Large Language Models (LLMs) have demonstrated exceptional capabilities, yet selecting the most reliable response from multiple LLMs remains a challenge, particularly in resource-constrained settings. Existing approaches often depend on costly external verifiers, human evaluators, or self-consistency techniques that require multiple samples from a single model. While multi-LLM systems produce more diverse responses than single models and thus have greater potential, they often underperform compared to single LLM self-consistency. We propose a principled, novel and computationally efficient method to select the best response from multiple different LLMs using a calibrated log-likelihood score, implicitly leveraging the inherent knowledge and confidence of these models. Our method demonstrates improvements of approx. 4%, 3%, and 5% across both debate (multi-round LLM discussions) and non-debate (Best-of-N with multiple LLMs) settings on GSM8K, MMLU (6 subsets), and ARC datasets respectively.
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