“Social Choice: The Science of the Impossible?” in G.R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy (Macmillan and New York University Press, 1987), ch. 1B, pp. 116–131.
(with Georges Bordes and Michel Le Breton) “Social Welfare Functionals on Restricted Domains and in Economic Environments,” Journal of Public Economic Theory7 (2005), 1–25.
Arrow’s “impossibility” and similar classical theorems are usually proved for an unrestricted domain of preference profiles. Recent work extends Arrow’s theorem to various restricted but “saturating” domains of privately oriented, continuous, (strictly) convex, and (strictly) monotone “economic preferences” for private and/or public goods. For strongly saturating domains of more general utility profiles, this paper provides similar extensions of Wilson’s theorem and of the strong and weak “welfarism” results due to d’Aspremont and Gevers and to Roberts. Hence, for social welfare functionals with or without interpersonal comparisons of utility, most previous classification results in social choice theory apply equally to strongly saturating economic domains. PDF file of preprint
“Consistent Dynamic Social Choice Procedures,” preprint, Australian National University, 1975.
“Roberts' Weak Welfarism Theorem: A Minor Correction,” Stanford University Department of Economics Working Paper No. 99-021.
Roberts’ “weak neutrality” or “weak welfarism” theorem concerns Sen social welfare functionals which are defined on an unrestricted domain of utility function profiles and satisfy independence of irrelevant alternatives, the Pareto condition, and a form of weak continuity. Roberts claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued function defined on the Euclidean space of interpersonal utility vectors. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated. PDF file