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 [9]. 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, transfer monotonicity, continuity, and additivity. By adding recursive invariance, we obtain a class of asymmetric rules generalizing those Green characterizes. A multi-utilitarian rule satisfying strict monotonicity has an associated probability measure with full support.I would like to thank Youngsub Chun, Federico Echenique, Jerry Green, Biung-Ghi Ju, William Thomson, and Walter Trockel for comments and discussions. Two anonymous referees also provided comments that proved very useful. All errors are my own.