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Spherical Preferences

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  • Christopher P. Chambers
  • Federico Echenique

Abstract

We introduce and study the property of orthogonal independence, a restricted additivity axiom applying when alternatives are orthogonal. The axiom requires that the preference for one marginal change over another should be maintained after each marginal change has been shifted in a direction that is orthogonal to both. We show that continuous preferences satisfy orthogonal independence if and only if they are spherical: their indifference curves are spheres with the same center, with preference being "monotone" either away or towards the center. Spherical preferences include linear preferences as a special (limiting) case. We discuss different applications to economic and political environments. Our result delivers Euclidean preferences in models of spatial voting, quadratic welfare aggregation in social choice, and expected utility in models of choice under uncertainty.

Suggested Citation

  • Christopher P. Chambers & Federico Echenique, 2019. "Spherical Preferences," Papers 1905.02917, arXiv.org, revised Feb 2020.
    • Handle: RePEc:arx:papers:1905.02917
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    References listed on IDEAS

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    1. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804.
    2. Epstein, Larry G & Segal, Uzi, 1992. "Quadratic Social Welfare Functions," Journal of Political Economy, University of Chicago Press, vol. 100(4), pages 691-712, August.
    3. Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
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    5. Marc Henry & Ismael Mourifié, 2013. "Euclidean Revealed Preferences: Testing The Spatial Voting Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(4), pages 650-666, June.
    6. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
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    13. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    14. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2020. "Stochastic Dominance under Independent Noise," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1877-1900.
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    Cited by:

    1. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "Monotone Additive Statistics," Working Papers 2021-36, Princeton University. Economics Department..

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