We study a portioning setting in which a public resource such as time or money is to be divided among a given set of candidates, and each agent proposes a division of the resource. We consider two families of aggregation rules for this setting -- those based on coordinate-wise aggregation and those that optimize some notion of welfare -- as well as the recently proposed independent markets rule. We provide a detailed analysis of these rules from an axiomatic perspective, both for classic axioms, such as strategyproofness and Pareto optimality, and for novel axioms, some of which aim to capture proportionality in this setting. Our results indicate that a simple rule that computes the average of the proposals satisfies many of our axioms and fares better than all other considered rules in terms of fairness properties. We complement these results by presenting two characterizations of the average rule.

翻译：本研究探讨一种资源分配场景，其中公共资源（如时间或资金）需在给定候选集合中进行分配，每个参与者需提出具体的资源划分方案。我们针对该场景分析两类聚合规则体系——基于坐标维度聚合的规则与优化特定福利指标的规则——以及近期提出的独立市场规则。通过公理化视角对这些规则进行系统性分析，既涵盖策略防护性与帕累托最优性等经典公理，也包含若干旨在刻画该场景中比例性的新型公理。研究结果表明，计算提案平均值的简单规则满足多数公理要求，且在公平性指标上优于其他所有考察规则。我们进一步通过给出平均规则的两个特征刻画来完善这些结论。