A divisible public resource is to be divided among projects. We study rules that decide on a distribution of the budget when voters have ordinal preference rankings over projects. Examples of such portioning problems are participatory budgeting, time shares, and parliament elections. We introduce a family of rules for portioning, inspired by positional scoring rules. Rules in this family are given by a scoring vector (such as plurality or Borda) associating a positive value with each rank in a vote, and an aggregation function such as leximin or the Nash product. Our family contains well-studied rules, but most are new. We discuss computational and normative properties of our rules. We focus on fairness, and introduce the SD-core, a group fairness notion. Our Nash rules are in the SD-core, and the leximin rules satisfy individual fairness properties. Both are Pareto-efficient.

可分割的公共资源将在项目之间进行分配。我们研究规则，这些规则在选民对项目的顺序排名排名时决定预算的分配。这种分配问题的例子是参与式预算、时间共享和议会选举。受位置评分规则的启发，我们引入了一系列分割规则。该系列中的规则由将正值与投票中的每个排名相关联的评分向量（例如复数或 Borda）和聚合函数（例如 leximin 或 Nash 积）给出。我们的家庭包含经过充分研究的规则，但大多数都是新规则。我们讨论了规则的计算和规范属性。我们专注于公平，并引入了 SD-core，一个群体公平的概念。我们的纳什规则在 SD 核心中，并且 leximin 规则满足个体的公平属性。两者都是帕累托有效的。