Axiomatizations of approval voting

Abstract

Approval voting aggregates individual ballots by identifying the candidates who appear most frequently across a set of approved options. Axiomatic characterizations of this method provide a formal framework for understanding its structural properties and normative implications. These characterizations are categorized into three primary groups based on electoral assumptions. Within a variable electorate framework, approval voting is uniquely identified by the axioms of faithfulness, consistency, and cancellation. Alternatively, it can be defined through consistency combined with disjoint equality and either faithfulness or neutrality. In the context of a fixed electorate, the method is characterized by neutrality, equal treatment, and monotonicity, ensuring that candidate identities are irrelevant and that increased support for a candidate does not result in their exclusion. A third approach, involving a variable electorate drawn from a fixed set of voters, characterizes approval voting through faithfulness, weak consistency, disjoint inclusion, and dual consistency. These various axiomatic systems demonstrate that the method is naturally linked to the aggregation of dichotomous preferences and maintains specific properties regarding strategy-proofness and efficiency. Collectively, these formal derivations clarify the functional mechanics of approval voting as a rule for collective decision-making across diverse electoral conditions. – AI-generated abstract.