Theory and Decision

, Volume 15, Issue 2, pp 161–197 | Cite as

Condorcet's paradox

  • William V. Gehrlein

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abrams, R.: 1976, ‘The Voter's Paradox and the Homogeneity of Individual Preference Orders’, Public Choice 26, 19–27.Google Scholar
  2. Arrow, K. J.: 1963, Social Choice and Individual Values (2nd edn), Wiley, New York.Google Scholar
  3. Bacon, R. H.: 1963, ‘Approximations to Multivariate Normal Orthant Probabilities’, Annals of Mathematical Statistics 34, 191–198.Google Scholar
  4. Beck, N.: 1975, ‘A Note on the Probability of a Tied Election’, Public Choice 23, 75–79.Google Scholar
  5. Bell, C. E.: 1978, ‘What Happens When Majority Rule Breaks Down’, Public Choice 33, 121–126.Google Scholar
  6. Bell, C. E.: 1981, ‘A Random Graph Almost Surely Has a Hamiltonian Cycle When the Number of Alternatives is Large’, Econometrica.Google Scholar
  7. Bernholz, O.: 1973, ‘Logrolling, Arrow Paradox, and Cyclical Majorities’, Public Choice 15, 87–95.Google Scholar
  8. Bernholz, P.: 1974, ‘Logrolling, Arrow Paradox, and Decision Rules — A Generalization’, Kyklos 27, 49–62.Google Scholar
  9. Black, D.: 1948a, ‘On the Rationale of Group Decision Making’, Journal of Political Economy 56, 23–43.Google Scholar
  10. Black, D.: 1948b, ‘Un Approcio Alla Teoria Delle Decisioni di Comitato’, Giornale Delgi Economisti e Annali di Economica 7 (new series), 262–284.Google Scholar
  11. Black, D.: 1948c, ‘The Decisions of a Committee Using a Special Majority’, Econometrica 16, 245–261.Google Scholar
  12. Black, D.: 1948d, ‘The Elasticity of Committee Decisions with an Altering Size of Majority’, Econometrica 16, 262–270.Google Scholar
  13. Black, D.: 1949a, ‘The Elasticity of Committee Decisions with Alterations in the Members' Preference Structures’, South African Journal of Economics 17, 88–102.Google Scholar
  14. Black, D.: 1949b, ‘The Theory of Elections in Single-Member Constituences’, Canadian Journal of Economics and Political Science 15, 158–175.Google Scholar
  15. Black, D.: 1949c, ‘Some Theoretical Schemes of Proportional Representation’, Canadian Journal of Economics and Political Science 15, 334–343.Google Scholar
  16. Black, D.: 1958, The Theory of Committees and Elections, Cambridge University Press, Cambridge.Google Scholar
  17. Blin, J. M.: 1973, ‘Intransitive Social Orderings and the Probability of the Condorcet Effect’, Kyklos 26, 25–35.Google Scholar
  18. Blydenburgh, J. C.: 1971, ‘The Closed Rule and the Paradox of Voting’, Journal of Politics 33, 57–71.Google Scholar
  19. Bowen, B. D.: 1972, ‘Toward an Estimate of the Frequency of Occurrence of the Paradox of Voting in U.S. Senate Roll Call Votes’, in Biemi and Weisberg, (eds.), Probability Models of Collective Decision Making, Charles E. Merrill, Columbus, Ohio, pp. 181–203.Google Scholar
  20. Buckley, J. J.: 1975, ‘A Note on Unconditional Probabilities and the Voter's Paradox’, Public Choice 24, 111–114.Google Scholar
  21. Buckley, J. J. and Westen, T. E.: 1979, ‘The Probability of the Voter's Paradox for an Even Number of Voters’, Journal of Interdisciplinary Modeling and Simulation 2, 185–210.Google Scholar
  22. Campbell, C. D. and Tullock, G.: 1965, ‘A Measure of the Importance of Cyclical Majorities’, Economic Journal 7, 853–857.Google Scholar
  23. Campbell, C. D. and Tullock, G.: 1966, ‘The Paradox of Voting - A Possible Method of Calculation’, American Political Science Review 60, 684–685.Google Scholar
  24. Chamberlain, G. and Rothschild, M.: 1981, ‘A Note on the Probability of Casting a Decisive Vote’, Journal of Economic Theory, in press.Google Scholar
