Uncertainty measures: The big picture

TL;DR

This paper critically reviews various theories of uncertainty beyond classical probability, highlighting their classifications, relationships, and levels of generality to provide a comprehensive overview of the field.

Contribution

It offers a systematic organization and critical assessment of diverse uncertainty theories, clarifying their connections and degrees of generality.

Findings

Classical probability cannot fully describe second-order uncertainty.

Uncertainty theories can be grouped into clusters with shared rationales.

The landscape of uncertainty theories is complex with interconnected frameworks.

Abstract

Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty have been proposed, many of them generalisations of classical probability. As we show here, such frameworks can be organised into clusters sharing a common rationale, exhibit complex links, and are characterised by different levels of generality. Our goal is a critical appraisal of the current landscape in uncertainty theory.