[EM] 04/04/02 - Rob LeGrand's Three way Tie:

[Adam Tarr]

Don Davidson wrote:

>Rob LeGrand, you wrote:
>
>49:Reagan>Anderson>Carter
>33:Carter>Anderson>Reagan
>18:Anderson>Carter>Reagan
>
>Donald: If this example above is an Approval election then it would be nice
>if at least one voter only approved one candidate.  As it is, your election
>is a three way tie.

I would think that the mistake here is obvious, but since this is the 
second time in three days you have said something to this effect, I will 
state the obvious.  Nobody would vote for their last place choice in an 
approval election.  It would be equivalent to not showing up at 
all.  Likewise, everyone would vote for their fist choice.  The only 
question would be whether people vote for their second choice as well.  So 
the actual election results will fall somewhere between

49:Reagan
33:Carter
18:Anderson

and

49:Reagan,Anderson
51 Carter,Anderson

 From a game theoretic standpoint, the following result is an equilibrium:

49 Reagan
33 Carter, Anderson
18 Anderson

I say it's an equilibrium because nobody has any reason to regret the way 
they voted.  I would suppose (although I have seen no proof of it) that 
such an equilibrium can only exist for the sincere Condorcet winner.

-Adam