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Published September 2020 | Submitted
Journal Article Open

Spherical Preferences


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.

Additional Information

© 2020 Elsevier Inc. Received 4 September 2019, Revised 15 May 2020, Accepted 22 June 2020, Available online 8 July 2020. Echenique thanks The National Science Foundation for its support through the grants SES 1558757 and CNS 1518941. We are grateful to the associate editor and two anonymous referees for useful comments and suggestions.

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August 22, 2023
October 20, 2023