Juho,

If instead the votes were
>
> 45: L>>C>R 20: C>>R>L 35: R>>C>L then all the candidates are in the  
> initial DM set, so C is eliminated and then the "new DM set" is {R}  
> so R wins.
  

In this case Ranked Preferences would elect L. 
Imagine that this is the first election after the abandonment of  FPP, and you have just unveiled
this result in front of an audience of  supporters of  Condorcet methods, IRV and even DSC.

http://wiki.electorama.com/wiki/DSC

They ask you "what is so special about this election profile that you can justify electing the
FPP winner? There is nothing remarkable about it, just that all the voters really want to elect their
favourites."  What do you say to them?

I  think it is just impossible to justify collecting the information that tells us who the Majority Loser
is and then electing that candidate. If  I really believed that on those sincere ballots L should win,
then I would push the DMC(Ranking) method which interprets all candidates ranked above bottom
(or equal bottom) as approved (and so doesn't ask or  "want to know" the voters' ranking of 
unapproved candidates).

That method is very simple. If  the
45: L>>C>R 
20: C>>R>L 
35: R>>C>L

votes are sincere, then the DMC(Ranking) election will look just like FPP
(with the embarrassing ML "information" thankfully concealed).

BTW, DMC(Ranking) is one of the single-winner methods that for what it's
worth I "endorse" as a practical reform proposal for the US.

I hope the readers of this list  
will point out any potential weaknesses.
Unfortunately the fact that your method is so complicated and  such a daunting chore to operate makes
this less likely.
In principle I think all the candidates should be compared  
simultaneously against each others. 
This seems to be just an aesthetic prejudice of yours that you don't justify. The traditional justification
for doing it that way is that other ways tend to fail mono-raise. You haven't suggested that your method
meets that. (DMC does).


Chris  Benham



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