Subset Preferences in Linear and Nonlinear Utility Theory

Independence axions based on subset structures are examined within three theories of decision under risk when outcomes are subsets of items. The theories are the linear (expected) utility theory of von Neumann and Morgenstern, weighted linear utility theory, and skew symmetric bilinear (SSB) utility theory. The effects of the independence axioms on subset utilities include several additive and multiplicative decompositions.