Congressional Apportionment: A Multiobjective Optimization Approach

References

• Agnew R (2008) Optimal congressional apportionment. Amer. Math. Monthly 115(4):297–303.Crossref, Google Scholar
• Balinski M (2005) What is just? Amer. Math. Monthly 112(6):502–511.Crossref, Google Scholar
• Balinski M, Young H (1974) A new method for congressional apportionment. Proc. Natl. Acad. Sci. USA 71(11):4602–4606.Crossref, Google Scholar
• Balinski M, Young H (1977) Apportionment schemes and the quota method. Amer. Math. Monthly 84(6):450–455.Crossref, Google Scholar
• Balinski M, Young H (1980) The Webster method of apportionment. Proc. Natl. Acad. Sci. USA 77(1):1–4.Crossref, Google Scholar
• Balinski M, Young H (1982) Fair Representation: Meeting the Ideal of One Man, One Vote (Yale University Press, New Haven, CT).Google Scholar
• Basso LJ, Goic M, Olivares M, Sauré D, Thraves C, Carranza A, Weintraub GY, Covarrubia J, Escobedo C, Jara N, Moreno A (2023) Analytics saves lives during the COVID-19 crisis in Chile. INFORMS J. Appl. Analytics 53(1):9–31.Google Scholar
• Birkhoff G (1976) House monotone apportionment schemes. Proc. Natl. Acad. Sci. USA 73(3):684–686.Crossref, Google Scholar
• Biró P, de Klundert JV, Manlove D, Pettersson W, Andersson T, Burnapp L, Chromy P, et al. (2021) Modelling and optimisation in European kidney exchange programmes. Eur. J. Oper. Res. 291(2):447–456.Crossref, Google Scholar
• Brennan Center for Justice (2022) Redistricting in the courts. Accessed January 10, 2022, https://www.brennancenter.org/issues/gerrymandering-fair-representation/redistricting/redistricting-courts.Google Scholar
• Burer S, Vandenbussche D (2006) A finite branch-and-bound algorithm for nonconvex quadratic programming via semidefinite relaxations. Math. Programming 113(2):259–282.Crossref, Google Scholar
• Burt O, Harris C Jr (1963) Letter to the editor—Apportionment of the U.S. House of Representatives: A minimum range, integer solution, allocation problem. Oper. Res. 11(4):648–652.Link, Google Scholar
• Delorme M, Garcia S, Gondzio J, Kalcsics J, Manlove D, Pettersson W (2023) New algorithms for hierarchical optimization in kidney exchange programs. Oper. Res., ePub ahead of print January 25, https://doi.org/10.1287/opre.2022.2374.Link, Google Scholar
• Dobbs K (2016) Optimal placement of family planning centers. Senior Independent Study thesis, Paper 7208, The College of Wooster, Wooster, OH.Google Scholar
• Drton M, Schwingenschlogl U (2005) Asymptotic seat bias formulas. Metrika 62(1):23–31.Crossref, Google Scholar
• Edelman P (2006) Minimum total deviations apportionment. Simeone B, Pukelsheim F, eds. Mathematics and Democracy (Springer, Berlin), 55–64.Crossref, Google Scholar
• El-Helaly S (2019) The Mathematics of Voting and Apportionment (Birkhäuser, Cham, Switzerland).Crossref, Google Scholar
• Ernst L (1994) Apportionment methods for the House of Representatives and the court challenges. Management Sci. 40(10):1207–1227.Link, Google Scholar
• Gilbert E, Schatz J (1964) Letter to the editor—An ill-conceived proposal for apportionment of the US House of Representatives. Oper. Res. 12(5):768–773.Link, Google Scholar
• Glorie K, van de Klundert J, Wagelmans A (2014) Kidney exchange with long chains: An efficient pricing algorithm for clearing barter exchanges with branch-and-price. Manufacturing Serv. Oper. Management 16(4):498–512.Link, Google Scholar
• Goldmacher S (2021) New York loses house seat after coming up 89 people short on census. New York Times (April 26), https://www.nytimes.com/2021/04/26/nyregion/new-york-census-congress.html.Google Scholar
