# Proportional Justified Representation

arXiv: https://arxiv.org/abs/1611.09928 · HTML: https://mlsanity.com/paper/1611.09928/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2016.

## Built on by (most cited first, 25 of 25)

- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)
- [Online Approval Committee Elections](https://mlsanity.com/paper/2202.06830/) (2022)
- [Strengthening Proportionality in Temporal Voting](https://mlsanity.com/paper/2505.22513/) (2025)
- [Proportionally Representative Clustering](https://mlsanity.com/paper/2304.13917/) (2023)
- [Strategyproof and Proportionally Fair Facility Location](https://mlsanity.com/paper/2111.01566/) (2021)
- [DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections](https://mlsanity.com/paper/2107.07356/) (2021)
- [Core-Stable Committees under Restricted Domains](https://mlsanity.com/paper/2108.01987/) (2021)
- [Random Rank: The One and Only Strategyproof and Proportionally Fair Randomized Facility Location Mechanism](https://mlsanity.com/paper/2205.14798/) (2022)
- [Proportional Representation in Metric Spaces and Low-Distortion Committee Selection](https://mlsanity.com/paper/2312.10369/) (2023)
- [Full Proportional Justified Representation](https://mlsanity.com/paper/2501.12015/) (2025)
- [The Price of Proportional Representation in Temporal Voting](https://mlsanity.com/paper/2605.11157/) (2026)
- [Representative Ranking for Deliberation in the Public Sphere](https://mlsanity.com/paper/2503.18962/) (2025)
- [Metritocracy: Representative Metrics for Lite Benchmarks](https://mlsanity.com/paper/2506.09813/) (2025)
- [Question the Questions: Auditing Representation in Online Deliberative Processes](https://mlsanity.com/paper/2511.04588/) (2025)
- [Proportional Selection in Networks](https://mlsanity.com/paper/2502.03545/) (2025)
- [Proportional Committee Elections with Positive and Negative Votes](https://mlsanity.com/paper/2503.01985/) (2025)
- [A Linear Theory of Multi-Winner Voting](https://mlsanity.com/paper/2503.03082/) (2025)
- [Large Language Models for Designing Participatory Budgeting Rules](https://mlsanity.com/paper/2602.09349/) (2026)
- [Strengthening Full Justified Representation: Efficient Verification and Computation](https://mlsanity.com/paper/2608.11500/) (2026)
- [Data as Voters: Core Set Selection Using Approval-Based Multi-Winner Voting](https://mlsanity.com/paper/2304.09995/) (2023)
- [Fairness in the Multi-Secretary Problem](https://mlsanity.com/paper/2511.23097/) (2025)
- [A General Theory of Proportionality with Additive Utilities](https://mlsanity.com/paper/2602.08504/) (2026)
- [Multi-Winner Voting with Argumentative Ballots](https://mlsanity.com/paper/2608.23247/) (2026)
- [Proportional Representation in Temporal Voting with Ranked Preferences](https://mlsanity.com/paper/2609.30555/) (2026)

## Abstract (arXiv)

The goal of multi-winner elections is to choose a fixed-size committee based on voters' preferences. An important concern in this setting is representation: large groups of voters with cohesive preferences should be adequately represented by the election winners. In an influential paper, Aziz et al. proposed two axioms that aim to capture this idea: justified representation (JR) and its strengthening extended justified representation (EJR). We observe that EJR is incompatible with the highly desirable Perfect Representation (PR) criterion, and propose a relaxation of EJR, which we call Proportional Justified Representation (PJR). PJR is more demanding than JR, but, unlike EJR, it is compatible with PR, as well as with a stronger variant of this axiom, which we term Fractional Perfect Representation (FPR). Moreover, just like EJR, PJR can be used to characterise the classic Proportional Approval Voting (PAV) rule in the class of weighted PAV rules. On the other hand, we show that EJR provides stronger guarantees with respect to average voter satisfaction than PJR does.