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 [6]. 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 dropping monotonicity, we characterize the class of generalized multi-utilitarian rules. These rules are associated with a signed measure which assigns total measure one to the set of weighted utilitarian rules.