# Multi-Attribute Proportional Representation

arXiv: https://arxiv.org/abs/1509.03389 · HTML: https://mlsanity.com/paper/1509.03389/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Sep 2015.

## Built on by (most cited first, 4 of 4)

- [DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections](https://mlsanity.com/paper/2107.07356/) (2021)
- [Online Selection of Diverse Committees](https://mlsanity.com/paper/2105.09295/) (2021)
- [Multi-Group Proportional Representation in Retrieval](https://mlsanity.com/paper/2407.08571/) (2024)
- [Fairly Allocating Utility in Constrained Multiwinner Elections](https://mlsanity.com/paper/2211.12820/) (2022)

## Abstract (arXiv)

We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should have. We look for a set that fits as much as possible the desired distributions on all attributes. Examples of applications include choosing members of a representative committee, where candidates are described by attributes such as sex, age and profession, and where we look for a committee that for each attribute offers a certain representation, i.e., a single committee that contains a certain number of young and old people, certain number of men and women, certain number of people with different professions, etc. With a single attribute the problem collapses to the apportionment problem for party-list proportional representation systems (in such case the value of the single attribute would be a political affiliation of a candidate). We study the properties of the associated subset selection rules, as well as their computation complexity.