Utility-Probability Duality: A New Perspective on Decision Making

Title: Utility-Probability Duality: A New Perspective on Decision Making

Authors: Ali Abbas and James E. Matsheson

Abstract: This research introduces a duality between probability distributions and utility functions. The primary problem is to maximize the expected utility over a set of probability distributions. To develop the dual problem, they scale the utility function between zero and one, ensuring it shares the same mathematical properties as a cumulative probability function. They show that reversing the roles of the two functions in the expected utility formulation provides a natural "dual" problem. Many known results for the primary problem can be reinterpreted in the dual problem. For example, they introduce a new quantity, the aspiration equivalent, as the "dual" of the certain equivalent. The aspiration equivalent provides a new method for choosing between lotteries and a win-win situation for principal-agent delegation when used as a target. They also present several new dual results, such as utility dominance relationships and a new saddle-point method for allocating lotteries to decision-makers.

Keywords: utility, probability, duality, aspiration equivalent, utility dominance

Link to Article: https://arxiv.org/abs/0311004v1 Authors: arXiv ID: 0311004v1