Multi-Attribute Proportional Representation

TL;DR

This paper addresses the problem of selecting a subset of items that best matches desired attribute distributions, with applications in representative committee formation and proportional representation systems.

Contribution

It introduces a formal framework for multi-attribute proportional representation and analyzes the properties and computational complexity of the subset selection rules.

Findings

The problem generalizes apportionment to multiple attributes.

Certain selection rules are computationally hard to compute.

The framework applies to various real-world representation scenarios.

Abstract

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.