classical-disjunction-effect-model

name	classical-disjunction-effect-model
description	Classical probability model that reproduces the disjunction effect in human decision making without violating the law of total probability. Use when analyzing the disjunction effect, Prisoner's Dilemma decision paradox, quantum-like cognition models, classical vs quantum decision models, or ambiguity representation in choice behavior.
metadata	{"arxiv_id":"2603.23233","published":"2026-03-24","authors":"arXiv:2603.23233","tags":["disjunction-effect","classical-probability","quantum-cognition","decision-making","prisoner-dilemma"]}

Classical Disjunction Effect Model

Description

New classical decision process model that reproduces the disjunction effect while strictly obeying the law of total probability. Shows classical and quantum-like approaches have equal observable expressiveness.

Core Theory

The Disjunction Effect

• Violation of sure-thing principle in human decision making
• Conventionally taken to require quantum-like models
• Most studied in Prisoner's Dilemma context

Key Insight: Certainty-Only Premise

• Conventional classical model implicitly assumes certainty-only: no room for ambiguity
• Standard partition assumptions force every participant to be certain opponent will defect or cooperate
• This is the hidden assumption, not a fundamental limitation of classical probability

New Classical Model

• Each participant carries continuous expectation parameter for anticipated opponent defection likelihood
• Participant pool partitioned by expectation level
• Ambiguity set = union of interior expectation bins
• Can realize ANY empirically observed triple of defection rates across three information conditions
• Strictly obeys classical law of total probability

Classical vs Quantum Equivalence

• Theorem: For any triple produced by standard quantum-like model, exists classical instance reproducing it exactly
• Classical and quantum approaches have same observable-rate expressiveness
• Substantive difference: how ambiguity is represented and event semantics
• Not a breakdown of classical probability

Usage Patterns

Pattern 1: Disjunction Effect Modeling

Model disjunction effect using continuous expectation parameter instead of certainty-only assumption.

Pattern 2: Classical-Quantum Comparison

Prove equivalence of classical and quantum-like models for specific decision tasks.

Pattern 3: Ambiguity Representation

Study how different frameworks represent ambiguity in sequential decisions.

Activation Keywords

• disjunction effect
• sure-thing principle
• quantum-like decision models
• classical probability cognition
• prisoner's dilemma decision
• ambiguity representation
• 析取效应
• 确定性原则
• 类量子决策模型

Pitfalls

• Framework addresses representational differences, not capability differences
• Requires careful interpretation of "mental events" vs physical events
• Equivalence proven for observable rates, not for underlying mechanisms