Positionalist voting rules: a general definition and axiomatic characterizations

The paper proposes a general definition of positionalist voting rules. Unlike the commonly-employed scoring rules, our notion of positionalism allows for non-linear criteria to be included in the requisite class. We define a voting rule as positionalist if, for any profile of strict individual orderings, any two alternatives are compared collectively solely on the basis of their positional scores according to the individual rankings. In contrast to the class of scoring rules, however, we do not restrict attention to linear aggregation procedures. Two plausible unanimity properties are examined in the context of our new class of positionalist rules and, moreover, we characterize the lexicographic extensions that refine the plurality rule and its inverse counterpart.