Monotone Randomized Apportionment

Published Online:https://doi.org/10.1287/opre.2024.1362

References

  • ACE Electoral Knowledge Network (2022) Electoral system (chamber 1). Accessed June 30, 2026, https://aceproject.org/epic-en.Google Scholar
  • Adams J (1776) Letter to John Penn. Accessed June 30, 2026, https://founders.archives.gov/documents/Adams/06-04-02-0026-0003.Google Scholar
  • Aziz H, Lev O, Mattei N, Rosenschein JS, Walsh T (2019) Strategyproof peer selection using randomization, partitioning, and apportionment. Artificial Intelligence 275:295–309.CrossrefGoogle Scholar
  • Balinski ML, Young HP (1978) Stability, coalitions and schisms in proportional representation systems. Amer. Political Sci. Rev. 72(3):848–858.CrossrefGoogle Scholar
  • Balinski ML, Young HP (2001) Fair Representation: Meeting the Ideal of One Man, One Vote, 2nd ed. (Brookings Institution Press, Washington, DC).Google Scholar
  • Borcea J, Brändén P, Liggett TM (2009) Negative dependence and the geometry of polynomials. J. Amer. Math. Soc. 22(2):521–567.CrossrefGoogle Scholar
  • Brändén P, Jonasson J (2012) Negative dependence in sampling. Scandinavian J. Statist. 39(4):830–838.CrossrefGoogle Scholar
  • Brewer KRW, Hanif M (1983) An Introduction to Sampling with Unequal Probabilities, vol. 15 (Springer, New York).CrossrefGoogle Scholar
  • Byrka J, Skowron P, Sornat K (2018) Proportional approval voting, harmonic k-median, and negative association. 45th Internat. Colloquium Automata Languages Programming (Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Wadern, Germany).Google Scholar
  • Cembrano J, Correa J, Griesbach SM, Verdugo V (2026) Online proportional apportionment. Proc. 2026 Annual ACM-SIAM Sympos. Discrete Algorithms (SODA) (SIAM, Philadelphia), 4846–4860.Google Scholar
  • Charikar M, Li S (2012) A dependent LP-rounding approach for the k-median problem. Proc. 39th Internat. Colloquium on Automata, Languages, and Programming (ICALP 2012), Lecture Notes in Computer Science, vol. 7391 (Springer, Berlin, Heidelberg), 194–205. Google Scholar
  • Chekuri C, Vondrák J, Zenklusen R (2010) Dependent randomized rounding via exchange properties of combinatorial structures. Proc. 51st Annual IEEE Sympos. Foundations of Comput. Sci. (FOCS 2010) (IEEE, Piscataway, NJ), 575–584.Google Scholar
  • Chen XH, Dempster AP, Liu JS (1994) Weighted finite population sampling to maximize entropy. Biometrika 81(3):457–469.CrossrefGoogle Scholar
  • Cheng Y, Jiang Z, Munagala K, Wang K (2020) Group fairness in committee selection. ACM Trans. Econom. Comput. 8(4):1–18.CrossrefGoogle Scholar
  • Deville J-C, Tillé Y (1998) Unequal probability sampling without replacement through a splitting method. Biometrika 85(1):89–101.CrossrefGoogle Scholar
  • European Parliament (2019) Rule of procedure. Accessed June 30, 2026, https://www.europarl.europa.eu/doceo/document/RULES-9-2019-07-02_EN.pdf.Google Scholar
  • Gandhi R, Khuller S, Parthasarathy S, Srinivasan A (2006) Dependent rounding and its applications to approximation algorithms. J. ACM 53(3):324–360.CrossrefGoogle Scholar
  • German Federal Ministry of Justice (2008) Gesetz zur Änderung des Wahl- und Abgeordnetenrechts vom 17. Accessed June 30, 2026, http://www.bgbl.de/xaver/bgbl/start.xav?startbk=Bundesanzeiger_BGBl&jumpTo=bgbl108010s0394.pdf.Google Scholar
  • Gölz P, Peters D, Procaccia AD (2026) In this apportionment lottery, the house always wins. Oper. Res. 74(1):390–407.LinkGoogle Scholar
  • Grafström A (2009) Non-rejective implementations of the Sampford sampling design. J. Statist. Planning Inference 139(6):2111–2114.CrossrefGoogle Scholar
  • Grimmett G (2004) Stochastic apportionment. Amer. Math. Monthly 111(4):299–307.CrossrefGoogle Scholar
  • Hájek J (1981) Sampling from a Finite Population, Number 37 in Statistics (Dekker, New York).Google Scholar
  • Hedayat A, Lin BY, Stufken J (1989) The construction of ΠPS sampling designs through a method of emptying boxes. Ann. Statist. 17(4):1886–1905.CrossrefGoogle Scholar
  • Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. J. Amer. Statist. Assoc. 47(260):663–685.CrossrefGoogle Scholar
  • Madow WG (1949) On the theory of systematic sampling, II. Ann. Math. Statist. 20(3):333–354.CrossrefGoogle Scholar
  • Myerson RB (1981) Optimal auction design. Math. Oper. Res. 6(1):58–73.LinkGoogle Scholar
  • Naor J, Srinivasan A, Wajc D (2025) Online dependent rounding schemes for bipartite matchings, with applications. Proc. 2025 Annual ACM-SIAM Sympos. Discrete Algorithms (SODA) (SIAM, Philadelphia), 3116–3154.Google Scholar
  • Panconesi A, Srinivasan A (1997) Randomized distributed edge coloring via an extension of the Chernoff–Hoeffding bounds. SIAM J. Comput. 26(2):350–368.CrossrefGoogle Scholar
  • Robinson EA, Ullman D (2010) A Mathematical Look at Politics (CRC Press, Boca Raton, FL).CrossrefGoogle Scholar
  • Sampford MR (1967) On sampling without replacement with unequal probabilities of selection. Biometrika 54(3–4):499–513.CrossrefGoogle Scholar
  • Srinivasan A (2001) Distributions on levelsets with applications to approximation algorithms. Proc. 42nd IEEE Sympos. Foundations Comput. Sci. (IEEE Computer Society, Washington, DC), 588–597.Google Scholar
  • Szpiro G (2010) Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Thomson W (2011) Fair allocation rules. Arrow KJ, Sen A, Suzumura K, eds. Handbook of Social Choice and Welfare, vol. 2 (Elsevier, Amsterdam), 393–506.CrossrefGoogle Scholar
  • Tillé Y (2006) Sampling Algorithms, Springer Series in Statistics (Springer, New York).Google Scholar
  • Tillé Y (2023) Remarks on some misconceptions about unequal probability sampling without replacement. Comput. Sci. Rev. 47:100533.CrossrefGoogle Scholar
  • Wajc D (2017) Negative association—Definition, properties, and applications. Accessed June 30, 2026, https://www.cs.cmu.edu/∼dwajc/notes/Negative%20Association.pdf.Google Scholar
  • Yates F, Grundy PM (1953) Selection without replacement from within strata with probability proportional to size. J. Roy. Statist. Soc. Ser. B Methodological 15(2):253–261.CrossrefGoogle Scholar
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