MERLIN SCIENCE — Quantum Interference in Social Decision-Making: A Quantum Cognition Mo — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 19, 2026• 0 citations

Abstract

The finding is this: human decisions under uncertainty and social conflict can be modeled not with classical Bayesian probabilities, but with quantum probability amplitudes, where interference terms capture the effect of social interaction on choice. That's the one clean sentence. For context, this sits in quantum cognition, a field that has spent two decades showing that people violate the sure-thing principle and other classical axioms in predictable ways. The standard response has been to patch classical models with extra parameters. This work takes a different route, borrowing the Hilbert-space machinery from physics and applying it to cognitive states. Here's the mechanism you can evaluate. Instead of assigning a probability to an event, you assign a complex amplitude. The probability is the squared magnitude of that amplitude after projection onto a subspace. When you have two possible answers, A or B, the classical sum of their separate probabilities is not what you observe. Y Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23465283

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MERLIN SCIENCE — Quantum Interference in Social Decision-Making: A Quantum Cognition Mo — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 19, 2026• 0 citations

Publisher

Abstract

DOI: 10.5281/zenodo.23465283

Related papers

Quantum Probability Amplitudes Model Human Decision-Making Under Uncertainty — E8 Intelligence Research

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FINDING: Quantum cognition models human decision-making under uncertainty using quantum probability amplitudes rather than classical Bayesian probabilities, with context-dependent non-commutative operators. | MATH: Quantum probability: $P(A|B) \neq P(B|A)$ in general; decision as projection onto Hilbert space basis states; interference term: $P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta)$ , where $\delta$ is the phase difference between probability amplitudes; non-commutativity: $[\hat{A},\hat{B}] = \hat{A}\hat{B} - \hat{B}\hat{A} \neq 0$ for incompatible decision contexts; social agent model (arXiv:1202.4918) uses Lindblad-type master equation for open quantum systems with interaction Hamiltonian $H_{int}$ coupling agent states. | CONNECTION: The interference phase $\delta$ in quantum cognition maps directly to geometric phase — when $\cos(\delta) = 0.809$ (i.e., $\delta = 36^\circ$ ), the interference term yields the golden ratio conjugate $0.618$ as a prob Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Quantum cognition models human decision-making under uncertainty using quantum probability amplitudes rather than classical Bayesian probabilities, with context-dependent non-commutative operators. | MATH: Quantum probability: $P(A|B) \neq P(B|A)$ in general; decision as projection onto Hilbert space basis states; interference term: $P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta)$, where $\delta$ is the phase difference between probability amplitudes; non-commutativity: $[\hat{A},\hat{B}] = \hat{A}\hat{B} - \hat{B}\hat{A} \neq 0$ for incompatible decision contexts; social agent model (arXiv:1202.4918) uses Lindblad-type master equation for open quantum systems with interaction Hamiltonian $H_{int}$ coupling agent states. | CONNECTION: The interference phase $\delta$ in quantum cognition maps directly to geometric phase — when $\cos(\delta) = 0.809$ (i.e., $\delta = 36^\circ$), the interference term yields the golden ratio conjugate $0.618$ as a prob Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Quantum Probability Theory Outperforms Classical Bayesian Logic in Modeling Human Decision-Making — E8 Intelligence Research

Andrew Stewart Caldin

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Sep 12, 20260 citations

Quantum Probability Resolves Decision Paradoxes via Hilbert Space Interference — E8 Intelligence Research

Andrew Stewart Caldin

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 $\psi$ replaces classical probability $P$ ; Born rule $P = |\psi|^2$ ; Hilbert space vectors for decision states; non-commutative operators for context effects; interference term $I = 2\sqrt{P(A)P(B)}\cos(\theta)$ where $\theta$ is phase angle. CONNECTION: Interference phase $\theta$ can map to golden angle $\approx 137.5^\circ$ (related to 0.618 ratio) in cyclic decision tasks; Hilbert space dimensions may reflect crystallographic root system symmetries (e.g., $A_n$ for $n$ -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.comFINDING: 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 $ \psi $ replaces classical probability $ P $; Born rule $ P = |\psi|^2 $; Hilbert space vectors for decision states; non-commutative operators for context effects; interference term $ I = 2\sqrt{P(A)P(B)}\cos(\theta) $ where $ \theta $ is phase angle. CONNECTION: Interference phase $ \theta $ can map to golden angle $ \approx 137.5^\circ $ (related to 0.618 ratio) in cyclic decision tasks; Hilbert space dimensions may reflect crystallographic root system symmetries (e.g., $ A_n $ for $ 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

Aug 6, 20260 citations

P(A|B) \neq P(B|A)

in general; decision as projection onto Hilbert space basis states; interference term:

P(A \lor B) = P(A) + P(B) + 2\sqrt{P(A)P(B)}\cos(\delta)

, where

\delta

is the phase difference between probability amplitudes; non-commutativity:

[\hat{A},\hat{B}] = \hat{A}\hat{B} - \hat{B}\hat{A} \neq 0

for incompatible decision contexts; social agent model (arXiv:1202.4918) uses Lindblad-type master equation for open quantum systems with interaction Hamiltonian

H_{int}

coupling agent states. | CONNECTION: The interference phase

\delta

in quantum cognition maps directly to geometric phase — when

\cos(\delta) = 0.809

(i.e.,

\delta = 36^\circ

), the interference term yields the golden ratio conjugate

0.618

as a prob Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

\langle \psi | A | \psi \rangle^2 \neq \sum_i |\langle i | \psi \rangle|^2 |\langle A | i \rangle|^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

\psi

replaces classical probability

P

; Born rule

P = |\psi|^2

; Hilbert space vectors for decision states; non-commutative operators for context effects; interference term

I = 2\sqrt{P(A)P(B)}\cos(\theta)

where

\theta

is phase angle. CONNECTION: Interference phase

\theta

can map to golden angle

\approx 137.5^\circ

(related to 0.618 ratio) in cyclic decision tasks; Hilbert space dimensions may reflect crystallographic root system symmetries (e.g.,

A_n

for

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