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In This Apportionment Lottery, the House Always Wins

Paul Gölz¹; Dominik Peters²; Ariel D. Procaccia³

¹ University of California, Berkeley, Berkeley, California 94720; and Cornell University, Ithaca, New York 14850 · ² Centre National de la Recherche Scientifique, Laboratoire d’Analyse et de Modélisation des Systèmes pour l’Aide à la Décision, Université Paris Dauphine–Paris Sciences & Lettres, 75016 Paris, France · ³ School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138;

Randomized Apportionment: A Fairer Distribution of Seats The question of how to apportion the seats of the U.S. House of Representatives to states has fueled century-long political debates and sparked mathematical theory. Traditional deterministic methods, such as the Hamilton method or the currently used Huntington–Hill method, may result in paradoxes or substantially deviate from proportionality. In their paper “In This Apportionment Lottery, the House Always Wins,” Gölz, Peters, and Procaccia propose a randomized approach that ensures each state receives its exact proportional share of seats in expectation and its proportional share, up to rounding, ex post. By incorporating randomization, the authors argue, the system can better adhere to the principle of proportional representation, minimizing the impact of small counting errors and ensuring fairness over time. In addition, their approach achieves house monotonicity, a property that prevents counterintuitive outcomes when the total number of seats changes. This is achieved through a novel cumulative rounding technique, a generalization of dependent rounding on bipartite graphs with potential applications beyond apportionment, including EU commission nominations and resource allocation.

DOI

10.1287/opre.2022.0419

Volume

74 (1)

Pages

390-407

Language

en

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BibTeX

Sources

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