From Self-Check to Consensus: Bayesian Strategic Decoding in Large Language Models

Large Language Models exhibit logical inconsistency across multi-turn inference processes, undermining correctness in complex inferential tasks. Challenges arise from ensuring that outputs align with both factual correctness and human intent. Approaches like single-agent reflection and multi-agent debate frequently prioritize consistency, but at the expense of accuracy. To address this problem, we propose a novel game-theoretic consensus mechanism that enables LLMs to self-check their outputs during the decoding stage of output generation. Our method models the decoding process as a multistage Bayesian Decoding Game, where strategic interactions dynamically converge to a consensus on the most reliable outputs without human feedback or additional training. Remarkably, our game design allows smaller models to outperform much larger models through game mechanisms ( e.g. , 78.1 LLaMA13B vs. 76.6 PaLM540B). As a model-agnostic method, our approach consistently improves even the latest models, enhancing DeepSeek-7B’s performance on MMLU by 12.4%. Our framework effectively balances correctness and consistency, demonstrating that properly designed game-theoretic mechanisms can significantly enhance the self-verification capabilities of language models across various tasks and model architectures.