>C 51-27,   C>A 75-25,   A>B 48-26.
In Schulze(Winning Votes), and I think also in any method that meets "beatpath GMC"
and mono-raise, the 26C truncators can virtually guarantee that C be elected by using
the "random-fill" strategy. That is silly and unfair.
Also, by artificially denying  the clearly strongest candidate  any method that doesn't
elect C must be vulnerable to Pushover, certainly much more than those that do elect C.

(not that that is a very relevant strategy problem for the methods like WV that have the
much easier and safer random-fill strategy for the C>>(B<=>C) voters.)

Chris  Benham

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