[EM] New Criterion: The Co-operation/Defection Criterion

[MIKE OSSIPOFF]

I'd said:
 
> There is only one candidate B. It would be nice if {A,B}
> could be replaced
> with a larger set of candidates, but the crierion would
> then probably be
> unattainable.


[unquote]
 
You wrote:
 
By allowing multiple "B" candidates, my criterion is stronger than
yours, and it is attainable.
 
[unquote]
 
By what method?
 
If you're right, that's good news.
 
I don't deny that yur criterion is stronger. I merely question whether
it's attainable.


> You had said:

 
> As far as methods that will satisfy it, we at least have
> some clumsy 
> ones. Any Condorcet method used to complete
> majority-defeat-
> disqualification or CDTT (i.e. Schwartz set that replaces
> sub-majority
> wins with ties) will do the trick. These methods would also
> satisfy
> SDSC fully.
> 
> [endquote]

I'd replied:
 
> Worth checking out. But, even if you're correct about that,
> how many of those methods
> meet FBC?

You write:

None of them satisfy FBC, but neither does your version of MMPO.

[endquote]
 
As has already been asked, do you have an FBC failure example for MMPO?
 
Do you mean that, by ranking a compromise over your favorite, you could get
the compromise into a tie, by lessening the compromise's pairwise opposition and
increasing your favorite's pairwise opposition--Where otherwise your favorite would
go into the tie and lose?
 
Can you show an example?
 
 
I'd said:
 
> Can those methods be shown to meet CD? Of course, the
> burden of proof, in the 
> form of a failure example, is on the person claiming that
> they don't. ...because it's
> often easier to show noncompliance than compliance. But
> even so, what method other
> than MMPO can be shown to meet CD?

[endquote]
 

I am quite confident I can convince you that my above-listed methods
satisfy CD.

Try this method:
1. If possible, eliminate every candidate with a majority loss
2. If there is a CW among remaining candidates, elect him
3. Otherwise elect somebody arbitrarily (doesn't matter)

Isn't it pretty clear that this meets your criterion?

[endquote]

I feel that FBC is more important than CD. 
 
If I had to choose between FBC and CD, I'd choose FBC.
 
If solve-its-own-ties MMPO (which is what I mean by MMPO) 
can be shown to fail FBC, then I'd drop it.
 
But, by the same token, do your CD-complying methods meet FBC?
 
If MMPO fails FBC, can you suggest a method that meets FBC, SFC &/or SDSC, and CD?
 
Can CD be shown to be incompatible with FBC?
 
I'd said:
 
> So, A and B can't not be tied.

[endquote]

You wrote:
 
Okay, that's true. But this is a point where my version of the criterion
is stronger than yours.
 
[endquote]
 
1. But what method meets it? And does that method meet FBC? Is it simple enough to propose
   to the public?
 
2. Can you show an example where MMPO fails FBC?
 
3. If it does, is there a method that meets FBC, SFC &/or SDSC, and CD?