Decision Theory with Prospect Interference and Entanglement

TL;DR

This paper introduces a quantum-inspired decision theory that models human decision anomalies like the disjunction effect and conjunction fallacy through interference and entanglement, providing quantitative explanations for these phenomena.

Contribution

It develops a mathematical framework using Hilbert spaces to explain decision anomalies via interference effects, advancing beyond classical decision theories.

Findings

Disjunction effect explained by intention interference under uncertainty.

Conjunction fallacy modeled by interference terms, matching experimental data.

Interference effects predict and unify multiple decision-making fallacies.

Abstract

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage's sure-thing principle, known as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analysed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect and novel experiments testing the combined interplay between the two effects are suggested.