Reinforcement Learning from Human Feedback (RLHF), the standard for aligning Large Language Models (LLMs) with human values, is known to fail to satisfy properties that are intuitively desirable, such as respecting the preferences of the majority \cite{ge2024axioms}. To overcome these issues, we propose the use of a probabilistic Social Choice rule called \emph{maximal lotteries} as a replacement for RLHF. We show that a family of alignment techniques, namely Nash Learning from Human Feedback (NLHF) \cite{munos2023nash} and variants, approximate maximal lottery outcomes and thus inherit its beneficial properties. We confirm experimentally that our proposed methodology handles situations that arise when working with preferences more robustly than standard RLHF, including supporting the preferences of the majority, providing principled ways of handling non-transitivities in the preference data, and robustness to irrelevant alternatives. This results in systems that better incorporate human values and respect human intentions.