(joint with Nicole Scholz)

In this paper, we study choice under objective risk where the primitive is enriched to include an exogenous equivalence relation on the space of lotteries. We seek conditions on this enlarged primitive, ensuring the existence of an expected utility representation in which the Bernoulli utility index may depend on the partition generated by the equivalence relation. We term this model the Partition Dependent Expected Utility (PDEU) and show examples of recent choice models in the literature on non-expected utility that fall into this class. We prove representation theorems characterizing PDEU preferences when the partition generates convex cells, and under different continuity assumptions. Our theorems address partitions with both countable and uncountable elements, with cells that can be lower-dimensional, fully dimensional, or a combination of both. We show that for fully dimensional cells, the parameters of the representation are suitably unique, but this is not the case for lower-dimensional cells. We conclude with a discussion of the technical challenges that may arise when studying partitions with non-convex cells.