[Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions

[raphfrk at netscape.net]

From: Paul Kislanko <jpkislanko at bellsouth.net>



> If I understand the meaning of the original example correctly, the answer is
> Asset voting.

> Give every voter 100 points. By the conditions given, both the A and B
> voters think C is 80% as good as their true favorite, so give 5/9 of their
> points to their favorite and 4/9 to C.
>
> A's total is 55 x 5/9 = 275/9
> B's total is 45 x 5/9 = 225/9
> C's total is 55 x 4/9 + 45 x 4/9 = 100 x 4/9 = 400/9 so C wins.

That isn't how asset voting works.  You assign your vote to the elector
that you most trust.  The elector can then assign the vote to any candidate
after negotitation.  

There is a fractional version, but if you trust someone with 4/5 of your
vote, why don't you trust them with 100% of your vote ?

If the candidates are the electors, then the votes would go:

A: 55
C: 0
B: 45

A then wins due to having a majority.  There is no reason for him to
assign any of his votes to C.

However, in practice, it might end up

A: 49
C: 11
B: 40

Anyway, the tactical situation is:

A will win if no transfers occur, otherwise, any 2 candidates can
determine the winner.

C doesn't care who wins between A and B, so can convincingly say "Elect me or I 
abstain" as the default is just as good as B winning.

B can then transfer his votes to C since he has nothing to lose.

However, in practice, B would probably just let A win.  Even if the chance is small 
that C was bluffing and thus votes for him, it is better than certainty of not 
being elected if he transfers his votes to C.

Also, the B party would benefit from not electing C as it strengthens larger 
parties.  B would also gain due to not having being bluffing when he said to C
"Elect me or I also abstain".

Under asset (single winner anyway), it might be better to have electors and
candidates separate.  

The odds based asset is interesting.  This would make it worth combining votes
even if one side had a majority.  There is no threshold where it isn't worth it.
There is still the conflict between the electorate and the candidates.  A voter
might prefer the compromise, but a candidate will value being elected more than
the issues the voter supported him for.



 


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