[EM] Some hard example for Approval Voting

[Jobst Heitzig]

Hello Forest!

Yesterday I wondered whether under Approval Voting there 
would always be some equilibrium of the following kind:
All voters specify "sincere" approvals in the sense that when they prefer X to Y 
they do not approve of Y without approving of X; and no group of voters can improve
their result by changing their specified approvals to some different 
but still "sincere" (!) set of approvals.

I hoped that such weak kinds of equilibria might exist always.

Unfortunately, I get the impression that in the following example 
there is no such equilibrium:

3 D>C>A>B
3 D>A>B>C
5 A>B>C>D
4 C>B>D>A

So, can someone specify a "sincere" way of voting which would be 
proof against "sincere" strategies in the above sense?

For example, the following is not such an equilibrium:
3 D>C>>A>B
3 D>A>>B>C
5 A>B>>C>D
4 C>B>>D>A
Here B wins, but 8 of the 11 voters which prefer A to B can switch to
3 D>C>A>>B
5 A>>B>C>D
without voting "insincerely", but making A the winner.

Also, the following is not an equilibrium of the desired kind:
3 D>C>>A>B
3 D>A>B>C (all or none approved)
5 A>B>C>>D
4 C>>B>D>A
Here C wins, but the 8 voters which prefer A to C can switch to
3 D>A>>B>C
5 A>>B>C>D
without voting "insincerely", but making A the winner.

And so on... 

So, can anybody forecast what will happen with these preferences under Approval Voting??

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