Voting with evaluations: When should we sum? What should we sum?

Most studies of the voting literature take place in the arrovian framework, in which voters rank the available alternatives, and where Arrow's impossibility theorem prevails. I consider a different informational basis for social decisions, by allowing individuals to evaluate alternatives rather than to rank them. Voters express their opinion by assigning to each alternative an evaluation from a given set. I focus on additive rules, which follow the utilitarian paradigm. If the evaluations are numbers, the elected alternative is the one with the highest sum of evaluations. I generalize this notion to any set of evaluations, taking into account the possibility of qualitative ones. I provide an axiomatization for each of the two main additive rules: "Range Voting" when the set of evaluations is [0, 1] and "Evaluative Voting" when the set of evaluations is finite.