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