# Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation

arXiv: https://arxiv.org/abs/1402.3044 · HTML: https://mlsanity.com/paper/1402.3044/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2014.

## Built on by (most cited first, 13 of 13)

- [Drawing a Map of Elections](https://mlsanity.com/paper/2504.03809/) (2025)
- [Core-Stable Committees under Restricted Domains](https://mlsanity.com/paper/2108.01987/) (2021)
- [Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions](https://mlsanity.com/paper/2306.09835/) (2023)
- [Multi-Group Proportional Representation in Retrieval](https://mlsanity.com/paper/2407.08571/) (2024)
- [Polynomial-Time Algorithm for Thiele Voting Rules with Voter Interval Preferences](https://mlsanity.com/paper/2604.05953/) (2026)
- [Bribery as a Measure of Candidate Success: Complexity Results for Approval-Based Multiwinner Rules](https://mlsanity.com/paper/2104.09130/) (2021)
- [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)
- [Computing Thiele Rules on Interval Elections and their Generalizations](https://mlsanity.com/paper/2605.03067/) (2026)
- [Fine-Grained Complexity and Algorithms for the Schulze Voting Method](https://mlsanity.com/paper/2103.03959/) (2021)
- [Algorithms for Structured Elections under Thiele Voting Rules](https://mlsanity.com/paper/2607.28575/) (2026)
- [Multi-Dimensional Matching](https://mlsanity.com/paper/2609.29958/) (2026)
- [Reverse Sequential Proportional Approval Voting Rule: Proportionality and Approximation Guarantees](https://mlsanity.com/paper/2609.35331/) (2026)

## Abstract (arXiv)

We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of K items that maximize the total derived utility of all the agents (i.e., in our example we are to pick K movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases.