Portioning using ordinal preferences: Fairness and efficiency

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.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This article studies rules for distributing a divisible public resource among projects when voters have ordinal preference rankings. It introduces a family of rules based on positional scoring rules and discusses their computational and normative properties. The focus is on fairness, and the concept of SD-core is introduced to measure group fairness.