  25. Chamberlin, J. R. and Cohen, M. D.: 1978, ‘Towards Applicable Social Choice Theory: A Comparison of Social Choice Functions Under Spatial Model Assumptions’, American Political Science Review 72, 1341–1356.Google Scholar
  26. Condorcet, Marquis de: 1785, Essai sur l'application de l'analyse a la probilite des decisions rendues a la pluralite dex voix, Paris, 1785 (reprinted in 1973 by Chelsea Press, New York).Google Scholar
  27. Craven, J.: 1971, ‘Majority Voting and Social Choice’, Review of Economic Studies 38, 265–267.Google Scholar
  28. DeMeyer, F. and Plott, C. R.: 1970, ‘The Probability of a Cyclical Majority’, Econometrica 38, 345–354.Google Scholar
  29. Dobra, J. and Tullock, G.: 1981, ‘An Approach to Empirical Measures of Voting Paradoxes’, Public Choice 36, 193–194.Google Scholar
  30. Downs, A.: 1961, ‘In Defense of Majority Voting’, Journal of Political Economy 69, 192–199.Google Scholar
  31. Fishburn, P. C.: 1973a, The Theory of Social Choice, Princeton University Press.Google Scholar
  32. Fishburn, P. C.: 1973b, ‘A Proof of May's Theorem P(m, 4) = 2P(m, 3)’, Behavioral Science 18, 212.Google Scholar
  33. Fishburn, P. C.: 1973c, ‘Voter Concordance, Simple Majorities and Group Decision Methods’, Behavioral Science 18, 364–376.Google Scholar
  34. Fishburn, P. C.: 1974, ‘Paradoxes of Voting’, American Political Science Review 68, 537–546.Google Scholar
  35. Fishburn, P. C.: 1976, ‘Acceptable Social Choice Lotteries’, Prepared for the International Symposium on Decision Theory and Social Ethics, held in Bavaria.Google Scholar
  36. Fishburn, P. C. and Gehrlein, W. V.: 1980a, ‘Social Homogeneity and Condorcet's Paradox’, Public Choice 35, 403–420.Google Scholar
  37. Fishburn, P. C. and Gehrlein, W. V.: 1980b, ‘The Paradox of Voting: Effects of Individual Indifference and Intransitivity’, Journal of Public Economics 14, 83–94.Google Scholar
  38. Fishburn, P. C., Gehrlein, W. V., and Maskin, E.: 1979a, ‘A Progress Report on Kelly's Majority Conjectures’, Economics Letters 2, 313–314.Google Scholar
  39. Fishburn, P. C., Gehrlein, W. V. and Maskin, E.: 1979b, ‘Condorcet Proportions and Kelly's Conjectures’, Discrete Applied Mathematics 1, 229–252.Google Scholar
  40. Garman, M. B. and Kamien, M. I.: 1968, ‘The Paradox of Voting: Probability Calculations’, Behavioral Science 13, 306–316.Google Scholar
  41. Gehrlein, W. V.: 1978, ‘Condorcet Winners in Dual Cultures’, Presented at National Meeting of the Public Choice Society.Google Scholar
  42. Gehrlein, W. V.: 1979, ‘A Representation for Quadrivariate Normal Positive Orthant Probabilities’, Communications in Statistics - Simulation and Computation B8, 349–358.Google Scholar
  43. Gehrlein, W. V.: 1981a, ‘The Frequency of Condorcet's Paradox in Large Groups’, Proceedings of the Northeast American Institute for Decision Sciences, Washington, D.C., pp. 121–123.Google Scholar
  44. Gehrlein, W. V.: 1981b, ‘The Expected Probability of Condorcet's Paradox’, Economics Letters, 7, 33–37.Google Scholar
  45. Gehrlein, W. V. and Bonwit, T.: 1981, ‘Juveniles' Preferences for Television Watching and Other Activities’, Proceedings of the Southeast American Institute for Decision Sciences, Charlotte, NC, pp. 170–171.Google Scholar
  46. Gehrlein, W. V.: 1981c, ‘Qualities of the Probability of a Condorcet Winner’, Proceedings of the Northeast American Institute for Decision Sciences, Boston, Massachusetts, pp. 133–135.Google Scholar
  47. Gehrlein, W. V.: 1981d, ‘Single Stage Election Procedures for Large Electorates’, Journal of Mathematical Economics, 8, 263–275.Google Scholar
  48. Gehrlein, W. V. and Fishburn, P. C.: 1976a, ‘Condorcet's Paradox and Anonymous Preference Profiles’, Public Choice 26, 1–18.Google Scholar
