Computational Politics: Electoral Systems
Determining the winner in Lewis Carroll’s 1876 electoral system is complete for parallel access to NP .
For any electoral system that is neutral, consistent, and Condorcet, determining the winner is complete for parallel access to NP .
For each census in US history, a simulated annealing algorithm yields provably fairer (in a mathematically rigorous sense) congressional apportionments than any of the classic algorithms—even the algorithm currently used in the United States .
KeywordsPower Index Electoral System Condorcet Winner Electoral College Election Scheme
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- 1.L. Adleman. Time, space, and randomness. Technical Report MIT/LCS/TM-131, MIT, Cambridge, MA, April1979.Google Scholar
- 2.K. Arrow. Social Choice and Individual Values. John Wiley and Sons, 1951 revised editon, 1963.Google Scholar
- 3.M. Balinski and H. Young. Fair Representation: Meeting the Ideal of One Man, One Vote. Yale University Press, New Haven, 1982.Google Scholar
- 4.M. Balinski and H. Young. Fair representation: Meeting the ideal of one man, one vote. In H. Young, editor, Fair Allocation, pages 1–29. American Mathematical Society, 1985. Proceedings of Symposia in Applied Mathematics, V. 33.Google Scholar
- 9.D. Black. Theory of Committees and Elections. Cambridge University Press, 1958.Google Scholar
- 13.M. J. A. N. de Caritat, Marquis de Condorcet. Essai sur l’Application de L’Analyse á la Probabilité des Décisions Rendues á la Pluraliste des Voix. 1785. Facsimile reprint of original published in Paris, 1972, by the Imprimerie Royale.Google Scholar
- 14.C. Dodgson. A method of taking votes on more than two issues, 1876. Pamphlet printed by the Clarendon Press, Oxford, and headed “not yet published” (see the discussions in [31,9], both of which reprint this paper).Google Scholar
- 15.P. Dubey and L. Shapley. Mathematical properties of the Banzhaf power index. Mathematics of Operations Research, 4(2):99–131, May 1979.Google Scholar
- 17.M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, 1979.Google Scholar
- 18.J. Hartmanis. Generalized Kolmogorov complexity and the structure of feasible computations. In Proceedings of the 24th IEEE Symposium on Foundations of Computer Science, pages 439–445. IEEE Computer Society Press, 1983.Google Scholar
- 21.E. Hemaspaandra. The complexity of Kemeny elections. In preparation.Google Scholar
- 24.L. Hemaspaandra, K. Rajasethupathy, P. Sethupathy, and M. Zimand. Power balance and apportionment algorithms for the United States Congress. ACM Journal of Experimental Algorithmics, 3(1), 1998. URL http://www.jea.acm.org/1998/HemaspaandraPower, 16pp.
- 26.J. Kemeny and L. Snell. Mathematical Models in the Social Sciences. Ginn, 1960.Google Scholar
- 29.I. Mann and L. Shapley. Values of large games, IV: Evaluating the electoral college by Monte Carlo techniques. Research Memorandum RM-2651 (ASTIA No. AD 246277), The Rand Corporation, Santa Monica, CA, September 1960.Google Scholar
- 30.I. Mann and L. Shapley. Values of large games, VI: Evaluating the electoral college exactly. Research Memorandum RM-3158-PR, The Rand Corporation, Santa Monica, CA, 1962.Google Scholar
- 31.I. McLean and A. Urken. Classics of Social Choice. University of Michigan Press, 1995.Google Scholar
- 33.C. Papadimitriou and M. Yannakakis. On complexity as bounded rationality. In Proceedings of the 26th ACM Symposium on Theory of Computing, pages 726–733. ACM Press, 1994.Google Scholar
- 36.L. Shapley. Measurement of power in political systems. In W. Lucas, editor, Game Theory and its Applications, pages 69–81. American Mathematical Society, 1981. Proceedings of Symposia in Applied Mathematics, V. 24.Google Scholar
- 38.H. Simon. The Sciences of the Artificial. MIT Press, 1969. Second edition, 1981.Google Scholar
- 39.M. Sipser. Borel sets and circuit complexity. In Proceedings of the 15th ACM Symposium on Theory of Computing, pages 61–69. ACM Press, 1983.Google Scholar
- 40.P Straffin, Jr. Homogeneity, independence, and power indices. Public Choice, 30 (Summer), 1977.Google Scholar
- 41.United States Department of Commerce et al. versus Montana et al. US Supreme Court Case 91–860. Decided March 31, 1992.Google Scholar