[EM] All uncovered options may be definitely defeated

[Chris Benham]

Jobst Heitzig wrote:

>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:
>
>Example:
>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...
>
>Jobst
>
Since these Condorcet methods that meet Definite Majority (ASM, DMC, 
Smith//Approval) all meet
Smith, then your concern about "covering defeats" can only be about 
situations with more than three
candidates in the Smith/Schwartz set.

For public political elections that for me is not a practical worry, 
whereas Definite Majority applies in
many relatively common-place 3-candidate scenarios.

Chris Benham





>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:
>
>Example:
>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...
>
>Jobst
>  
>
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>