In the context of multi-agent multi-armed bandits (MA-MAB), fairness is often reduced to outcomes: maximizing welfare, reducing inequality, or balancing utilities. However, evidence in psychology, economics, and Rawlsian theory suggests that fairness is also about process and who gets a say in the decisions being made. We introduce a new fairness objective, procedural fairness, which provides equal decision-making power for all agents, lies in the core, and provides for proportionality in outcomes. Empirical results confirm that fairness notions based on optimizing for outcomes sacrifice equal voice and representation, while the sacrifice in outcome-based fairness objectives (like equality and utilitarianism) is minimal under procedurally fair policies. We further prove that different fairness notions prioritize fundamentally different and incompatible values, highlighting that fairness requires explicit normative choices. This paper argues that procedural legitimacy deserves greater focus as a fairness objective, and provides a framework for putting procedural fairness into practice.

翻译：在多智能体多臂赌博机（MA-MAB）的背景下，公平性通常被简化为结果导向：最大化社会福利、减少不平等或平衡效用。然而，心理学、经济学和罗尔斯理论中的证据表明，公平性也关乎过程以及谁在决策中拥有话语权。本文提出了一种新的公平性目标——程序公平性，它为所有智能体提供平等的决策权，位于核心地位，并确保结果的比例性。实证结果证实，基于结果优化的公平性概念牺牲了平等的话语权和代表性，而在程序公平策略下，基于结果的公平性目标（如平等主义和功利主义）的牺牲是最小的。我们进一步证明，不同的公平性概念优先考虑根本不同且互不相容的价值观，强调公平性需要明确的规范性选择。本文认为，程序合法性应作为公平性目标得到更多关注，并提供了一个将程序公平性付诸实践的框架。