Quasi-Separable Preferences
(formerly: Conditionally Additive Utility Representations)
Advances in economic theory have made decision theoretic models increasingly complex. Utility functions often lack additive separability, which is a major obstacle for decision theoretic axiomatizations. We address this challenge by providing a representation theorem for utility functions of quasi-separable preferences of the form \(u(x,y,z)=f(x,z) + g(y,z)\) on subsets of topological product spaces. These functions are additively separable only when holding \(z\) fixed. We then generalize the result to spaces with more than three dimensions and provide axiomatizations for preferences with reference points as well as consumption preferences with dependence across time periods. Our results allow us to generalize the theory of additive representations to simplexes and surfaces.