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

[MIKE OSSIPOFF]

--- En date de : Lun 24.10.11, MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit :
> Co-operation/Defection Criterion (CD): 
>  
> Premise:
>  
> A majority prefer A and B to everyone else, and the rest of
> the voters all prefer everyone else to A and B.
>  
> Candidate A is the Condorcet candidate
>  
> Voting is sincere except that the B voters (voters
> preferring B to everyone) else refuse to vote A over anyone.
> 
>  
> Requirement:
>  
> The Condorcet candidate wins.
>  
> [end of CD definition]
>  
> I’m only aware of one method that meets CD:  MMPO.
 
You wrote:
 
it seems like a combination
of SDSC and SFC.
 
endquote
 
It has things in common with them, but it's much more difficult to comply
with than SFC is.
 
You wrote:
 
 Basically A will have a majority over B
 
endquote
 
Not necessarily. A will certainly have a pairwise win over B. When the non {A,B} 
candidates lose, and MMPO is applied to its A,B tie, that pairwise win will mean
that B has a greater pairwise opposition than A does.
 
You wrote:
 
, and B will
have a majority over third candidate C (if there are only three)
 
endquote
 
Correct. And if there are more than three candidates,then B will have majority pairwise
opposition against each of them.
 
 
You wrote
 
, and
A will not have a voted majority over C. A might even lose to C (unless
"Condorcet candidate" is defined on cast votes), but it won't be by a
majority.
 
endquote
 
Correct. But A and B will get the same pairwise opposition from C.
 
You wrote:
 
In this scenario, SDSC prevents C from winning and SFC prevents B from
winning.
 
endquote
 
SFC doesn't apply to A and B, because there's no majority voting A (the Condorcet candidate) over
B.
 
 
You wrote:
 
I'm assuming cast ballots look something like this:
48 C>A
~26 A>B
~26 B (sincere is B>A)
Is this wrong?
 
endquote
 
That looks right. It meets CD's premise.
 
In that example, A has a majority defeat against B. But A's status as Condorcet candidate, and the sincere
voting, only guarantee that A has a pair-win against B. But that's all MMPO needs for A to win.