# A General Theory of Proportionality with Additive Utilities

arXiv: https://arxiv.org/abs/2602.08504 · HTML: https://mlsanity.com/paper/2602.08504/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 27 of 27)

- [Justified Representation in Approval-Based Committee Voting](https://mlsanity.com/paper/1407.8269/) (2014)
- [Multi-Winner Voting with Approval Preferences](https://mlsanity.com/paper/2007.01795/) (2020)
- [Proportional Participatory Budgeting with Additive Utilities](https://mlsanity.com/paper/2008.13276/) (2020)
- [Proportional Justified Representation](https://mlsanity.com/paper/1611.09928/) (2016)
- [Robust and Verifiable Proportionality Axioms for Multiwinner Voting](https://mlsanity.com/paper/2302.01989/) (2023)
- [Fair Allocation of Indivisible Public Goods](https://mlsanity.com/paper/1805.03164/) (2018)
- [Fair Public Decision Making](https://mlsanity.com/paper/1611.04034/) (2016)
- [Proportionality and the Limits of Welfarism](https://mlsanity.com/paper/1911.11747/) (2019)
- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Participatory Budgeting: Data, Tools, and Analysis](https://mlsanity.com/paper/2305.11035/) (2023)
- [Phragm'en's Voting Methods and Justified Representation](https://mlsanity.com/paper/2102.12305/) (2021)
- [The (Computational) Social Choice Take on Indivisible Participatory Budgeting](https://mlsanity.com/paper/2303.00621/) (2023)
- [Proportional Rankings](https://mlsanity.com/paper/1612.01434/) (2016)
- [Multiwinner Elections with Diversity Constraints](https://mlsanity.com/paper/1711.06527/) (2017)
- [Group Fairness in Committee Selection](https://mlsanity.com/paper/1905.04438/) (2019)
- [Proportionality Degree of Multiwinner Rules](https://mlsanity.com/paper/1810.08799/) (2018)
- [Approximately Stable Committee Selection](https://mlsanity.com/paper/1910.14008/) (2019)
- [Proportionality in Approval-Based Participatory Budgeting](https://mlsanity.com/paper/2302.03672/) (2023)
- [Approximate Core for Committee Selection via Multilinear Extension and Market Clearing](https://mlsanity.com/paper/2110.12499/) (2021)
- [Method of Equal Shares with Bounded Overspending](https://mlsanity.com/paper/2409.15005/) (2024)
- [A Generalised Theory of Proportionality in Collective Decision Making](https://mlsanity.com/paper/2307.06077/) (2023)
- [Full Proportional Justified Representation](https://mlsanity.com/paper/2501.12015/) (2025)
- [Collective Schedules: Scheduling Meets Computational Social Choice](https://mlsanity.com/paper/1803.07484/) (2018)
- [A Rule for Committee Selection with Soft Diversity Constraints](https://mlsanity.com/paper/1803.11437/) (2018)
- [Committee Monotonicity and Proportional Representation for Ranked Preferences](https://mlsanity.com/paper/2406.19689/) (2024)
- [Fair Multiwinner Elections with Allocation Constraints](https://mlsanity.com/paper/2305.02868/) (2023)
- [Proportional Committee Elections with Positive and Negative Votes](https://mlsanity.com/paper/2503.01985/) (2025)

## Abstract (arXiv)

We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints, participatory budgeting (including constraints specifying how funds must be allocated to projects from different pools), and public decision-making. Axioms of proportionality have recently been defined for this general model, but the proposed rules apply only to approval ballots, where each voter submits a subset of candidates she finds acceptable. We propose proportional rules for cardinal ballots, where each voter assigns a numerical value to each candidate corresponding to her utility if that candidate is selected. In developing these rules, we also introduce methods that produce proportional rankings, ensuring that every prefix of the ranking satisfies proportionality.