We study a discrete fair division problem where $n$ agents have additive valuation functions over a set of $m$ goods. We focus on the well-known $α$-EFX fairness criterion, according to which the envy of an agent for another agent is bounded multiplicatively by $α$, after the removal of any good from the envied agent's bundle. The vast majority of the literature has studied $α$-EFX allocations under the assumption that full knowledge of the valuation functions of the agents is available. Motivated by the established literature on the distortion in social choice, we instead consider $α$-EFX algorithms that operate under limited information on these functions. In particular, we assume that the algorithm has access to the ordinal preference rankings, and is allowed to make a small number of queries to obtain further access to the underlying values of the agents for the goods. We show (near-optimal) tradeoffs between the values of $α$ and the number of queries required to achieve those, with a particular focus on constant EFX approximations. We also consider two interesting special cases, namely instances with a constant number of agents, or with two possible values, and provide improved positive results.

翻译：我们研究一个离散公平分配问题，其中$n$个智能体对$m$件物品具有可加估值函数。我们关注著名的$α$-EFX公平性准则：在从被嫉妒智能体的物品束中移除任意一件物品后，智能体对另一智能体的嫉妒值以乘性因子$α$为界。现有文献绝大多数在假设智能体估值函数完全已知的条件下研究$α$-EFX分配。受社会选择理论中失真度研究的启发，我们转而考虑在有限信息条件下运行的$α$-EFX算法。特别地，我们假设算法仅能获取序数偏好排序，并允许通过少量查询进一步获取智能体对物品的潜在估值。我们揭示了$α$值与实现该值所需查询次数之间的（近似最优）权衡关系，重点关注常数EFX近似情形。同时，我们考察了两个特殊场景——智能体数量恒定或估值仅取两种可能值的实例，并给出了改进的积极结果。