The flexible and generalized nature of large language models has allowed for their application in a wide array of language-based domains.Much like their human contemporaries, these models are capable of engaging in discussions and debates as a means of improving answer quality.We first take a theoretical approach to analyzing debate and provide a framework through which debate can be mathematically examined.Building on this framework, we provide several theoretical results for multi-agent debate.In particular, we demonstrate that similar model capabilities, or similar model responses, can result in static debate dynamics where the debate procedure simply converges to the majority opinion. When this majority opinion is the result of a common misconception (ingrained in the models through shared training data) debate is likely to converge to answers associated with that common misconception.Using insights from our theoretical results we then propose three interventions which improve the efficacy of debate. For each intervention, we provide theoretical results demonstrating how debate is improved.We also demonstrate that these interventions result in better performance on four common benchmark tasks.