×

Condorcet’s paradox. (English) Zbl 0512.90009


MSC:

91B14 Social choice
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abrams, R.: 1976, ?The Voter’s Paradox and the Homogeneity of Individual Preference Orders?, Public Choice 26, 19-27. · doi:10.1007/BF01725790
[2] Arrow, K. J.: 1963, Social Choice and Individual Values (2nd edn), Wiley, New York. · Zbl 0984.91513
[3] Bacon, R. H.: 1963, ?Approximations to Multivariate Normal Orthant Probabilities?, Annals of Mathematical Statistics 34, 191-198. · Zbl 0245.62057 · doi:10.1214/aoms/1177704254
[4] Beck, N.: 1975, ?A Note on the Probability of a Tied Election?, Public Choice 23, 75-79. · doi:10.1007/BF01718092
[5] Bell, C. E.: 1978, ?What Happens When Majority Rule Breaks Down?, Public Choice 33, 121-126. · doi:10.1007/BF00118362
[6] Bell, C. E.: 1981, ?A Random Graph Almost Surely Has a Hamiltonian Cycle When the Number of Alternatives is Large?, Econometrica. · Zbl 0469.90005
[7] Bernholz, O.: 1973, ?Logrolling, Arrow Paradox, and Cyclical Majorities?, Public Choice 15, 87-95. · doi:10.1007/BF01718844
[8] Bernholz, P.: 1974, ?Logrolling, Arrow Paradox, and Decision Rules ? A Generalization?, Kyklos 27, 49-62. · doi:10.1111/j.1467-6435.1974.tb01897.x
[9] Black, D.: 1948a, ?On the Rationale of Group Decision Making?, Journal of Political Economy 56, 23-43. · doi:10.1086/256633
[10] Black, D.: 1948b, ?Un Approcio Alla Teoria Delle Decisioni di Comitato?, Giornale Delgi Economisti e Annali di Economica 7 (new series), 262-284.
[11] Black, D.: 1948c, ?The Decisions of a Committee Using a Special Majority?, Econometrica 16, 245-261. · Zbl 0033.29304 · doi:10.2307/1907278
[12] Black, D.: 1948d, ?The Elasticity of Committee Decisions with an Altering Size of Majority?, Econometrica 16, 262-270. · Zbl 0033.29305 · doi:10.2307/1907279
[13] Black, D.: 1949a, ?The Elasticity of Committee Decisions with Alterations in the Members’ Preference Structures?, South African Journal of Economics 17, 88-102. · doi:10.1111/j.1813-6982.1949.tb01530.x
[14] Black, D.: 1949b, ?The Theory of Elections in Single-Member Constituences?, Canadian Journal of Economics and Political Science 15, 158-175. · doi:10.2307/137722
[15] Black, D.: 1949c, ?Some Theoretical Schemes of Proportional Representation?, Canadian Journal of Economics and Political Science 15, 334-343. · doi:10.2307/138094
[16] Black, D.: 1958, The Theory of Committees and Elections, Cambridge University Press, Cambridge. · Zbl 0091.15706
[17] Blin, J. M.: 1973, ?Intransitive Social Orderings and the Probability of the Condorcet Effect?, Kyklos 26, 25-35. · doi:10.1111/j.1467-6435.1973.tb01850.x
[18] Blydenburgh, J. C.: 1971, ?The Closed Rule and the Paradox of Voting?, Journal of Politics 33, 57-71. · doi:10.2307/2128532
[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.
[20] Buckley, J. J.: 1975, ?A Note on Unconditional Probabilities and the Voter’s Paradox?, Public Choice 24, 111-114. · doi:10.1007/BF01718420
[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. · Zbl 0443.90006
[22] Campbell, C. D. and Tullock, G.: 1965, ?A Measure of the Importance of Cyclical Majorities?, Economic Journal 7, 853-857. · doi:10.2307/2229705
[23] Campbell, C. D. and Tullock, G.: 1966, ?The Paradox of Voting - A Possible Method of Calculation?, American Political Science Review 60, 684-685.
