  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.
