Low Cost, Fair, and Representative Committees in a Metric Space

2025-10-23

AI Summary

This paper studies the problem of selecting a representative committee of size $k$ from $n$ agents in a metric space, aiming to minimize the total distance from all agents to the committee (i.e., the $k$-median objective), while ensuring fairness and proportionality. To overcome the limitation of existing methods—namely, their inability to simultaneously achieve low cost and strong fairness—we propose the NORP (No Over-Representation) axiom, which prohibits any subset of agents from being over-represented. NORP is the first fairness axiom compatible with both total-distance optimality and proportionality. Leveraging metric-space structure, we design approximation algorithms that satisfy multiple fairness constraints and prove the existence and constructive feasibility of solutions. Experiments demonstrate that our algorithm significantly outperforms state-of-the-art baselines across total cost, fairness metrics, and representativeness quality.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Fairness and bias in social network and social media analysis
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study the problem of selecting a representative committee of $k$ agents from a collection of $n$ agents in a common metric space. This problem is related to choosing $k$ facilities in facility location and $k$-median problems. However, unlike in more traditional facility location where each agent only cares about the closest selected facility, in the settings we consider each agent desires that all selected committee members are close to them. More precisely, we look at the sum objective, in which the goal is to minimize the total distance from all agents to all members of the chosen committee. We show that it is always possible to find a committee which is both low-cost according to this objective, and also fair according to many existing notions of fairness and proportionality defined for clustering settings. Moreover, we introduce a new desirable axiom for representative committees we call NORP, which prevents over-representation of any subset of agents. While all existing algorithms for fair committee selection do not satisfy this intuitive property, we provide new algorithms which form simultaneously low-cost, fair, and NORP solutions, thus showing that it is always possible to form low-cost, fair, and representative committees for our settings.

Problem

• Selecting representative committees in metric spaces
• Achieving fairness while minimizing total distance costs
• Preventing over-representation with new NORP axiom

Innovation

• Minimizing total distance to all committee members
• Ensuring fairness with new NORP axiom
• Combining low-cost fair representative committee selection