Approval voting, of course, isn’t a Condorcet system either. In fact it can pick the Condorcet loser—even in a situation with a strong Nash equilibrium.
Really? This isn’t obvious to me, and a quick attempt to construct a counterexample has failed and Google doesn’t turn anything up either. Could you give a hint about how to construct this?
I got the result from http://dimacs.rutgers.edu/Workshops/DecisionTheory2/laslier.pdf . This deals with the preferences of the voters as utility functions (in such a way that it’s not all that easy for me to turn it into “X voters want candidate Y”), but has at least one example that would elect the Condorcet winner with probability only 1/64 while the Condorcet loser would be elected with probability 31⁄64...
Really? This isn’t obvious to me, and a quick attempt to construct a counterexample has failed and Google doesn’t turn anything up either. Could you give a hint about how to construct this?
I got the result from http://dimacs.rutgers.edu/Workshops/DecisionTheory2/laslier.pdf . This deals with the preferences of the voters as utility functions (in such a way that it’s not all that easy for me to turn it into “X voters want candidate Y”), but has at least one example that would elect the Condorcet winner with probability only 1/64 while the Condorcet loser would be elected with probability 31⁄64...