Condorcet Consistency of Approval Voting: a Counter Example in Large Poisson Games

Approval Voting is analyzed in a context of large elections with strategic voters: the Myerson’s Large Poisson Games. We first establish the Magnitude Equivalence Theorem which substantially reduces the complexity of computing the magnitudes of the pivot outcomes. Furthermore, we show that the Condorcet Winner need not be the Winner of the election in equilibrium under Approval Voting. Indeed, a “paradoxical” example is provided where a candidate ranked first by more than half of the voters is not the Winner of the election.