Modeling the Disjunction Effect within Classical Probability: A New Decision Process Model and Comparison with Quantum-like Models

TL;DR

This paper introduces a new classical decision process model that can replicate disjunction effects observed in human decision making, challenging the necessity of quantum-like models by showing classical models can produce similar empirical patterns.

Contribution

A novel classical model with continuous expectation parameters is proposed, capable of reproducing disjunction effects and matching quantum-like models in observable predictions.

Findings

Classical model can realize any observed disjunction effect pattern.

Classical and quantum-like models have equivalent observable expressiveness.

Ambiguity representation differs fundamentally between classical and quantum-like approaches.

Abstract

The disjunction effect in human decision making is often taken to show that the classical law of total probability is violated, motivating quantum-like models. We re-examine this claim for the Prisoner's Dilemma disjunction effect. Under the mental-event reading of the opponent-choice events, the conventional classical decision-process model implicitly builds in a certainty-only premise: its standard partition assumptions leave no room for ambiguity, forcing every participant to be certain that the opponent will defect or will cooperate. We relax this by introducing a new classical model in which each participant carries a continuous expectation parameter representing the anticipated likelihood of opponent defection, and the participant pool is partitioned by expectation level; the resulting ambiguity set is precisely the union of the interior expectation bins. In contrast, under the quantum-like event semantics, ambiguous pure states are generic (dense and of full unitarily invariant measure on the unit sphere), so "certainty states" are mathematically exceptional. We prove that an instance of our classical model can realize any empirically observed triple of defection rates across the three information conditions, including strong disjunction-effect patterns, while strictly obeying the classical law of total probability. We further prove that for any such triple produced by a standard quantum-like model of the same experiment, there exists a classical instance reproducing it exactly. In this sense, classical and quantum-like approaches have the same observable-rate expressiveness; their substantive difference lies in how ambiguity is represented and in their respective event semantics, not in a breakdown of classical probability.