Formal utilitarianism and range voting

•In formal utilitarian voting, voters assign a real number to each alternative.•The alternative with the highest total score wins.•Range voting is the same, only each score must be between zero and one.•We give axiomatic characterizations via reinforcement and overwhelming majority.•We also use two new axioms: maximal expressiveness, and “no minority overrides”.

In formal utilitarian voting, each voter assigns a numerical value to each alternative, and society chooses the alternative with the highest total value. Range voting   is similar, except that each voter’s values are constrained to lie in the interval [0,1][0,1]. We characterize these rules via the axioms of anonymity, neutrality, reinforcement, overwhelming majority, and two novel conditions: maximal expressiveness, and an absence of “minority overrides”.