Quantum Cognition: Hilbert‑Space Interference Explains Decision‑Making Deviations from Classical Probability — E8 Intelligence Research

**FINDING:** Quantum cognition models human decision making with Hilbert‑space probability amplitudes, producing observable interference effects that deviate from classical Kolmogorovian probabilities. **MATH:** - State vector |ψ⟩ ∈ ℂⁿ representing a mental state. - Projectors P_A, P_B for mutually exclusive choices A, B (P_A + P_B = I). - Classical probability P(A) = ⟨ψ|P_A|ψ⟩ is replaced by the **Born rule** with possible **interference term**: \[ P(A\ or\ B)={| A|ψ|²+| B|ψ|²}classical sum + 2\,\![ψ|A B|ψ] . \] - In the "order‑effect" experiments the probability of answering Q₁ then Q₂ is \[ P(Q₂=y|Q₁=x)=\|P_{Q₂=y}P_{Q₁=x}|ψ\|², \] which is generally **non‑commutative**: \(P_{Q₂}P_{Q₁}≠ P_{Q₁}P_{Q₂}\). - The **quantum‑Bayesian update** after a measurement uses Lüders rule: \[ |ψ'={P_{Q₁=x}| Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com