[EM] Re: Equilibrium in Approval Voting

[Adam Tarr]

Alex wrote:

>So not every election of the Condorcet candidate is a Nash equilibrium, 
>but every Nash equilibrium elects the Condorcet candidate.

This looks right, assuming of course that a Condorcet winner exists.

>Is every Nash equilibrium sincere?  Have to think about that.  Seems like 
>every Nash equilibrium should be sincere under approval voting, but I'll 
>have to get to that later.

Well it really depends on the definition of sincerity, I suppose.  But by 
most reasonable definitions, approval voting _never_ gives incentive to 
vote insincerely, since your strategy is simply a question of where to set 
your approval cutoff.  In plurality voting, to give an alternate example, a 
Nash equilibrium could easily involve burying your favorite, which is 
insincere by most definitions.

Again, the location of Nash equilibria isn't really a function of the 
strategy (or sincerity) of the voters; the only things that matter are the 
preferences of the voters and the nature of the voting method.  The 
strategies used only dictate whether or not the result will settle on an 
equilibrium.

-Adam