Majorisation as a theory for uncertainty

TL;DR

This paper proposes majorisation as a comprehensive theoretical framework for quantifying and comparing uncertainty across various distributions and real-world applications like climate and energy systems.

Contribution

It introduces operations based on majorisation to analyze uncertainty and demonstrates their effectiveness through diverse examples.

Findings

Majorisation provides a consistent way to compare uncertainties.

The approach applies to climate projections and energy systems.

Operational tools for uncertainty assessment are developed.

Abstract

Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We present operations that can be applied to study uncertainty in a range of settings and demonstrate our approach to assessing uncertainty with examples from well known distributions and from applications of climate projections and energy systems.