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 > > >------------------------------------------------------------------------ > >---- >election-methods mailing list - see http://electorama.com/em for list info > > ---- election-methods mailing list - see http://electorama.com/em for list info