• Grimmett G (2004) Stochastic apportionment. Amer. Math. Monthly 111(4):299–307.Crossref, Google Scholar
• Guo X, Li L, Xie H, Shi W (2020) Improved multi-objective optimization model for policy design of rental housing market. Sustainability 12(14):5710.Crossref, Google Scholar
• Gurobi (2021) Non-convex quadratic optimization. Accessed April 13, 2022, https://www.gurobi.com/nonconvex-quadratic-optimization/.Google Scholar
• Hershberger S (2022) Courts, commissions, and consultations: How mathematicians are working to end gerrymandering. Notices Amer. Math. Soc. 69(4):616–623.Crossref, Google Scholar
• Hillier F, Lieberman G (2015) Introduction to Operations Research, 10th ed. (McGraw-Hill, New York).Google Scholar
• Horst R (1976) An algorithm for nonconvex programming problems. Math. Programming 10(1):312–321.Crossref, Google Scholar
• Huntington E (1921a) The mathematical theory of the apportionment of representatives in Congress. Proc. Natl. Acad. Sci. USA 7(4):123–127.Crossref, Google Scholar
• Huntington E (1921b) A new method of apportionment of representatives. Quart. Pub. Amer. Statist. Assoc. 17(135):859–870.Google Scholar
• Huntington E (1928a) The apportionment of representatives in Congress. Trans. Amer. Math. Soc. 30(1):85–110.Crossref, Google Scholar
• Huntington E (1928b) The apportionment situation in Congress. Science 68(1772):579–582.Crossref, Google Scholar
• INFORMS (2018) FCC: Advancing wireless communication. Accessed June 20, 2023, https://www.informs.org/Impact/O.R.-Analytics-Success-Stories/Advancing-Wireless-Communication.Google Scholar
• Johnson M (2007) Planning models for the provision of affordable housing. Environ. Planning B. Urban Anal. City Sci. 34(3):501–523.Google Scholar
• Johnson M, Hurter A (1998) An optimization model for location of subsidized housing in metropolitan areas. Location Sci. 16(1–4):257–279.Crossref, Google Scholar
• Kahneman D, Tversky A (1979) Prospect theory: An analysis of decision under risk. Econometrica 47(2):263–292.Crossref, Google Scholar
• Koslap K (2021) How apportionment is calculated. Accessed June 21, 2023, https://www.census.gov/newsroom/blogs/random-samplings/2021/04/how-apportionment-is-calculated.html.Google Scholar
• Koslap K (2023) Personal communication.Google Scholar
• Lauwers L, Puyenbroeck T (2006a) The Balinski-Young comparison of divisor methods is transitive. Soc. Choice Welfare 26(3):603–606.Crossref, Google Scholar
• Lauwers L, Puyenbroeck T (2006b) The Hamilton apportionment method is between the Adams method and the Jefferson method. Math. Oper. Res. 31(2):390–397.Link, Google Scholar
• Lefkowitz J (2021) State loses representation. Times Union (August 1), https://www.timesunion.com/opinion/article/State-loses-representation-16354704.php.Google Scholar
• Leyvraz J, Rochat J (1975) On an apportionment method. Belgian J. Oper. Res. Statist. Comput. Sci. 15(1):1–10.Google Scholar
• Linderoth J (2005) A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math. Programming 103(2):251–282.Crossref, Google Scholar
• Marshall A, Olkin I, Pukelsheim F (2002) A majorization comparison of apportionment methods in proportional representation. Soc. Choice Welfare 19(4):885–900.Crossref, Google Scholar
• Mehrotra A, Johnson E, Nemhauser G (1998) An optimization based heuristic for political districting. Management Sci. 44(8):1100–1114.Link, Google Scholar
• National Conference of State Legislatures (2021) Redistricting and the Supreme Court: The most significant cases. Accessed January 10, 2022, https://www.ncsl.org/research/redistricting/redistricting-and-the-supreme-court-the-most-significant-cases.aspx.Google Scholar