  49. Gehrlein, W. V. and Fishburn, P. C.: 1976b, ‘The Probability of the Paradox of Voting: A Computable Solution’, Journal of Economic Theory 13, 14–25.Google Scholar
  50. Gehrlein, W. V. and Fishburn, P. C.: 1978a, ‘Probabilities of Election Outcomes For Large Electorates’, Journal of Economic Theory 19, 38–49.Google Scholar
  51. Gehrlein, W. V. and Fishburn, P. C.: 1978b, ‘The Effects of Abstentions on Election Outcomes’, Public Choice 33, 69–82.Google Scholar
  52. Gehrlein, W. V. and Fishburn, P. C.: 1979a, ‘Proportions of Profiles With a Majority Candidate’, Computers and Mathematics with Applications 5, 117–124.Google Scholar
  53. Gehrlein, W. V. and Fishburn, P. C.: 1979b, ‘Effects of Abstentions on Voting Procedure in Three-Candidate Elections’, Behavioral Science 24, 346–354.Google Scholar
  54. Gehrlein, W. V. and Fishburn, P. C.: 1981, ‘Scoring and Majority Agreements for Large Electorates with Arbitrary Preferences’, Mathematical Social Sciences, forthcoming.Google Scholar
  55. Gillett, R.: 1977, ‘Collective Indecision’, Behavioral Science 22, 383–390.Google Scholar
  56. Gillett, R.: 1978, ‘A Recursion Relation For the Probability of the Paradox of Voting’, Journal of Economic Theory 18, 318–327.Google Scholar
  57. Gillett, R.: 1979, ‘Borda Indecision’, unpublished manuscript.Google Scholar
  58. Gillett, R.: 1980a, ‘The Asymptotic Likelihood of Agreement Between Plurality and Condorcet Outcomes’, Behavioral Science 25, 23–32.Google Scholar
  59. Gillett, R.: 1980b, ‘The Comparative Likelihood of an Equivocal Outcome Under Plurality, Condorcet and Borda Voting Procedures’, Public Choice 35, 483–491.Google Scholar
  60. Granger, G. G.: 1956, La Mathematique Sociale de Marquis de Condorcet, Presses Universitaires de France, Paris.Google Scholar
  61. Guilbaud, G. T.: 1952, ‘Les Theories de L.interet general et le probleme logique de l'agregation’, Economie Appliquee 5, 501–584.Google Scholar
  62. Hansen, T. J. and Prince, B. L.: 1973, ‘The Paradox of Voting: An Elementary Solution for the Case of Three Alternatives’, Public Choice 15, 103–117.Google Scholar
  63. Huntingdon, E. V.: 1938, ‘A Paradox in the Scoring of Competing Teams’, Science 88, 287–288.Google Scholar
  64. Inada, K. I.: 1964, ‘A Note on the Simple Majority Decision Rule’, Econometrica 32, 525–531.Google Scholar
  65. Jamison, D. T.: 1975, ‘The Probability of Intransitive Majority Rule: An Empirical Study’, Public Choice 23, 87–94.Google Scholar
  66. Jamison, D. and Luce, E.: 1972, ‘Social Homogeneity and the Probability of Intransitive Majority Rule’, Journal of Economic Theory 5, 79–87.Google Scholar
  67. Johnson, N. L. and Kotz, S.: 1972, Distributions in Statistics: Continuous Multivariate Distributions, John Wiley, New York, 1972.Google Scholar
  68. Kelly, J. S.: 1974, ‘Voting Anomalies, The Number of Voters, and the Number of Alternatives’, Econometrica 42, 239–251.Google Scholar
  69. Kendall, M. G. and Stuart, A.: 1963, The Advanced Theory of Statistics, Griffin Publishing, London.Google Scholar
  70. Klahr, D.: 1966, ‘A Computer Simulation of the Paradox of Voting’, American Political Science Review 60, 284–390.Google Scholar
  71. Koehler, D.: 1975, ‘Vote Trading and the Voting Paradox: A Proof of Logical Equivalence’, American Political Science Review 69, 954–960.Google Scholar
  72. Kuga, K. and Nagatani, H.: 1974, ‘Voter Antagonism and The Paradox of Voting’, Econometrica 42, 1045–1067.Google Scholar
  73. Ludwin, W. G.: 1976, ‘Voting Methods: A Simulation’, Public Choice 25, 19–30.Google Scholar
  74. Margolis, H.: 1977, ‘Probability of a Tie Election’, Public Choice 31, 135–138.Google Scholar
