# Settling the Score: Portioning with Cardinal Preferences

arXiv: https://arxiv.org/abs/2307.15586 · HTML: https://mlsanity.com/paper/2307.15586/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2023.

## Built on by (most cited first, 6 of 6)

- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)
- [Temporal Elections: Welfare, Strategyproofness, and Proportionality](https://mlsanity.com/paper/2408.13637/) (2024)
- [Learning Unanimously Acceptable Lotteries via Queries](https://mlsanity.com/paper/2604.17505/) (2026)
- [The End Justifies the Mean: A Linear Ranking Rule for Proportional Sequential Decisions](https://mlsanity.com/paper/2605.12717/) (2026)
- [Fraud-Proof Revenue Division on Subscription Platforms](https://mlsanity.com/paper/2511.04465/) (2025)
- [AI of the People, by the People, for the People: A Social Choice Approach to Collective Control of Artificial Intelligence](https://mlsanity.com/paper/2605.16291/) (2026)

## Abstract (arXiv)

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.