Conditionally Additive Utility Representations

Advances in behavioral economics have made decision theoretic models increasingly complex. Utility models incorporating insights from psychology often lack additive separability, a major obstacle for decision theoretic axiomatizations. We address this challenge by providing representation theorems which yield utility functions of the form u(x,y,z)=f(x,z) + g(y,z). We call these representations conditionally separable as they are additively separable only once holding fixed z. Our representation theorems have a wide range of applications. For example, extensions to finitely many dimensions yield both consumption preferences with reference points Sum_i u_i(x_i,r), as well as consumption preferences over time with dependence across time periods Sum_t u_t(x_t,x_{t-1}).