Simple Characterizations of Approval Voting

With D. Peters
Working paper (August 2019)

Approval voting allows every voter to cast a ballot of approved alternatives and chooses the alternatives with the largest number of approvals. Due to its simplicity and superior theoretical properties it is a serious contender for use in real-world elections. We support this claim by giving seven characterizations of approval voting based on normatively appealing axioms. All our results involve the reinforcement axiom, which requires choices to be consistent across different electorates. In addition, we consider strategyproofness, consistency with majority opinions, consistency under cloning alternatives, and invariance under removing inferior alternatives. We prove our results by reducing them to a single base theorem, for which we give a simple and intuitive proof.