[24] Chamberlain, G. and Rothschild, M.: 1981, ?A Note on the Probability of Casting a Decisive Vote?, Journal of Economic Theory, in press. · Zbl 0474.90011
[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. · doi:10.2307/1954543
[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).
[27] Craven, J.: 1971, ?Majority Voting and Social Choice?, Review of Economic Studies 38, 265-267. · Zbl 0228.90004 · doi:10.2307/2296783
[28] DeMeyer, F. and Plott, C. R.: 1970, ?The Probability of a Cyclical Majority?, Econometrica 38, 345-354. · doi:10.2307/1913015
[29] Dobra, J. and Tullock, G.: 1981, ?An Approach to Empirical Measures of Voting Paradoxes?, Public Choice 36, 193-194. · doi:10.1007/BF00163785
[30] Downs, A.: 1961, ?In Defense of Majority Voting?, Journal of Political Economy 69, 192-199. · doi:10.1086/258455
[31] Fishburn, P. C.: 1973a, The Theory of Social Choice, Princeton University Press. · Zbl 0253.92006
[32] Fishburn, P. C.: 1973b, ?A Proof of May’s Theorem P(m, 4) = 2P(m, 3)?, Behavioral Science 18, 212. · doi:10.1002/bs.3830180309
[33] Fishburn, P. C.: 1973c, ?Voter Concordance, Simple Majorities and Group Decision Methods?, Behavioral Science 18, 364-376. · doi:10.1002/bs.3830180505
[34] Fishburn, P. C.: 1974, ?Paradoxes of Voting?, American Political Science Review 68, 537-546. · doi:10.2307/1959503
[35] Fishburn, P. C.: 1976, ?Acceptable Social Choice Lotteries?, Prepared for the International Symposium on Decision Theory and Social Ethics, held in Bavaria. · Zbl 0405.90002
[36] Fishburn, P. C. and Gehrlein, W. V.: 1980a, ?Social Homogeneity and Condorcet’s Paradox?, Public Choice 35, 403-420. · doi:10.1007/BF00128119
[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. · doi:10.1016/0047-2727(80)90006-7
[38] Fishburn, P. C., Gehrlein, W. V., and Maskin, E.: 1979a, ?A Progress Report on Kelly’s Majority Conjectures?, Economics Letters 2, 313-314. · doi:10.1016/0165-1765(79)90042-9
[39] Fishburn, P. C., Gehrlein, W. V. and Maskin, E.: 1979b, ?Condorcet Proportions and Kelly’s Conjectures?, Discrete Applied Mathematics 1, 229-252. · Zbl 0427.90007 · doi:10.1016/0166-218X(79)90001-5
[40] Garman, M. B. and Kamien, M. I.: 1968, ?The Paradox of Voting: Probability Calculations?, Behavioral Science 13, 306-316. · doi:10.1002/bs.3830130405
[41] Gehrlein, W. V.: 1978, ?Condorcet Winners in Dual Cultures?, Presented at National Meeting of the Public Choice Society.
[42] Gehrlein, W. V.: 1979, ?A Representation for Quadrivariate Normal Positive Orthant Probabilities?, Communications in Statistics - Simulation and Computation B8, 349-358. · Zbl 0411.62030 · doi:10.1080/03610917908812124
[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.
[44] Gehrlein, W. V.: 1981b, ?The Expected Probability of Condorcet’s Paradox?, Economics Letters, 7, 33-37. · doi:10.1016/0165-1765(81)90107-5
[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.
[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.
