The intersection probability: betting with probability intervals

TL;DR

This paper introduces the intersection probability as a natural transformation for probability intervals, enabling decision making under uncertainty similar to belief functions, and discusses its theoretical foundations and potential applications.

Contribution

It proposes the intersection probability as a new, principled transformation for probability intervals, bridging the gap with decision-making frameworks.

Findings

The intersection probability aligns with belief function transformations.

It provides a credal rationale based on simplices in the probability space.

A decision-making framework analogous to the Transferable Belief Model is outlined.

Abstract

Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we propose the use of the intersection probability, a transform derived originally for belief functions in the framework of the geometric approach to uncertainty, as the most natural such transformation. We recall its rationale and definition, compare it with other candidate representives of systems of probability intervals, discuss its credal rationale as focus of a pair of simplices in the probability simplex, and outline a possible decision making framework for probability intervals, analogous to the Transferable Belief Model for belief functions.