Ranking multidimensional alternatives and uncertain prospects

Philippe Mongin and Marcus Pivato

Journal of Economic Theory, 2015, vol. 157, issue C, 146-171

Abstract: 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.

Keywords: Multiattribute utility; Separability; Subjective probability; Harsanyi; Koopmans; Ex ante versus ex post welfare (search for similar items in EconPapers)
JEL-codes: D70 D81 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (50)

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Related works:
Working Paper: Ranking Multidimensional Alternatives and Uncertain Prospects (2015)
Working Paper: Ranking Multidimensional Alternatives and Uncertain Prospects (2014)
Working Paper: Ranking Multidimensional Alternatives and Uncertain Prospects (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:157:y:2015:i:c:p:146-171

DOI: 10.1016/j.jet.2014.12.013

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