[EM] summary answers

[Jobst Heitzig]

Dear Curt!

You wrote:
> 1) Are there cases where you would consider a candidate outside the 
> Schwartz set to be the proper winner?
> 2) Are there cases where you would consider a candidate outside the 
> Smith set to be the proper winner?

Yes, definitely: When x,y,z<n/2, then in the sincere situation
x A>>D>B>C
y B>>D>C>A
z C>>D>A>B
the winner should be one of A,B,C, with probability x/n, y/n, z/n, respectively, since D is not approved by anyone. 

DFC (Democratic Fair Choice) gives this result!

> 3) In a two candidate race, if 51% mildly preferred A to B, and 49% 
> passionately preferred B to A, who should win?

That's very difficult since we cannot really compare intersubjectively how passionately one is. 

But at least with the sincere votes
51 A>B, both approved
49 B>>A, only B approved,
I guess that the approval winner B has an equal claim to win than the majority winner A. 

DFC takes this into account by electing A with 51% probability and B with 49% probability!
  
> I was surprised to find out that some of you might say "B".  If that is 
> true, then I find the discussion emphasis on Condorcet tiebreakers kind 
> of odd. 

I perfectly agree with you!

Yours, Jobst
______________________________________________________________
Verschicken Sie romantische, coole und witzige Bilder per SMS!
Jetzt bei WEB.DE FreeMail: http://f.web.de/?mc=021193