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Computational Politics: Electoral Systems

  • Edith Hemaspaandra
  • Lane A. Hemaspaandra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)

Abstract

This paper discusses three computation-related results in the study of electoral systems:
  1. 1.

    Determining the winner in Lewis Carroll’s 1876 electoral system is complete for parallel access to NP [22].

     
  2. 2.

    For any electoral system that is neutral, consistent, and Condorcet, determining the winner is complete for parallel access to NP [21].

     
  3. 3.

    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 [24].

     

Keywords

Power Index Electoral System Condorcet Winner Electoral College Election Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. Adleman. Time, space, and randomness. Technical Report MIT/LCS/TM-131, MIT, Cambridge, MA, April1979.Google Scholar
  2. 2.
    K. Arrow. Social Choice and Individual Values. John Wiley and Sons, 1951 revised editon, 1963.Google Scholar
  3. 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. 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
  5. 5.
    J. Bartholdi, III, C. Tovey, and M. Trick. The computational difficulty of manipulating an election. Social Choice and Welfare, 6:227–241, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    J. Bartholdi III, C. Tovey, and M. Trick. Voting schemes for which it can be difficult to tell who won the election. Social Choice and Welfare, 6:157–165, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    J. Bartholdi III, C. Tovey, and M. Trick. How hard is it to control an election ? Mathematical and Computer Modeling, 16(8/9):27–40, 1992.CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    R. Beigel, L. Hemachandra, and G. Wechsung. Probabilistic polynomial time is closed under parity reductions. Information Processing Letters, 37(2):91–94, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    D. Black. Theory of Committees and Elections. Cambridge University Press, 1958.Google Scholar
  10. 10.
    S. Buss and L. Hay. On truth-table reducibility to SAT. Information and Computation, 91(1):86–102, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy I: Structural properties. SIAM Journal on Computing, 17(6):1232–1252, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung. The boolean hierarchy II: Applications. SIAM Journal on Computing, 18(1):95–111, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 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. 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. 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
  16. 16.
    W. Feller. An introduction to probability theory and its applications. Wiley, New York, 1968.zbMATHGoogle Scholar
  17. 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. 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
  19. 19.
    L. Hemachandra. The strong exponential hierarchy collapses. Journal of Computer and System Sciences, 39(3):299–322, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    L. Hemachandra and G. Wechsung. Kolmogorov characterizations of complexity classes. Theoretical Computer Science, 83:313–322, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    E. Hemaspaandra. The complexity of Kemeny elections. In preparation.Google Scholar
  22. 22.
    E. Hemaspaandra, L. Hemaspaandra, and J. Rothe. Exact analysis of Dodgson elections: Lewis Carroll’s 1876 voting system is complete for parallel access to NP. Journal of the ACM, 44(6):806–825, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    E. Hemaspaandra, L. Hemaspaandra, and J. Rothe. Raising NP lower bounds to parallel NP lower bounds. SIGACT News, 28(2):2–13, 1997.CrossRefGoogle Scholar
  24. 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.
  25. 25.
    J. Kadin. PNP[logn] and sparse Turing-complete sets for NP. Journal of Computer and System Sciences, 39(3):282–298, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    J. Kemeny and L. Snell. Mathematical Models in the Social Sciences. Ginn, 1960.Google Scholar
  27. 27.
    J. Köbler, U. Schöning, and K. Wagner. The difference and truth-table hierarchies for NP. RAIRO Theoretical Informatics and Applications, 21:419–435, 1987.zbMATHGoogle Scholar
  28. 28.
    R. Ladner, N. Lynch, and A. Selman. A comparison of polynomial time reducibilities. Theoretical Computer Science, 1(2):103–124, 1975.zbMATHCrossRefMathSciNetGoogle Scholar
  29. 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. 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. 31.
    I. McLean and A. Urken. Classics of Social Choice. University of Michigan Press, 1995.Google Scholar
  32. 32.
    R. Niemi and W. Riker. The choice of voting systems. Scientific American, 234:21–27, 1976.CrossRefGoogle Scholar
  33. 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
  34. 34.
    K. Prasad and J. Kelly. NP-completeness of some problems concerning voting games. International Journal of Game Theory, 19:1–9, 1990.zbMATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    K. Regan and J. Royer. On closure properties of bounded two-sided error complexity classes. Mathematical Systems Theory, 28(3):229–244, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  36. 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
  37. 37.
    L. Shapley and M. Shubik. A method of evaluating the distribution of power in a committee system. American Political Science Review, 48:787–792, 1954.CrossRefGoogle Scholar
  38. 38.
    H. Simon. The Sciences of the Artificial. MIT Press, 1969. Second edition, 1981.Google Scholar
  39. 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. 40.
    P Straffin, Jr. Homogeneity, independence, and power indices. Public Choice, 30 (Summer), 1977.Google Scholar
  41. 41.
    United States Department of Commerce et al. versus Montana et al. US Supreme Court Case 91–860. Decided March 31, 1992.Google Scholar
  42. 42.
    S. Toda. PP is as hard as the polynomial-time hierarchy. SIAM Journal on Computing, 20(5):865–877, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    S. Toda and M. Ogiwara. Counting classes are at least as hard as the polynomialtime hierarchy. SIAM Journal on Computing, 21(2):316–328, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  44. 44.
    L. Valiant. The complexity of computing the permanent. Theoretical Computer Science, 8(2):189–201, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  45. 45.
    L. Valiant. The complexity of enumeration and reliability problems. SIAM Journal on Computing, 8(3):410–421, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  46. 46.
    K. Wagner. More complicated questions about maxima and minima, and some closures of NP. Theoretical Computer Science, 51(1–2):53–80, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  47. 47.
    K. Wagner. Bounded query classes. SIAM Journal on Computing, 19(5):833–846, 1990.zbMATHCrossRefMathSciNetGoogle Scholar
  48. 48.
    H. Young and A. Levenglick. A consistent extension of Condorcet’s election principle. SIAM Journal on Applied Mathematics, 35(2):285–300, 1978.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Edith Hemaspaandra
    • 1
  • Lane A. Hemaspaandra
    • 2
  1. 1.Department of Computer ScienceRochester Institute of TechnologyRochesterUSA
  2. 2.Department of Computer ScienceUniversity of RochesterRochesterUSA

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