English

Approximately Fair and Population Consistent Budget Division via Simple Payment Schemes

Computer Science and Game Theory 2025-10-06 v2 Theoretical Economics

Abstract

In approval-based budget division, a budget needs to be distributed to candidates based on the voters' approval ballots over these candidates. In the pursuit of a simple, consistent, and approximately fair rule for this setting, we introduce the maximum payment rule (MP). Under this rule, each voter controls a part of the budget and, in each step, the corresponding voters allocate their entire budget to the candidate approved by the largest number of voters with non-zero budget. We show that MP meets our criteria as it satisfies monotonicity and a demanding population consistency condition and gives a 22-approximation to a fairness notion called average fair share (AFS). Moreover, we generalize MP to the class of sequential payment rule and prove that it is the most desirable rule in this class: all sequential payment rules but MP and one other rule fail monotonicity while only allowing for a small improvement in the approximation ratio to AFS.

Keywords

Cite

@article{arxiv.2412.02435,
  title  = {Approximately Fair and Population Consistent Budget Division via Simple Payment Schemes},
  author = {Haris Aziz and Patrick Lederer and Xinhang Lu and Mashbat Suzuki and Jeremy Vollen},
  journal= {arXiv preprint arXiv:2412.02435},
  year   = {2025}
}

Comments

This paper (version 1) has been accepted at EC'25. The current version is in preparation for a revision at a journal, which caused significant changes in the presentation of the results and lead to a new title

R2 v1 2026-06-28T20:21:22.392Z