Contextual Risk and Its Relevance in Economics

TL;DR

This paper introduces 'contextual risk' in economics, proposing a quantum-like probabilistic framework to model decision-making under uncertainty influenced by context, addressing classical paradoxes and highlighting the relevance of non-Kolmogorovian models.

Contribution

It develops a formalism based on the hidden measurement approach and sphere model to represent contextual risk, bridging economics and quantum-like probabilistic structures.

Findings

Contextual risk models are inherently non-Kolmogorovian.

Quantum-like structures can explain economic paradoxes.

The formalism applies to situations with ambiguity and context influence.

Abstract

Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity' depending on the existence of a (classical Kolmogorovian) probabilistic structure modeling these uncertainty situations. On the other hand, evidence of everyday life suggests that 'context' plays a fundamental role in human decisions under uncertainty. Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian quantum-like framework. In this paper we introduce the notion of 'contextual risk' with the aim of modeling a substantial part of the situations in which usually only 'ambiguity' is present. More precisely, we firstly introduce the essentials of an operational formalism called 'the hidden measurement approach' in which probability is introduced as a consequence of fluctuations in the interaction between entities and contexts. Within the hidden measurement approach we propose a 'sphere model' as a mathematical tool for situations in which contextual risk occurs. We show that a probabilistic model of this kind is necessarily non-Kolmogorovian, hence it requires either the formalism of quantum mechanics or a generalization of it. This insight is relevant, for it explains the presence of quantum or, better, quantum-like, structures in economics, as suggested by some authors, and can serve to solve the aforementioned paradoxes.