Quantum Probability Models of Human Decision-Making Under Uncertainty — E8 Intelligence Research

FINDING: Human decision-making under uncertainty violates classical probability axioms (total law of probability, commutativity of conjunction) and is better modeled by quantum probability formalism — superposition, interference, non-commuting observables. MATH: Core formalism: - Classical: P(A) = Σ P(A|Bᵢ)P(Bᵢ) — Law of Total Probability - Quantum: P(A) = |⟨A|ψ⟩|² where |ψ⟩ = α|B₁⟩ + β|B₂⟩ - Interference term: P(A) = |α⟨A|B₁⟩ + β⟨A|B₂⟩|² = |α|²|⟨A|B₁⟩|² + |β|²|⟨A|B₂⟩|² + 2|α||β|Re[⟨A|B₁⟩⟨B₂|A⟩] - The cross-term 2|α||β|Re[...] is the interference — absent in classical probability - Non-commutativity: [A,B] = AB − BA ≠ 0 (order of judgment/decision matters) - Key experimental violations: disjunction effect (Tversky-Shafir), conjunction fallacy (Linda problem), order effects in Gallup polls - Projection operators: P_A = |A⟩⟨A|, measurement collapses state - Density matrix: ρ = Σ pᵢ|ψᵢ⟩⟨ψᵢ| for mixed states CONNECTION: - Hilbert space structure implies complex amplitudes — the same ℂ² Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com