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Ranking Multidimensional Alternatives and Uncertain Prospects

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  • Mongin, Philippe
  • Pivato, Marcus

Abstract

We introduce a two-stage ranking of multidimensional alternatives, including uncertain prospects as particular case, when these objects can be given a suitable matrix form. The first stage defines a ranking of rows and a ranking of columns, and the second stage ranks matrices by applying natural monotonicity conditions to these auxiliary rankings. Owing to the Debreu-Gorman theory of additive separability, this framework is sufficient to generate very precise numerical representations. We apply them to three main types of multidimensional objects: streams of commodity baskets through time, monetary input-output matrices, and most extensively, uncertain prospects either in a social or an individual context of decision. Among other applications, the new approach delivers the strongest existing form of Harsanyi's (1955) Aggregation Theorem and casts light on the classic comparison between the ex ante and ex post Pareto principle. It also provides a novel derivation of subjective probability from preferences, in the style of Anscombe and Aumann (1963).

Suggested Citation

  • Mongin, Philippe & Pivato, Marcus, 2012. "Ranking Multidimensional Alternatives and Uncertain Prospects," MPRA Paper 42515, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:42515
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    References listed on IDEAS

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    1. repec:hal:cesptp:hal-01241819 is not listed on IDEAS
    2. Dorian Jullien, 2016. "Under Uncertainty, Over Time and Regarding Other People: Rationality in 3D," GREDEG Working Papers 2016-20, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), University of Nice Sophia Antipolis.
    3. Zuber, Stéphane, 2016. "Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 78-83.
    4. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," Les Cahiers de Recherche 1057, HEC Paris.
    5. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    6. Mongin, Philippe & Pivato, Marcus, 2016. "Social preference under twofold uncertainty," MPRA Paper 71776, University Library of Munich, Germany.
    7. Antoine Billot & Vassili Vergopoulos, 2016. "Aggregation of Paretian preferences for independent individual uncertainties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 973-984, December.
    8. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Documents de travail du Centre d'Economie de la Sorbonne 17028, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01539444, HAL.
    10. Takashi Hayashi, 2016. "Consistent updating of social welfare functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 569-608, March.
    11. Antoine Billot & Vassili Vergopoulos, 2014. "Utilitarianism with Prior Heterogeneity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01021399, HAL.
    12. Mark Schneider, 2016. "Dual Process Utility Theory: A Model of Decisions Under Risk and Over Time," Working Papers 16-23, Chapman University, Economic Science Institute.
    13. Paul J. Healy & Yaron Azrieli & Christopher P. Chambers, 2016. "Incentives in Experiments: A Theoretical Analysis," Working Papers 16-03, Ohio State University, Department of Economics.

    More about this item

    Keywords

    additively separable; multiattribute decisions; utilitarian; social welfare; social aggregation; ex ante Pareto; input-output matrix; subjective expected utility;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D57 - Microeconomics - - General Equilibrium and Disequilibrium - - - Input-Output Tables and Analysis
    • D60 - Microeconomics - - Welfare Economics - - - General

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