Confirmation Bias Quantum Probability

---
name: confirmation-bias-quantum-probability
description: "Quantum probability framework modeling confirmation bias as optimal evidence selection in sequential hypothesis testing. Use when analyzing confirmation bias, sequential evidence sampling, active inference, quantum probability models of cognition, binary hypothesis testing, or rational decision-making under uncertainty."
metadata:
  arxiv_id: "2606.23325"
  published: "2026-06-22"
  authors: "arXiv:2606.23325"
  tags: [quantum-probability, confirmation-bias, active-inference, hypothesis-testing, cognition]
---

# Confirmation Bias as Optimal Evidence Selection

## Description

Quantum probability framework showing confirmation bias emerges from optimal evidence choice in sequential binary hypothesis testing. Observations modeled by matrices on square-root probability space rather than random variables.

## Core Theory

### Square-Root Probability Space
- Work on space of square-root probabilities (quantum probability structures)
- Observations = matrices, not random variables on probability space
- Optimal evidence choice minimizes expected error probability

### Key Results
1. **Confirmation bias as rationality**: Optimal evidence choice in sequential sampling implicitly leads to confirmation bias
2. **Two evolutionary advantages**:
   - Minimum memory capacity required
   - Error probability reduces exponentially in sample size
3. **Active inference agreement**: Evidence maximizing information (active inference) agrees with evidence minimizing error probability

### Mathematical Framework
- Binary hypothesis testing on square-root probability space
- Matrix-valued observations
- Optimal evidence selection protocol
- Active quantum inference protocol

## Usage Patterns

### Pattern 1: Sequential Evidence Analysis
Model how agents accumulate evidence under confirmation bias using optimal evidence selection on matrix observation space.

### Pattern 2: Active Inference Protocol
Implement evidence-seeking behavior that maximizes information gain, shown equivalent to error-minimizing evidence choice.

### Pattern 3: Memory-Efficient Decision Making
Show confirmation bias provides minimum memory capacity for sequential decisions with exponential error reduction.

## Activation Keywords
- confirmation bias
- quantum probability
- sequential hypothesis testing
- active inference
- optimal evidence selection
- square-root probability
- 确认偏误
- 量子概率
- 顺序假设检验

## Pitfalls
- "Quantum-like" = modeling formalism, not biological quantum computation claim
- Framework applies to rational decision-making, not irrational behavior
- Requires matrix-valued observations, not classical random variables