Condorcet's paradox

Abrams, R.: 1976, ?The Voter's Paradox and the Homogeneity of Individual Preference Orders?, Public Choice 26, 19?27.

Arrow, K. J.: 1963, Social Choice and Individual Values (2nd edn), Wiley, New York.

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Beck, N.: 1975, ?A Note on the Probability of a Tied Election?, Public Choice 23, 75?79.

Bell, C. E.: 1978, ?What Happens When Majority Rule Breaks Down?, Public Choice 33, 121?126.

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Bernholz, O.: 1973, ?Logrolling, Arrow Paradox, and Cyclical Majorities?, Public Choice 15, 87?95.

Bernholz, P.: 1974, ?Logrolling, Arrow Paradox, and Decision Rules ? A Generalization?, Kyklos 27, 49?62.

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Black, D.: 1948c, ?The Decisions of a Committee Using a Special Majority?, Econometrica 16, 245?261.

Black, D.: 1948d, ?The Elasticity of Committee Decisions with an Altering Size of Majority?, Econometrica 16, 262?270.

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Blin, J. M.: 1973, ?Intransitive Social Orderings and the Probability of the Condorcet Effect?, Kyklos 26, 25?35.

Blydenburgh, J. C.: 1971, ?The Closed Rule and the Paradox of Voting?, Journal of Politics 33, 57?71.

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.

Buckley, J. J.: 1975, ?A Note on Unconditional Probabilities and the Voter's Paradox?, Public Choice 24, 111?114.

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.

Campbell, C. D. and Tullock, G.: 1965, ?A Measure of the Importance of Cyclical Majorities?, Economic Journal 7, 853?857.

Campbell, C. D. and Tullock, G.: 1966, ?The Paradox of Voting - A Possible Method of Calculation?, American Political Science Review 60, 684?685.

Chamberlain, G. and Rothschild, M.: 1981, ?A Note on the Probability of Casting a Decisive Vote?, Journal of Economic Theory, in press.

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.

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).

Craven, J.: 1971, ?Majority Voting and Social Choice?, Review of Economic Studies 38, 265?267.

DeMeyer, F. and Plott, C. R.: 1970, ?The Probability of a Cyclical Majority?, Econometrica 38, 345?354.

Dobra, J. and Tullock, G.: 1981, ?An Approach to Empirical Measures of Voting Paradoxes?, Public Choice 36, 193?194.

Downs, A.: 1961, ?In Defense of Majority Voting?, Journal of Political Economy 69, 192?199.

Fishburn, P. C.: 1973a, The Theory of Social Choice, Princeton University Press.

Fishburn, P. C.: 1973b, ?A Proof of May's Theorem P(m, 4) = 2P(m, 3)?, Behavioral Science 18, 212.

Fishburn, P. C.: 1973c, ?Voter Concordance, Simple Majorities and Group Decision Methods?, Behavioral Science 18, 364?376.

Fishburn, P. C.: 1974, ?Paradoxes of Voting?, American Political Science Review 68, 537?546.

Fishburn, P. C.: 1976, ?Acceptable Social Choice Lotteries?, Prepared for the International Symposium on Decision Theory and Social Ethics, held in Bavaria.

Fishburn, P. C. and Gehrlein, W. V.: 1980a, ?Social Homogeneity and Condorcet's Paradox?, Public Choice 35, 403?420.

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.

Fishburn, P. C., Gehrlein, W. V., and Maskin, E.: 1979a, ?A Progress Report on Kelly's Majority Conjectures?, Economics Letters 2, 313?314.

Fishburn, P. C., Gehrlein, W. V. and Maskin, E.: 1979b, ?Condorcet Proportions and Kelly's Conjectures?, Discrete Applied Mathematics 1, 229?252.

Garman, M. B. and Kamien, M. I.: 1968, ?The Paradox of Voting: Probability Calculations?, Behavioral Science 13, 306?316.

Gehrlein, W. V.: 1978, ?Condorcet Winners in Dual Cultures?, Presented at National Meeting of the Public Choice Society.

Gehrlein, W. V.: 1979, ?A Representation for Quadrivariate Normal Positive Orthant Probabilities?, Communications in Statistics - Simulation and Computation B8, 349?358.

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.

Gehrlein, W. V.: 1981b, ?The Expected Probability of Condorcet's Paradox?, Economics Letters, 7, 33?37.

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.

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.

Gehrlein, W. V.: 1981d, ?Single Stage Election Procedures for Large Electorates?, Journal of Mathematical Economics, 8, 263?275.

Gehrlein, W. V. and Fishburn, P. C.: 1976a, ?Condorcet's Paradox and Anonymous Preference Profiles?, Public Choice 26, 1?18.

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.

Gehrlein, W. V. and Fishburn, P. C.: 1978a, ?Probabilities of Election Outcomes For Large Electorates?, Journal of Economic Theory 19, 38?49.

Gehrlein, W. V. and Fishburn, P. C.: 1978b, ?The Effects of Abstentions on Election Outcomes?, Public Choice 33, 69?82.

Gehrlein, W. V. and Fishburn, P. C.: 1979a, ?Proportions of Profiles With a Majority Candidate?, Computers and Mathematics with Applications 5, 117?124.

