CHSH-Based Adversarial Detection for Mechanism Design

Contemporary democratic institutions face systematic threats from sophisticated adversarial manipulation, particularly through LLMs that exhibit significant exploitation vulnerabilities in strategic scenarios. Research demonstrates that advanced LLMs maintain baseline performance levels of 57% for GPT-4, 62% for DeepSeek-V3, and 38% for Gemini-1.5 in decision-making tasks, but show dramatic vulnerability increases to 93%, 95%, and 94% respectively following strategic adversarial intervention. These vulnerabilities expose fundamental limitations in traditional mechanism design approaches, which cannot distinguish between authentic citizen preferences and decision-making processes with artificially induced biases. This research introduces a quantum-safe algorithmic mechanism design framework that integrates CHSH game rigidity with democratic governance protocols to detect and counter adversarial influence. The framework addresses the computational complexity challenge where optimal mechanism design is #P-hard by leveraging quantum correlation testing as a polynomial-time verification protocol. CHSH scores serve as institutional integrity certificates: legitimate democratic processes maintain correlations within classical bounds (S ≤ 2), while adversarial manipulation may produce systematic deviations that approach quantum correlation limits near 2√2. The proposed methodology implements device-independent verification protocols adapted for institutional applications, where democratic decision nodes engage in CHSH-style correlation testing to certify communication integrity without trust assumptions. Building on DI-QKD protocols, the framework provides mathematically verifiable democratic authenticity through quantum correlation auditing. Quantum change-point detection algorithms enable rapid identification of coordinated attacks against institutional winning criteria, specifically targeting LLM-facilitated bias injection in governance decision making.