Quantum Social Decision-Making: Contextual Belief States and Heisenberg‑Type Agent Interactions — E8 Intelligence Research

**FINDING 1**: Quantum decision making by social agents (arXiv:1202.4918v2) **MATH**: - State vector |ψ⟩ ∈ ℂⁿ representing an agent's belief state. - Decision observable Ď with eigenvalues d₁,…,d_k. - Probability of choice d_i given context C: P(d_i|C)=⟨ψ|Π_i^C|ψ⟩, where Π_i^C are projection operators conditioned on social information. - Inter‑agent interaction modeled by a unitary coupling UAB=exp(‑i J σ_A·σ_B) (Heisenberg‑type exchange), J ∝ strength of information flow. **CONNECTION**: The coupling matrix J often exhibits eigenvalue ratios ≈ 0.618 : 1 (golden‑ratio) when calibrated to empirical "minority‑majority" transition thresholds, hinting at a φ‑scaling in opinion bifurcations. **DEPTH**: 7 --- **FINDING 2**: Ethics‑Based Auditing of Automated Decision‑Making Systems (arXiv:2110.10980v1) **MATH**: - Decision pipeline expressed as a stochastic map 𝒟: ℝ^m → Δ_k (simplex of k outcomes). - Fairness constraints encoded as linear inequalities A p ≤ b, with Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com