Gehrlein, W. V. and Fishburn, P. C.: 1979b, ?Effects of Abstentions on Voting Procedure in Three-Candidate Elections?, Behavioral Science 24, 346?354.

Gehrlein, W. V. and Fishburn, P. C.: 1981, ?Scoring and Majority Agreements for Large Electorates with Arbitrary Preferences?, Mathematical Social Sciences, forthcoming.

Gillett, R.: 1977, ?Collective Indecision?, Behavioral Science 22, 383?390.

Gillett, R.: 1978, ?A Recursion Relation For the Probability of the Paradox of Voting?, Journal of Economic Theory 18, 318?327.

Gillett, R.: 1979, ?Borda Indecision?, unpublished manuscript.

Gillett, R.: 1980a, ?The Asymptotic Likelihood of Agreement Between Plurality and Condorcet Outcomes?, Behavioral Science 25, 23?32.

Gillett, R.: 1980b, ?The Comparative Likelihood of an Equivocal Outcome Under Plurality, Condorcet and Borda Voting Procedures?, Public Choice 35, 483?491.

Granger, G. G.: 1956, La Mathematique Sociale de Marquis de Condorcet, Presses Universitaires de France, Paris.

Guilbaud, G. T.: 1952, ?Les Theories de L.interet general et le probleme logique de l'agregation?, Economie Appliquee 5, 501?584.

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.

Huntingdon, E. V.: 1938, ?A Paradox in the Scoring of Competing Teams?, Science 88, 287?288.

Inada, K. I.: 1964, ?A Note on the Simple Majority Decision Rule?, Econometrica 32, 525?531.

Jamison, D. T.: 1975, ?The Probability of Intransitive Majority Rule: An Empirical Study?, Public Choice 23, 87?94.

Jamison, D. and Luce, E.: 1972, ?Social Homogeneity and the Probability of Intransitive Majority Rule?, Journal of Economic Theory 5, 79?87.

Johnson, N. L. and Kotz, S.: 1972, Distributions in Statistics: Continuous Multivariate Distributions, John Wiley, New York, 1972.

Kelly, J. S.: 1974, ?Voting Anomalies, The Number of Voters, and the Number of Alternatives?, Econometrica 42, 239?251.

Kendall, M. G. and Stuart, A.: 1963, The Advanced Theory of Statistics, Griffin Publishing, London.

Klahr, D.: 1966, ?A Computer Simulation of the Paradox of Voting?, American Political Science Review 60, 284?390.

Koehler, D.: 1975, ?Vote Trading and the Voting Paradox: A Proof of Logical Equivalence?, American Political Science Review 69, 954?960.

Kuga, K. and Nagatani, H.: 1974, ?Voter Antagonism and The Paradox of Voting?, Econometrica 42, 1045?1067.

Ludwin, W. G.: 1976, ?Voting Methods: A Simulation?, Public Choice 25, 19?30.

Margolis, H.: 1977, ?Probability of a Tie Election?, Public Choice 31, 135?138.

Marz, R. H., Casstevens, T. W., and Casstevens, H. T.: 1973, ?The Hunting of the Paradox?, Public Choice 15, 97?102.

May, R. M.: 1971, ?Some Mathematical Remarks On the Paradox of Voting?, Behavioral Science 16, 143?151.

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.

Niemi, R. G.: 1970, ?The Occurrence of the Paradox of Voting in University Elections?, Public Choice 8, 91?100.

Niemi, R. G. and Riker, W. H.: 1976, ?The Choice of Voting Systems?, Scientific American 234, 21?27.

Niemi, R. G. and Weisberg, H. F.: ?A Mathematical Solution for the Probability of the Paradox of Voting?, Behavioral Science 13, 317?323.

Paris, D. C.: 1975, ?Plurality Distortion and Majority Rule?, Behavioral Science 20, 125?133.

Pomeranz, J. E. and Weil, R. L.: 1970, ?The Cyclical Majority Problem?, Communications of the ACM 13, 251?254.

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.

Riker, W. H.: 1958, ?The Paradox of Voting and Congressional Rules for Voting on Amendments?, American Political Science Review 52, 349?366.

Rosenthal, R. W.: 1975, ?Voting Majority Sizes?, Econometrica 43, 293?299.

Ruben, H.: 1954, ?On the Moments of Order Statistics in Samples from Normal Populations?, Biometrika 41, 200?227.

Sen, A.: 1970, Collective Choice and Social Welfare, Holden-Day, San Francisco.

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.

Srivastava, M. S. and Khatri, C. G.: 1979, An Introduction to Multivariate Statistics, North Holland Publishing, New York.

Steck, G. P.: 1962, ?Orthant Probabilities for the Equicorrelated Multivariate Normal Distribution?, Biometrika 49, 433?445.

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.

Tullock, G.: 1959, ?Problems of Majority Voting?, Journal of Political Economy 67, 57?79.

Tullock, G.: 1967, ?The General Irrelevance of the General Impossibility Theorem?, Quarterly Journal of Economics 81, 256?270.

Tullock, G. and Campbell, C. D.: 1979, ?Computer Simulation of a Small Voting System?, Economic Journal 80, 97?104.

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.

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.

Williamson, O. E. and Sargent, T. J.: 1967, ?Social Choice: A Probabilistic Approach?, Economic Journal 77, 797?813.