Some general results on the metric rationalization for social decision rules

The purpose of this paper is twofold. First, to provide a transparent characterization of the family of metrizable social decision rules. Second, to provide the necessary and sufficient conditions for a reasonable metric rationalization. Theorem 1 establishes that the class of metrizable social decision rules is uniquely characterized by a variant of the well-known Pareto condition. Theorem 2 establishes that positional rules can be characterized in terms of a special class of additively decomposable quasi-metric rationalizations. Theorem 3 characterizes strong positional rules in terms of reasonable metric rationalizations.