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The New Mathematics of Democracy

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Listed:
  • Bailey Flanigan
  • Ismar Volic

Abstract

This article surveys emerging directions in the mathematics of democracy. It uses three case studies --- voting theory, participatory budgeting, and deliberative democracy --- to highlight how contemporary challenges motivate rigorous mathematical research that incorporates real-world data, institutional constraints, and implementation feasibility. Within each case, we highlight active and promising research frontiers, evidence of real-world impact, practical applications, and opportunities for getting involved.

Suggested Citation

  • Bailey Flanigan & Ismar Volic, 2026. "The New Mathematics of Democracy," Papers 2608.16869, arXiv.org, revised Sep 2026.
    • Handle: RePEc:arx:papers:2608.16869
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    File URL: https://arxiv.org/pdf/2608.16869
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    References listed on IDEAS

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    1. Bailey Flanigan & Paul Gölz & Anupam Gupta & Brett Hennig & Ariel D. Procaccia, 2021. "Fair algorithms for selecting citizens’ assemblies," Nature, Nature, vol. 596(7873), pages 548-552, August.
    2. David McCune & Jennifer Wilson, 2026. "Can ranked-choice voting elect the least popular candidate?," Papers 2602.21504, arXiv.org, revised Aug 2026.
    3. David McCune & E. E. Naber, 2026. "Ballot Exhaustion in Multiwinner Single Transferable Vote Elections," Papers 2605.12676, arXiv.org, revised Aug 2026.
    4. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2020. "The prevalence and consequences of ballot truncation in ranked-choice elections," Public Choice, Springer, vol. 184(1), pages 197-218, July.
    5. David McCune & Matthew I. Jones & Andy Schultz & Adam Graham-Squire & Ismar Volic & Belle See & Karen Xiao & Malavika Mukundan, 2026. "Candidate Moderation under Instant Runoff and Condorcet Voting: Evidence from the Cooperative Election Study," Papers 2603.03619, arXiv.org, revised Mar 2026.
    6. Sanyukta Deshpande & Nikhil Garg & Sheldon Jacobson, 2026. "Simpler than you think: the practical dynamics of ranked choice voting," Journal of Computational Social Science, Springer, vol. 9(2), pages 1-48, May.
    7. Simon Rey & Ulle Endriss & Ronald Haan, 2025. "A general framework for participatory budgeting with additional constraints," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(1), pages 5-41, February.
    8. David McCune & Adam Graham-Squire, 2024. "Monotonicity anomalies in Scottish local government elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 69-101, August.
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