Multi-Utilitarianism in Two-Agent Quasilinear Social Choice

We introduce a new class of rules for resolving quasilinear social choice problems. These rules extend those of Green. We call such rules multi-utilitarian rules. Each multi-utilitarian rule is associated with a probability measure over the set of weighted utilitarian rules, and is derived as the expectation of this probability. These rules are characterized by the axioms efficiency, translation invariance, monotonicity, continuity, and additivity. By adding recursive invariance, we obtain a class of asymmetric rules generalizing those Green characterizes. A multi-utilitarian rule satisfying strong monotonicity has an associated probability measure with full support.