Counterexamples on the Superiority of Approval versus Plurality

We present a simple voting environment with three candidates where the Condorcet winner exists. Under plurality rule, the derived game has a stable set where such a candidate is elected with probability one. However, no stable set of the approval game elects the Condorcet winner with positive probability. We also analyze the robustness of such an example to changes in the number of voters and their preferences. To conclude, we present a generic four‐candidate voting environment with the same properties.