arXiv:2510.07517v1 Announce Type: new Abstract: Multi-agent debate (MAD) aims to improve large language model (LLM) reasoning by letting multiple agents exchange answers and then aggregate their opinions. Yet recent studies reveal that agents are not neutral: they are prone to identity-driven sycophancy and self-bias, uncritically adopting a peer's view or stubbornly adhering to their own prior output, undermining the reliability of debate. In this work, we present the first principled framework that joins sycophancy and self-bias to mitigate and quantify identity bias in MAD. First, we formalize the debate dynamics as an identity-weighted Bayesian update process. Second, we propose response anonymization: by removing identity markers from prompts, agents cannot distinguish "self" from "peer", which forces equal weights on agent identity, thereby reducing bias. Third, we define the Identity Bias Coefficient (IBC), a principled metric that measures how often an agent follows a peer versus itself. Empirical studies across multiple models, datasets and debate rounds confirm that identity bias is widespread, with sycophancy far more common than self-bias. Our findings highlight the need to "mask" identity to ensure that MAD systems reason based on content rather than source identity. Code is released in https://github.com/deeplearning-wisc/MAD-identity-bias.