An information theory for preferences

TL;DR

This paper develops an information-theoretic framework linking utility functions to probability distributions, enabling utility assignment from partial preferences through maximum entropy principles.

Contribution

It introduces a novel utility density function concept and extends maximum entropy utility methods based on the duality between probability and utility.

Findings

Utility density functions are non-negative and integrate to one.

Maximum entropy utility can assign utility values from partial preference data.

The duality between probability and utility underpins the proposed framework.

Abstract

Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative of a normalized utility function. A utility density function is non-negative and integrates to unity. These two properties form the basis of a correspondence between utility and probability. A natural application of this analogy is a maximum entropy principle to assign maximum entropy utility values. Maximum entropy utility interprets many of the common utility functions based on the preference information needed for their assignment, and helps assign utility values based on partial preference information. This paper reviews maximum entropy utility and introduces further results that stem from the duality between probability and utility.