Ranking multidimensional alternatives and uncertain prospects

• Published in: Journal of economic theory Vol. 157; pp. 146 - 171
• Main Authors: Mongin, Philippe, Pivato, Marcus
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01-05-2015; Elsevier Science Publishing Company, Inc; Elsevier
• Subjects: Agglomeration; Baskets; Chemical Sciences; Commodities; Economic theory; Economics; Economics and Finance; Ex ante versus ex post welfare; Expected utility; Harsanyi; Humanities and Social Sciences; Impact analysis; Koopmans; Mathematical analysis; Multiattribute utility; Multidimensional analysis; Numerical analysis; Polymers; Probability; Ranking; Ratings & rankings; Representations; Separability; Social welfare; Streams; Studies; Subjective probability; Uncertainty; Utilities; Utility functions; Multiattribute utility; Separability; Ex ante versus ex post welfare; D70; D81; Harsanyi; Koopmans; Subjective probability
• ISSN: 0022-0531; 1095-7235
• DOI: 10.1016/j.jet.2014.12.013

We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically not of the Cartesian product form). We apply these representations to (1) streams of commodity baskets through time, (2) uncertain social prospects, (3) uncertain individual prospects. Concerning (1), we propose a finite horizon variant of Koopmans's (1960) [25] axiomatization of infinite discounted utility sums. The main results concern (2). We push the classic comparison between the ex ante and ex post social welfare criteria one step further by avoiding any expected utility assumptions, and as a consequence obtain what appears to be the strongest existing form of Harsanyi's (1955) [21] Aggregation Theorem. Concerning (3), we derive a subjective probability for Anscombe and Aumann's (1963) [1] finite case by merely assuming that there are two epistemically independent sources of uncertainty.