Constitutionally consistent voting rules over single-peaked domains
Résumé
Constitutional consistency requires that the voting rule produce the same outcome at any vote profile as the one it produces at its induced vote profile for any given set of voting rules (or constitution) consisting of the voting rule itself. We consider this type of consistency in two voting models with single-peaked preferences, one with a finite set of alternatives and the other, when the set of alternatives is the interval [0, 1]. We show that cumulative-threshold rules are the only unanimous, anonymous and constitutionally consistent voting rules. These rules assign monotone decreasing (increasing) thresholds to each alternative and pick the minimum (maximum) alternative from the range of the vote profile that receives more cumulative votes (votes received by all the alternatives smaller (or greater) than itself) than the threshold assigned to it. This class of rules consists of the min, max and median rules. The addition of continuity leads to the characterization of k-median rules in the interval voting model.