The New Mathematics of Democracy

Bailey Flanigan and Ismar Volic

Papers from arXiv.org

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.

Date: 2026-08
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