We propose a new model for aggregating preferences over a set of indivisible items based on a quantile value. In this model, each agent is endowed with a specific quantile, and the value of a given bundle is defined by the corresponding quantile of the individual values of the items within it. Our model captures the diverse ways in which agents may perceive a bundle, even when they agree on the values of individual items. It enables richer behavioral modeling that cannot be easily captured by additive valuation functions. We study the problem of maximizing utilitarian and egalitarian welfare within the quantile-based valuation setting. For each of the welfare functions, we analyze the complexity of the objectives. Interestingly, our results show that the complexity of both objectives varies significantly depending on whether the allocation is required to be balanced. We provide near-optimal approximation algorithms for utilitarian welfare, and for egalitarian welfare, we present exact algorithms whenever possible.

翻译：我们提出了一种基于分位数值的不可分割物品集偏好聚合新模型。在该模型中，每个智能体被赋予一个特定分位数，一个物品组合的价值定义为该组合内各物品个体值对应分位数的函数值。该模型能够刻画智能体在物品集上可能存在的多样化认知方式——即使他们对单个物品的价值判断一致。这种建模方式可实现对加法估值函数难以捕捉的丰富行为特征。我们研究了基于分位数估值框架下最大化功利主义福利和平等主义福利的问题。针对每种福利函数，我们分析了其目标复杂度。有趣的是，研究结果表明，两种福利目标的复杂度会随分配是否需要平衡而发生显著变化。针对功利主义福利，我们提供了近优近似算法；针对平等主义福利，我们在可能的情况下给出了精确算法。