• Owens F (1921) On the apportionment of representatives. Quart. Pub. Amer. Statist. Assoc. 17(136):958–968.Google Scholar
• Procaccia A (2021) Let’s raffle off congressional seats. Accessed August 7, https://www.bloomberg.com/opinion/articles/2021-05-05/post-census-raffle-would-make-congressional-reapportionment-fairer.Google Scholar
• Raber U (1998) A simplicial branch-and-bound method for solving nonconvex all-quadratic programs. J. Global Optim. 13(4):417–432.Crossref, Google Scholar
• Rawls J (1971) A Theory of Justice (Harvard University Press, Cambridge, MA).Crossref, Google Scholar
• Ricca F, Scozzari A, Simeone B (2013) Political districting: From classical models to recent approaches. Ann. Oper. Res. 204(204):271–299.Crossref, Google Scholar
• Roth A, Sonmez T, Unver M (2007) Efficient kidney exchange: Coincidence of wants in markets with compatibility-based preferences. Amer. Econom. Rev. 97(3):828–851.Crossref, Google Scholar
• Saari D (1978) Apportionment methods and the House of Representatives. Amer. Math. Monthly 85(10):792–802.Crossref, Google Scholar
• Schuster K, Pukelsheim F, Drton M, Draper N (2003) Seat bias apportionment methods for proportional representation. Electoral Stud. 22(4):651–676.Crossref, Google Scholar
• Schwingenschlogl U, Drton M (2004) Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation. Metrika 60(2):191–202.Crossref, Google Scholar
• Swamy R, King D, Jacobson S (2023) Multiobjective optimization for politically fair districting: A scalable multilevel approach. Oper. Res. 71(2):536–562.Link, Google Scholar
• U.S. Census Bureau (2021a) Computing apportionment. Accessed January 12, 2022, https://www.census.gov/topics/public-sector/congressional-apportionment/about/computing.html.Google Scholar
• U.S. Census Bureau (2021b) Historical apportionment data map. Accessed August 7, 2021, https://www.census.gov/library/visualizations/interactive/historical-apportionment-data-map.html.Google Scholar
• Validi H, Buchanan A, Lykhovyd E (2022) Imposing contiguity constraints in political districting models. Oper. Res. 70(2):867–892.Link, Google Scholar
• Wan Z (2006) Parameterized integer programming models for multifactors representatives apportionment. Soc. Sci. J. 43(2):259–272.Crossref, Google Scholar
• Wang H (2021) How 26 people in the census count helped Minnesota beat New York for a House seat. NPR (May 1), https://www.npr.org/2021/05/01/991671730/how-26-people-in-the-census-count-helped-minnesota-beat-new-york-for-a-house-sea.Google Scholar
• Wright T (2014) Lagrange’s identity and congressional apportionment. Amer. Math. Monthly 121(6):523–528.Crossref, Google Scholar
• Wright T (2021) From Cauchy–Schwarz to the House of Representatives: Applications of Lagrange’s identity. Math. Magazine 94(4):244–256.Crossref, Google Scholar
• Young HP (2001) Dividing the House: Why Congress should reinstate an old reapportionment formula. Accessed August 7, 2001, https://www.brookings.edu/research/dividing-the-house-why-congress-should-reinstate-an-old-reapportionment-formula/.Google Scholar
• Young HP (2004) Fairness in apportionment. Accessed August 7, 2021, https://www.census.gov/history/pdf/Fairness_in_Apportionment_Young.pdf.Google Scholar
• Zhong Q, Karner A, Kuby M, Golub A (2019) A multiobjective optimization model for locating affordable housing investments while maximizing accessibility to jobs by public transportation. Environ. Planning B. Urban Anal. City Sci. 46(3):490–510.Crossref, Google Scholar