[EM] MMPO & FBC. MMPO, PC & SDSC.

[Kevin Venzke]

Hi Mike,

--- En date de : Jeu 27.10.11, MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit :
> Kevin--
>  
> You said that MMPO, as I define it (applied to its own
> ties) fails FBC.
>  
> Presumably you're referring to an allegedly possible
> situation in which Favorite (F) can't win in a
> tie, but Compromise (C) can. So you befefit by making C get
> into the tie, where otherwise F would have.
> You do that by ranking C over F, to lower C's maximum
> pairwise opposition (MPO), and raise that of F.
>  
> Are you sure that works?

Your definition of MMPO is a Condorcet method, so there is no need to
look further.

If MMPO solving its own ties (with no Condorcet winner checking)
satisfied FBC it would be revolutionary, as the first FBC-satisfying
method that eliminates candidates and recalculates scores. This kind
of mechanic is a major problem for FBC because it makes it unclear 
how a given vote will end up affecting the outcome.

FBC-satisfying methods tend to use votes in a very straightforward
manner with no curve balls.

> If C can win in a tie, and F can't, then it must be that C
> has less MPO than does F.
>  
> But, if so, then why do you need to vote C over F to get C
> into the tie?

I am envisioning different numbers of candidates involved in the tie.
So, C can win in a two-way, but C and F both lose a three-way.

> MMPO, PC, and SDSC:
>  
> There have been conflicing statements about whether PC
> (Condorcet//MinMax(wv) ) and MMPO
> meet SDSC.
>  
> I said in an earlier post that Bucklin is the only method I
> know to meet SDSC.
>  
> I hesitate to say for sure right now, but now it seems to
> me that PC and MMPO meet SDSC.
>  
> Has anyone posted examples in which PC &/or MMPO fail
> SDSC?

Well, the WV methods like Schulze, Tideman, and River, as well as MDDA
and MAMPO, all satisfy SDSC. The methods I am proposing to satisfy your
new criterion also satisfy it.

This is the (plain) MMPO example: A majority votes for ABC in some
order over D, and the minority votes D over all of ABC in some order.
ABC are in a cycle each of whose links is stronger than the size of
the combined ABC blocs. So, D has the lowest opposition and wins. It's
a failure of clone-winner, Condorcet Loser, and SDSC.

Kevin