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Quantum Probability Framework for Human Decision-Making Under Uncertainty — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 18, 2026• 0 citations
Publisher

Abstract

FINDING: Quantum probability replaces classical Kolmogorov probability in modeling human decision-making under uncertainty and conflict, using non-commutative operators and complex amplitudes. | MATH: Quantum probability framework: \( P(A) = |\langle \psi | M_A | \psi \rangle|^2 \), where \( M_A \) is a projection operator; non-commutativity: \( [M_A, M_B] \neq 0 \) leads to interference terms; contextuality captured by Hilbert space dimension \( d \); Born rule replaces Bayes rule for sequential decisions. | CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries found in the provided sources. The Hilbert space structure is linear, not inherently harmonic. | DEPTH: 6 — The mathematical shift from classical to quantum probability is profound for cognitive modeling, but the findings lack specific constants, ratios, or geometric symmetries that would tie directly to universal mathematical structure. The connection to geometri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21989131

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FINDING: Human decision-making under uncertainty and conflict is best modeled by quantum probability theory, not classical Bayesian logic. | MATH: Quantum probability amplitudes replace classical probabilities; decision basis states are vectors in Hilbert space; interference terms (e.g., ⟨ψ∣A∣ψ⟩2≠∑i∣⟨i∣ψ⟩∣2∣⟨A∣i⟩∣2 \langle \psi | A | \psi \rangle^2 \neq \sum_i |\langle i | \psi \rangle|^2 |\langle A | i \rangle|^2 ⟨ψ∣A∣ψ⟩2=∑i​∣⟨i∣ψ⟩∣2∣⟨A∣i⟩∣2) account for context-dependent violations of the law of total probability. | CONNECTION: No explicit geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 or crystallographic symmetries reported. The Hilbert space structure is linear, not inherently harmonic. | DEPTH: 6 — Foundational shift in probability theory for cognition, but no direct link to geometric harmony or universal constants. The mathematical essence is the replacement of Kolmogorov axioms with quantum probability, which introduces complex phases and interference. No specific equations or constants beyond the standard quant Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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FINDING: Quantum cognition models human decision-making using quantum probability, not classical logic, to explain context effects and order effects. | MATH: Quantum probability amplitude (complex numbers), Born rule (P = |ψ|²), Hilbert space vectors for states, projection operators for decisions, non-commutative operators (AB ≠ BA) for order effects. No specific constants or ratios extracted. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 or crystallographic symmetries found in these sources. The Hilbert space structure is linear, not inherently harmonic in the golden-ratio sense. | DEPTH: 6 — The shift from classical to quantum probability is mathematically profound, but the sources lack explicit geometric constants or deep harmonic structure. The connection to universal mathematical structure is indirect (quantum formalism as a general probability framework). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum cognition models human decision-making using quantum probability, not classical Bayesian logic, to resolve paradoxes like order effects and context-dependence. MATH: Quantum probability amplitude ψ \psi ψ replaces classical probability P P P; Born rule P=∣ψ∣2 P = |\psi|^2 P=∣ψ∣2; Hilbert space vectors for decision states; non-commutative operators for context effects; interference term I=2P(A)P(B)cos⁡(θ) I = 2\sqrt{P(A)P(B)}\cos(\theta) I=2P(A)P(B)​cos(θ) where θ \theta θ is phase angle. CONNECTION: Interference phase θ \theta θ can map to golden angle ≈137.5∘ \approx 137.5^\circ ≈137.5∘ (related to 0.618 ratio) in cyclic decision tasks; Hilbert space dimensions may reflect crystallographic root system symmetries (e.g., An A_n An​ for n n n-choice decisions). DEPTH: 6 — Novel mathematical framework for cognition, but no direct geometric constants or base-60 links yet; interference term suggests potential harmonic ratios in decision dynamics. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com