Incoherence: a measure of complexity which quantifies ensemble divergence and aleatoric uncertainty

Abstract

Abstract This paper proposes a new measure, named incoherence, which can identify many features of complex systems. It achieves this by quantifying the uncertainty arising from the lack of reproducibility (known as aleatoric) in many real-world systems. This is vital for policy and decision-making, as currently this type of uncertainty is often misinterpreted as a lack of data (known as epistemic) or worse, as lack of confidence in the science. Rather than being an inevitable and irreducible feature of the system at hand, as has been the case with the climate crisis. This ambiguity can be used as an excuse for inaction, where establishing a contingencies-based approach to the decisions would have been much more effective. Incoherence is designed to be both highly intuitive and interpretable so it can be used across disciplines and domains. It does this by using the entropy of a system as a baseline measure, so that it can offer consistency across nearly any structure, dimensionality or data type, be it continuous or discrete.