Source Recursive Expected Utility on Rich Mixture Sets

Building on the Herstein-Milnor mixture set axiomatization of expected utility theory, we employ multiple mixture operators each modeling a source of uncertainty to arrive at a definition of rich mixture sets. This enables a weakening of the reduction of compound lottery axiom leading to an axiomatization of source recursive expected utility (SREU). In general, our approach allows for a broad range of source-based procedural preference and offers a tool to characterize them. In particular, when there is consistent preference for the ``same'' lottery resolved by the preferred source, SREU illuminates a preference for uncertainty being resolved more decisively by the preferred source