Universal Choice Spaces and Expected Utility: A Banach-type Functorial Fixed Point

This paper utilizes a Banach-type fixed point theorem in a functorial context to develop Universal Choice Spaces for addressing decision problems, focusing on expected utility and preference uncertainty. This generates an infinite sequence of optimal selection problems involving probability measures on utility sets. Each solution at a given stage addresses the preference ambiguity from the previous stage, enabling optimal choices at that level. The Universal Choice Space is characterized as a collection of finite-dimensional vectors of probability distributions, with the mth component being an arbitrary probability measure relevant to the mth stage of the problem. The space is derived as the canonical fixed point of a suitable endofunctor on an enriched category and simultaneously as the colimit of the sequence of iterations of this functor, starting from a suitable object.