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 preferred 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" moving away from 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 . As an extension, we consider an endogenous notion of orthogonality .
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 .
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preferred
maintained
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moving away from
either away or towards
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. As an extension, we consider an endogenous notion of orthogonality