[EM] All uncovered options may be definitely defeated (was: UncAAO, DMC, ASM, and TACC)

Jobst Heitzig heitzig-j at web.de
Sun Mar 11 15:47:22 PDT 2007

Dear Chris, 

you wrote:
> TACC having that curious property and so electing B here shows that
> it spectacularly fails the
> Definite Majority criterion. Maybe that is forgivable for a  FBC
> method like MAMPO, but not for a
> Condorcet method that bases its result on nothing but pairwise and
> approval information.

You're perfectly right here. It was before we studied definite 
majorities and found DMC that I proposed TACC. 

Unfortunately, there is no method that elects an option which is both 
uncovered and has not definite majority against it, simply because such 
options might not exist:

Pairwise defeats A>B>C>D>A, D>B, C>A, hence covering relation D>>A
Approval scores A>B>C>D, hence definite defeats A>>B>>C>>D.

It seems we have to decide whether we consider definite defeats or 
covering defeats more important...

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