Approval Voting with Fixed Electorates, Fixed Agendas and No Ballot Assumptions

We provide an axiomatic characterization of approval voting that does not impose any restriction on the structure of ballots. Voters submit abstract signals whose approval content is identified endogenously through the characterization itself. In contrast to the standard approach in the literature, we consider a fixed electorate and a fixed set of alternatives, and our analysis does not rely on consistency axioms or population-variation arguments. Approval voting is characterized by four axioms: (i) a richness condition requiring that every nonempty subset of alternatives can arise as the outcome under some unanimous profile; (ii) a unanimity axiom guaranteeing that alternatives supported by all voters are selected; and (iii) two axioms that adapt the classical principle of positive responsiveness to our abstract environment. Our results demonstrate that the distinctive properties of approval voting can be identified without presupposing any particular ballot format.