A Unified Theory of Human Judgements and Decision-Making under Uncertainty.

Sandro Sozzo,Raffaele Pisano

doi:10.3390/e22070738

Abstract

Growing empirical evidence reveals that traditional set-theoretic structures cannot in general be applied to cognitive phenomena. This has raised several problems, as illustrated, for example, by probability judgement errors and decision-making (DM) errors. We propose here a unified theoretical perspective which applies the mathematical formalism of quantum theory in Hilbert space to cognitive domains. In this perspective, judgements and decisions are described as intrinsically non-deterministic processes which involve a contextual interaction between a conceptual entity and the cognitive context surrounding it. When a given phenomenon is considered, the quantum-theoretic framework identifies entities, states, contexts, properties and outcome statistics, and applies the mathematical formalism of quantum theory to model the considered phenomenon. We explain how the quantum-theoretic framework works in a variety of judgement and decision situations where systematic and significant deviations from classicality occur.

Highlights

Set-theoretic algebraic structures, like Boolean algebras, are the building blocks of classical (Boolean) logic and classical (Kolmogorovian) probability
We review the quantum conceptual explanation that we have recently elaborated for the disjunction effect—the empirically observed deviations from classicality can be interpreted as underextension effects, the disjunction effect can be modelled by using the quantum-theoretic framework we have developed in Section 7 for conceptual disjunctions
We have recently developed a theoretical framework, along the lines sketched in Section 6.2, that uses the mathematical formalism of quantum theory to model human DM under uncertainty

Summary

Introduction

Set-theoretic algebraic structures, like Boolean algebras, are the building blocks of classical (Boolean) logic and classical (Kolmogorovian) probability. Whenever a specific cognitive phenomenon is studied and one identifies points (a)–(e) in it, namely, the conceptual entity, its states, properties, the relevant contexts and the statistics of measurement outcomes, the notions in (a)–(e) are represented in the quantum-theoretic framework in exactly the same way as entities, states, context, properties, probabilities and dynamics are represented in the Hilbert space formalism of quantum theory Proceeding in this way, one can in principle apply the quantum-theoretic framework to any judgement and decision. We show how a representation in Hilbert space can be constructed

Probability Judgement Errors

Decision-Making Errors

Elaboration of a SCoP Formalism for Cognitive Domains

Application of the SCoP Formalism to Human Probability Judgements

Application of the SCoP Formalism to Human Decisions

A Quantum Framework to Represent Concepts and Their Combinations

An Application to Conjunctive and Disjunctive Fallacies

An Application to the Disjunction Effect

A Quantum Framework for Ellsberg-Type Paradoxes

I are prepared by the questionnaire in the

Findings

Conclusions