  75. Marz, R. H., Casstevens, T. W., and Casstevens, H. T.: 1973, ‘The Hunting of the Paradox’, Public Choice 15, 97–102.Google Scholar
  76. May, R. M.: 1971, ‘Some Mathematical Remarks On the Paradox of Voting’, Behavioral Science 16, 143–151.Google Scholar
  77. National Bureau of Standards: 1959, ‘Tables of the Bivariate Normal Distribution Function and Related Functions’, Applied Mathematics Series 50, U.S. Government Printing Office, Washington, D.C.Google Scholar
  78. Niemi, R. G.: 1970, ‘The Occurrence of the Paradox of Voting in University Elections’, Public Choice 8, 91–100.Google Scholar
  79. Niemi, R. G. and Riker, W. H.: 1976, ‘The Choice of Voting Systems’, Scientific American 234, 21–27.Google Scholar
  80. Niemi, R. G. and Weisberg, H. F.: ‘A Mathematical Solution for the Probability of the Paradox of Voting’, Behavioral Science 13, 317–323.Google Scholar
  81. Paris, D. C.: 1975, ‘Plurality Distortion and Majority Rule’, Behavioral Science 20, 125–133.Google Scholar
  82. Pomeranz, J. E. and Weil, R. L.: 1970, ‘The Cyclical Majority Problem’, Communications of the ACM 13, 251–254.Google Scholar
  83. Riker, W. H.: 1961, ‘Voting and the Summation of Preferences: An Interpretive Bibliographical Review of Selected Developments During the Last Decade’, American Political Science Review 55, 900–911.Google Scholar
  84. Riker, W. H.: 1958, ‘The Paradox of Voting and Congressional Rules for Voting on Amendments’, American Political Science Review 52, 349–366.Google Scholar
  85. Rosenthal, R. W.: 1975, ‘Voting Majority Sizes’, Econometrica 43, 293–299.Google Scholar
  86. Ruben, H.: 1954, ‘On the Moments of Order Statistics in Samples from Normal Populations’, Biometrika 41, 200–227.Google Scholar
  87. Sen, A.: 1970, Collective Choice and Social Welfare, Holden-Day, San Francisco.Google Scholar
  88. Sevcik, K. E.: 1969, ‘Exact Probabilities of a Voter's Paradox Through Seven Issues and Seven Judges’, University of Chicago Institute for Computer Research Quarterly Report 22, Sec. III-B.Google Scholar
  89. Srivastava, M. S. and Khatri, C. G.: 1979, An Introduction to Multivariate Statistics, North Holland Publishing, New York.Google Scholar
  90. Steck, G. P.: 1962, ‘Orthant Probabilities for the Equicorrelated Multivariate Normal Distribution’, Biometrika 49, 433–445.Google Scholar
  91. Sullivan, T.: 1976, ‘Voter's Paradox and Logrolling: An Initial Framework for Committee Behavior on Appropriations and Ways and Means’, Public Choice 25, 31–44.Google Scholar
  92. Tullock, G.: 1959, ‘Problems of Majority Voting’, Journal of Political Economy 67, 57–79.Google Scholar
  93. Tullock, G.: 1967, ‘The General Irrelevance of the General Impossibility Theorem’, Quarterly Journal of Economics 81, 256–270.Google Scholar
  94. Tullock, G. and Campbell, C. D.: 1979, ‘Computer Simulation of a Small Voting System’, Economic Journal 80, 97–104.Google Scholar
  95. Weisberg, H. F. and Niemi, R. G.: 1972, ‘Probability Calculations for Cyclical Majorities in Congressional Voting’, in Niemi and Weisberg, (eds.), Probability Models of Collective Decision Making, Charles E. Merrill, Columbus, Ohio, pp. 204–231.Google Scholar
  96. Weisberg, H. G. and Niemi, R. G.: 1973, ‘A Pairwise Probability Approach to the Likelihood of the Paradox of Voting’, Behavioral Science 18, 109–117.Google Scholar
  97. Williamson, O. E. and Sargent, T. J.: 1967, ‘Social Choice: A Probabilistic Approach’, Economic Journal 77, 797–813.Google Scholar

Copyright information

© D. Reidel Publishing Co 1983

Authors and Affiliations

  • William V. Gehrlein
    • 1
  1. 1.Department of Business AdministrationUniversity of DelawareNewarkU.S.A.

Personalised recommendations