When Voters Strategize, Approval Voting Elects Condorcet Winners but Condorcet Methods can Elect Condorcet Losers

We show that approval voting strategic equilibria are closely related to honest Condorcet Winners. There exists an approval equilibrium with a clear font-runner F and runner-up R if and only if the F is the clear Condorcet Winner and R the Condorcet runner-up. In contrast, we show that margins-based Condorcet methods can elect a Condorcet Loser with non-zero probibility when voters vote tactically. With strategic agents, approval voting is better at electing Condorcet Winners than some Condorcet methods! It turns out these ideas were previously discovered by J.F. Laslier [6] and Burt Monroe [7].