[EM] MMPO//MMPO fails FBC? (was "New Criterion: The Co-operation/Defection Criterion")

[Kevin Venzke]

Hi Chris and Mike,

--- En date de : Jeu 27.10.11, C.Benham <cbenhamau at yahoo.com.au> a écrit :
> Kevin,
> Addressing Mike Ossipoff on EM, you recently (26 Oct 2011)
> wrote:
> 
> > None of them satisfy FBC, but neither does your
> version of MMPO. 
> 
> Mike's suggested version of  MMPO is to resolve ties
> by eliminating the tied losing
> candidates and then starting again
> 
> Can you please show us an example of it failing FBC?

Mike's method is Condorcet//MMPO//Condorcet//MMPO//etc. Being a 
Condorcet method it would be quite astonishing if it satisfied FBC 
since I think we mostly agree that Condorcet is incompatible with FBC.

However, even if Mike's method were just MMPO//MMPO//MMPO//etc I
still highly doubt that would satisfy FBC, because the candidate
eliminations and recalculations make it unclear that votes will work
as expected. I don't know how to say this much more clearly than that.
But let me ask you, how many FBC-satisfying methods involve eliminating
candidates and then recalculating scores once those candidates are
removed? Not a one. ICA, MDDA, and MAMPO all "disqualify" candidates
but the tie-breaking score at the end doesn't and couldn't depend on
which candidates are disqualified.

Hypothetically, off the top of my head, lowering your true favorite
could remove him from a three-way score tie which then (as a two-way)
is resolved for one of your "other" favorites, whereas the three-way
contest is resolved for a disliked candidate. Not a very likely 
problem, but that's not the point.

Kevin