Restricting independence to convex cones

Several nonexpected utility models restrict the independence axiom to parti cular families of convex cones. The present paper considers this possibilit y from an abstract point of view. A vector space is endowed with a complete and archimedean preorder satisfying independence on each convex cone of an arbitrary family covering the entire space. Necessary and sufficient condi tions are given for the representability of the preorder by a functional wh ich is linear on each cone of the family. (C) 2000 Elsevier Science S.A. Al l rights reserved. JEL classification: D810.