Collective Reasoning Among LLMs A Framework for Answer Validation Without Ground Truth

We present a collaborative framework where multiple large language models, namely GPT-4-0125-preview, Meta-LLaMA-3-70B-Instruct, Claude-3-Opus, and Gemini-1.5-Flash, work together to generate and respond to complex PhD-level probability questions in the absence of definitive ground truth. This study explores how inter-model consensus enhances response reliability and serves as a proxy for assessing the quality of generated questions. To quantify agreement and consistency, we employ statistical methods including chi-square tests, Fleiss' Kappa, and confidence interval analysis, measuring both response precision and question clarity. Our findings highlight that Claude and Gemini generate well-structured and less ambiguous questions, leading to higher inter-model agreement. This is reflected in their narrower confidence intervals and stronger alignment with answering models. Conversely, LLaMA demonstrates increased variability and lower reliability in question formulation, as indicated by broader confidence intervals and reduced consensus rates. These results suggest that multi-model collaboration not only enhances the reliability of responses but also provides a valuable framework for assessing and improving question quality in the absence of explicit ground truth. This research offers meaningful insights into optimizing AI-driven reasoning through collaborative large-language model interactions.