[EM] three-slot methods

[Kevin Venzke]

Forest,

 --- Forest Simmons <fsimmons at pcc.edu> a écrit : 
> I haven't had time to give these new 3-slot ideas too much thought yet,
> but my first question is, "Which of them satisfy the (weak) FBC?"
> 
> MCA and 3-slot CR both satisfy the (weak) FBC, but do any of these newer
> methods?

I put some thought into this question today, and my answers are not very happy 
ones.  Glad you asked, though.

The unnamed runoff method I most recently posted fails weak FBC badly.  I should've
thought about that one a bit more.  There's a problem in mixing approval defeats
with pairwise defeats.  If Favorite beats Compromise by approval, and it causes a cycle 
to be resolved in favor of Worst, you can't fix that by ranking Favorite=Compromise.
You have to take away Favorite's approval to break the cycle.

MAR fails weak FBC, it seems, because of the majority cutoff, and the fact that
the second round method doesn't meet IIA.  That is, it might be advantageous
to keep a (liked, but losing) candidate from meeting the cutoff, in order to
transfer the win to some compromise.

MAFP is the only method that meets weak FBC, because the second round is unaffected
by deleting losers.  Thus disapproving Favorite can only hurt Favorite, and not
help anyone else.

However, a little thought has led me to realize that MAFP is just MCA on its head.
When multiple candidates have a median rating of "middle" in MCA, the one with the
fewest "worst" ratings is elected.  In MAFP, it's the one with the most "top"
ratings.

Is this better?  It doesn't really seem like it!  ...Back to the drawing board, I
suppose.


Kevin Venzke
stepjak at yahoo.fr


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