Abstract
After pre-training, large language models are aligned with human preferences based on pairwise comparisons. State-of-the-art alignment methods (such as PPO-based RLHF and DPO) are built on the assumption of aligning with a single preference model, despite being deployed in settings where users have diverse preferences. As a result, it is not even clear that these alignment methods produce models that satisfy users on average -- a minimal requirement for pluralistic alignment. Drawing on social choice theory and modeling users' comparisons through individual Bradley-Terry (BT) models, we introduce an alignment method's distortion: the worst-case ratio between the optimal achievable average utility, and the average utility of the learned policy. The notion of distortion helps draw sharp distinctions between alignment methods: Nash Learning from Human Feedback achieves the minimax optimal distortion of (1/2 + o(1)) · β (for the BT temperature β), robustly across utility distributions, distributions of comparison pairs, and permissible KL divergences from the reference policy. RLHF and DPO, by contrast, suffer ≥ (1 - o(1)) · β distortion already without a KL constraint, and e^Ω(β) or even unbounded distortion in the full setting, depending on how comparison pairs are sampled.