Decision-making with E-admissibility given a finite assessment of choices

TL;DR

This paper investigates decision-making under uncertainty with limited rejection information, characterizing the most conservative E-admissibility extension and providing an algorithm for computation.

Contribution

It introduces a framework for decision-making with finite rejection data using choice functions and offers an algorithm to compute the conservative E-admissibility extension.

Findings

Characterization of the most conservative E-admissibility extension

Development of a linear feasibility algorithm for computation

Application of choice functions to decision-making with limited information

Abstract

Given information about which options a decision-maker definitely rejects from given finite sets of options, we study the implications for decision-making with E-admissibility. This means that from any finite set of options, we reject those options that no probability mass function compatible with the given information gives the highest expected utility. We use the mathematical framework of choice functions to specify choices and rejections, and specify the available information in the form of conditions on such functions. We characterise the most conservative extension of the given information to a choice function that makes choices based on E-admissibility, and provide an algorithm that computes this extension by solving linear feasibility problems.