# Piecewise additivity for non-expected utility

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## Abstract

A model of choice under purely subjective uncertainty, *Piecewise Additive Choquet Expected* utility, is introduced. PACE utility allows for optimism and pessimism simultaneously, but represents a minimal departure from expected utility. It can be seen as a continuous version of NEO-expected utility (Chateauneuf et al. in J Econ Theory 137:538–567, 2007) and, as such, is especially suited for applications with rich state spaces. The main theorem provides a preference foundation for PACE utility in the Savage framework of purely subjective uncertainty with an arbitrary outcome set.

## Keywords

Optimism Pessimism Inverse-S Choquet expected utility NEO-additive capacities Probabilistic sophistication## JEL Classification

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