Abstract
The apportionment problem deals with the fair distribution of a discrete set of \(k\) indivisible resources (such as legislative seats) to \(n\) entities (such as parties or geographic subdivisions). Highest averages methods are a frequently used class of methods for solving this problem. We present an \(O(n)\)-time algorithm for performing apportionment under a large class of highest averages methods. Our algorithm works for all highest averages methods used in practice.
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Lijphart, A.: Degrees of Proportionality of Proportional Representation Formulas. In: Grofman, B., Lijphart, A. (eds.) Electoral Laws and Their Political Consequences, pp. 170–179. Agathon Press Inc., New York (1986)
Athanasopoulos, B.: The Apportionment Problem and its Application in Determining Political Representation. Spoudai Journal of Economics and Business 43(3–4), 212–237 (1993)
Owens, F.W.: On the Apportionment of Representatives. Quarterly Publications of the American Statistical Association 17(136), 958–968 (1921)
Athanasopoulos, B.: Probabilistic Approach to the Rounding Problem with Applications to Fair Representation. In: Anastassiou, G., Rachev, S.T. (eds.) Approximation, Probability, and Related Fields, pp. 75–99. Springer US (1994)
Mayberry, J.P.: Allocation for Authorization Management (1978)
Campbell, R.B.: The Apportionment Problem. In: Michaels, J.G., Rosen, K.H. (eds.) Applications of Discrete Mathematics, Updated Edition, pp. 2–18. McGraw-Hill Higher Education, New York (2007)
Huntington, E.V.: The Apportionment of Representatives in Congress. Transactions of the American Mathematical Society 30(1), 85–110 (1928)
Balinski, M.L., Young, H.P.: On Huntington Methods of Apportionment. SIAM Journal on Applied Mathematics 33(4), 607–618 (1977)
Balinski, M.L., Young, H.P.: Fair Representation: Meeting the Ideal of One Man, One Vote. Yale University Press, New Haven and London (1982)
Dorfleitner, G., Klein, T.: Rounding with multiplier methods: An efficient algorithm and applications in statistics. Statistical Papers 40(2), 143–157 (1999)
Zachariasen, M.: Algorithmic aspects of divisor-based biproportional rounding. Technical report, Dept. of Computer Science, University of Copenhagen (June 2005)
Ito, A., Inoue, K.: Linear-time algorithms for apportionment methods. In: Proceedings of EATCS/LA Workshop on Theoretical Computer Science, University of Kyoto, Japan, pp. 85–91 (February 2004)
Ito, A., Inoue, K.: On d’hondt method of computing. IEICE Transactions D, 399–400 (February 2006)
Galil, Z., Megiddo, N.: A Fast Selection Algorithm and the Problem of Optimum Distribution of Effort. Journal of the ACM 26(1), 58–64 (1979)
Frederickson, G.N., Johnson, D.B.: The Complexity of Selection and Ranking in X + Y and Matrices with Sorted Columns. Journal of Computer and System Sciences 24(2), 197–208 (1982)
Frederickson, G.N., Johnson, D.B.: Generalized Selection and Ranking: Sorted Matrices. SIAM Journal on Computing 13(1), 14–30 (1984)
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Cheng, Z., Eppstein, D. (2014). Linear-Time Algorithms for Proportional Apportionment. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_46
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DOI: https://doi.org/10.1007/978-3-319-13075-0_46
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