| name | quantum-tug-of-war-decision |
| description | Quantum Tug-of-War (QTOW) decision making model — contextuality arises generatively from physically grounded constraints on decision dynamics. Conservation-based internal state updates and measurement-induced disturbance produce KCBS-type contextuality witnesses. Proves quantum probability is structurally necessary for adaptive decision dynamics, not merely descriptive. Use when: quantum decision making, contextuality in choices, TOW model, non-Kolmogorovian probability, adaptive learning dynamics, measurement-induced disturbance, arXiv:2601.10034.
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Quantum Tug-of-War Decision Making
Theoretical framework where contextuality in decision making arises generatively from
physically grounded constraints, not from assumed quantum probability.
Core Insight
Contextuality is a structural consequence of adaptive learning dynamics:
- Conservation-based internal state updates
- Measurement-induced disturbance
- Together preclude any non-contextual classical description
The TOW Model
Classical Tug-of-War (TOW)
Decision as resource allocation between competing options:
- Each option has an associated value/reward
- Agent allocates internal resources (attention, effort)
- Conservation law: total resource is fixed
Quantum Extension
Internal state → quantum density matrix ρ
Choice → projective measurement on ρ
Update → post-measurement state transformation
Key: measurement changes the state, creating path dependence
that no single classical hidden variable can explain.
KCBS Contextuality Witness
The model admits Klyachko-Can-Binicioglu-Shumovsky (KCBS) type contextuality
witnesses in a minimal single-system setting:
⟨A₁A₂⟩ + ⟨A₂A₃⟩ + ⟨A₃A₄⟩ + ⟨A₄A₅⟩ + ⟨A₅A₁⟩ ≥ -3 (classical bound)
Quantum systems can violate this bound, demonstrating contextuality.
Mathematical Framework
State Update Rule
ρ → M_k ρ M_k† / Tr(M_k ρ M_k†)
where M_k are measurement operators satisfying ∑ M_k† M_k = I
Conservation Constraint
∑ resources = constant across all decision steps
This constraint + measurement disturbance → no joint probability
distribution over all observables exists → contextuality
Implications
- Quantum probability is not merely convenient — it is an unavoidable
effective theory for adaptive decision dynamics
- Classical hidden variables are insufficient — no single unified internal
state can explain observed decision patterns
- Contextuality emerges from dynamics — not assumed, but derived from
conservation + measurement structure
Applications
- Behavioral economics: modeling preference reversals
- AI decision making: robust choices under contradictory evidence
- Cognitive modeling: explaining human irrationality patterns
- Multi-agent systems: distributed decision with information constraints
Relationship to Quantum Cognition
| Aspect | Standard Quantum Cognition | QTOW Approach |
|---|
| Basis | Assumes quantum probability | Derives it from dynamics |
| Contextuality | Postulated | Proven from conservation |
| Mechanism | Hilbert space formalism | Physical resource constraints |
| Minimality | Often multi-qubit | Single-system sufficient |
Activation Keywords
- quantum tug-of-war decision
- contextuality decision dynamics
- KCBS witness decision
- non-Kolmogorovian probability
- conservation-based decision
- measurement-induced contextuality
- adaptive decision dynamics quantum
- QTOW model
Related Skills
- quantum-neuroscience-analysis: Cross-disciplinary quantum-neuro methods
- extreme-quantum-cognition: Quantum learning for deliberative decisions
- thermocoherent-cognitive-dynamics: Physical basis of cognition
- neural-dynamics-decision-making: Neural decision models
