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Properties of multiwinner voting rules.

Edith Elkind1, Piotr Faliszewski2, Piotr Skowron1

  • 11University of Oxford, Oxford, UK.

Social Choice and Welfare
|April 1, 2020
PubMed
Summary

This study categorizes multiwinner voting rules, generalizing single-winner methods. Many existing committee selection rules fit into two broad classes, aiding in evaluating their properties.

Area of Science:

  • Computational Social Choice
  • Political Science
  • Game Theory

Background:

  • Committee selection rules, or multiwinner voting rules, determine representative committees of a specified size k from preference rankings.
  • Existing rules often generalize single-winner scoring methods, but lack a unifying framework.
  • Understanding the structure and properties of these rules is crucial for fair representation.

Purpose of the Study:

  • To identify and classify broad categories of committee selection rules.
  • To analyze existing multiwinner voting rules within these identified classes.
  • To formulate and evaluate desirable properties for committee selection mechanisms.

Main Methods:

  • Analyzing committee selection rules as generalizations of single-winner scoring rules.

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  • Classifying rules such as SNTV, Bloc, k-Borda, STV, Chamberlin-Courant, and Monroe.
  • Formulating abstract properties of multiwinner voting and evaluating rules against them.

    • Main Results:

    • Identification of two natural, broad classes encompassing many existing committee selection rules.
    • Demonstration that numerous established rules belong to one or both identified classes.
    • Systematic evaluation of considered rules based on formulated desirable properties.

    Conclusions:

    • The proposed classification provides a unifying framework for understanding committee selection rules.
    • The evaluation against desirable properties offers insights into the strengths and weaknesses of different voting mechanisms.
    • This work contributes to the theoretical foundation of fair and effective multiwinner voting systems.