Critical strategies under approval voting: Who gets ruled in and ruled out

We introduce the notion of a "critical strategy profile" under approval voting (AV), which facilitates the identification of all possible outcomes that can occur under AV. Included among AV outcomes are those given by scoring rules, single transferable vote, the majoritarian compromise, Condorcet systems, and others as well. Under each of these systems, a Condorcet winner may be upset through manipulation by individual voters or coalitions of voters, whereas AV ensures the election of a Condorcet winner as a strong Nash equilibrium wherein voters use sincere strategies. To be sure, AV may also elect Condorcet losers and other lesser candidates, sometimes in equilibrium. This multiplicity of (equilibrium) outcomes is the product of a social-choice framework that is more general than the standard preference-based one. From a normative perspective, we argue that voter judgments about candidate acceptability should take precedence over the usual social-choice criteria, such as electing a Condorcet or Borda winner.