Sequential Payment Rules: Approximately Fair Budget Divisions via Simple Spending Dynamics

Haris Aziz, Patrick Lederer, Xinhang Lu, Mashbat Suzuki and Jeremy Vollen

Papers from arXiv.org

Abstract: In approval-based budget division, a budget needs to be distributed to some candidates based on the voters' approval ballots over these candidates. In the pursuit of simple, well-behaved, and approximately fair rules for this setting, we introduce the class of sequential payment rules, where each voter controls a part of the budget and repeatedly spends his share on his approved candidates to determine the final distribution. We show that all sequential payment rules satisfy a demanding population consistency notion and we identify two particularly appealing rules within this class called the maximum payment rule (MP) and the $\frac{1}{3}$-multiplicative sequential payment rule ($\frac{1}{3}$-MP). More specifically, we prove that (i) MP is, apart from one other rule, the only monotonic sequential payment rule and gives a $2$-approximation to a fairness notion called average fair share, and (ii) $\frac{1}{3}$-MP gives a $\frac{3}{2}$-approximation to average fair share, which is optimal among sequential payment rules.

Date: 2024-12
New Economics Papers: this item is included in nep-cdm and nep-des
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2412.02435 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2412.02435

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().