Linear-Time Algorithms for Proportional Apportionment
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.
KeywordsRank Function Arithmetic Progression Diophantine Approximation Rounding Function Parliamentary System
Unable to display preview. Download preview PDF.
- 1.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)Google Scholar
- 2.Athanasopoulos, B.: The Apportionment Problem and its Application in Determining Political Representation. Spoudai Journal of Economics and Business 43(3–4), 212–237 (1993)Google Scholar
- 4.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)Google Scholar
- 5.Mayberry, J.P.: Allocation for Authorization Management (1978)Google Scholar
- 6.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)Google Scholar
- 9.Balinski, M.L., Young, H.P.: Fair Representation: Meeting the Ideal of One Man, One Vote. Yale University Press, New Haven and London (1982)Google Scholar
- 11.Zachariasen, M.: Algorithmic aspects of divisor-based biproportional rounding. Technical report, Dept. of Computer Science, University of Copenhagen (June 2005)Google Scholar
- 12.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)Google Scholar
- 13.Ito, A., Inoue, K.: On d’hondt method of computing. IEICE Transactions D, 399–400 (February 2006)Google Scholar