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Leximax Approximations and Representative Cohort Selection

Authors Monika Henzinger , Charlotte Peale , Omer Reingold , Judy Hanwen Shen

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Author Details

Monika Henzinger
  • Universität Wien, Austria
Charlotte Peale
  • Stanford University, CA, USA
Omer Reingold
  • Stanford University, CA, USA
Judy Hanwen Shen
  • Stanford University, CA, USA

Funding

  • Henzinger, Monika: This work was done in part as Stanford University Distinguished Visiting Austrian Chair. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 101019564 "The Design of Modern Fully Dynamic Data Structures (MoDynStruct)" and from the Austrian Science Fund (FWF) project "Fast Algorithms for a Reactive Network Layer (ReactNet)", P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020-2024.
  • Peale, Charlotte: Supported by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness.
  • Reingold, Omer: Supported by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness, the Sloan Foundation Grant 2020-13941 and the Simons Foundation investigators award 689988.
  • Shen, Judy Hanwen: Supported by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness.

Cite AsGet BibTex

Monika Henzinger, Charlotte Peale, Omer Reingold, and Judy Hanwen Shen. Leximax Approximations and Representative Cohort Selection. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.FORC.2022.2

Abstract

Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a population, a very appealing solution concept is lexicographic maximality (leximax) which offers a natural (pareto-optimal like) interpretation that the utility of no population can be increased without decreasing the utility of a population that is already worse off. However, finding a leximax solution can be highly dependent on small variations in the utility of certain groups. In this work, we explore new notions of approximate leximax solutions with three distinct motivations: better algorithmic efficiency, exploiting significant utility improvements, and robustness to noise. Among other definitional contributions, we give a new notion of an approximate leximax that satisfies a similarly appealing semantic interpretation and relate it to algorithmically-feasible approximate leximax notions. When group utilities are linear over cohort candidates, we give an efficient polynomial-time algorithm for finding a leximax distribution over cohort candidates in the exact as well as in the approximate setting. Furthermore, we show that finding an integer solution to leximax cohort selection with linear utilities is NP-Hard.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
Keywords
  • fairness
  • cohort selection
  • leximin
  • maxmin

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