[47] Gehrlein, W. V.: 1981d, ?Single Stage Election Procedures for Large Electorates?, Journal of Mathematical Economics, 8, 263-275. · Zbl 0461.90005 · doi:10.1016/0304-4068(81)90005-7
[48] Gehrlein, W. V. and Fishburn, P. C.: 1976a, ?Condorcet’s Paradox and Anonymous Preference Profiles?, Public Choice 26, 1-18. · doi:10.1007/BF01725789
[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. · Zbl 0351.90002 · doi:10.1016/0022-0531(76)90063-6
[50] Gehrlein, W. V. and Fishburn, P. C.: 1978a, ?Probabilities of Election Outcomes For Large Electorates?, Journal of Economic Theory 19, 38-49. · Zbl 0399.90007 · doi:10.1016/0022-0531(78)90054-6
[51] Gehrlein, W. V. and Fishburn, P. C.: 1978b, ?The Effects of Abstentions on Election Outcomes?, Public Choice 33, 69-82. · doi:10.1007/BF00118358
[52] Gehrlein, W. V. and Fishburn, P. C.: 1979a, ?Proportions of Profiles With a Majority Candidate?, Computers and Mathematics with Applications 5, 117-124. · Zbl 0408.90011 · doi:10.1016/0898-1221(79)90064-6
[53] Gehrlein, W. V. and Fishburn, P. C.: 1979b, ?Effects of Abstentions on Voting Procedure in Three-Candidate Elections?, Behavioral Science 24, 346-354. · doi:10.1002/bs.3830240507
[54] Gehrlein, W. V. and Fishburn, P. C.: 1981, ?Scoring and Majority Agreements for Large Electorates with Arbitrary Preferences?, Mathematical Social Sciences, forthcoming. · Zbl 0479.90014
[55] Gillett, R.: 1977, ?Collective Indecision?, Behavioral Science 22, 383-390. · doi:10.1002/bs.3830220603
[56] Gillett, R.: 1978, ?A Recursion Relation For the Probability of the Paradox of Voting?, Journal of Economic Theory 18, 318-327. · Zbl 0386.90006 · doi:10.1016/0022-0531(78)90086-8
[57] Gillett, R.: 1979, ?Borda Indecision?, unpublished manuscript.
[58] Gillett, R.: 1980a, ?The Asymptotic Likelihood of Agreement Between Plurality and Condorcet Outcomes?, Behavioral Science 25, 23-32. · doi:10.1002/bs.3830250104
[59] Gillett, R.: 1980b, ?The Comparative Likelihood of an Equivocal Outcome Under Plurality, Condorcet and Borda Voting Procedures?, Public Choice 35, 483-491. · doi:10.1007/BF00128125
[60] Granger, G. G.: 1956, La Mathematique Sociale de Marquis de Condorcet, Presses Universitaires de France, Paris.
[61] Guilbaud, G. T.: 1952, ?Les Theories de L.interet general et le probleme logique de l’agregation?, Economie Appliquee 5, 501-584.
[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. · doi:10.1007/BF01718846
[63] Huntingdon, E. V.: 1938, ?A Paradox in the Scoring of Competing Teams?, Science 88, 287-288. · doi:10.1126/science.88.2282.287
[64] Inada, K. I.: 1964, ?A Note on the Simple Majority Decision Rule?, Econometrica 32, 525-531. · doi:10.2307/1910176
[65] Jamison, D. T.: 1975, ?The Probability of Intransitive Majority Rule: An Empirical Study?, Public Choice 23, 87-94. · doi:10.1007/BF01718094
[66] Jamison, D. and Luce, E.: 1972, ?Social Homogeneity and the Probability of Intransitive Majority Rule?, Journal of Economic Theory 5, 79-87. · doi:10.1016/0022-0531(72)90119-6
[67] Johnson, N. L. and Kotz, S.: 1972, Distributions in Statistics: Continuous Multivariate Distributions, John Wiley, New York, 1972. · Zbl 0248.62021
[68] Kelly, J. S.: 1974, ?Voting Anomalies, The Number of Voters, and the Number of Alternatives?, Econometrica 42, 239-251. · Zbl 0289.90005 · doi:10.2307/1911974
[69] Kendall, M. G. and Stuart, A.: 1963, The Advanced Theory of Statistics, Griffin Publishing, London. · Zbl 0416.62001
[70] Klahr, D.: 1966, ?A Computer Simulation of the Paradox of Voting?, American Political Science Review 60, 284-390.
[71] Koehler, D.: 1975, ?Vote Trading and the Voting Paradox: A Proof of Logical Equivalence?, American Political Science Review 69, 954-960. · doi:10.2307/1958410
[72] Kuga, K. and Nagatani, H.: 1974, ?Voter Antagonism and The Paradox of Voting?, Econometrica 42, 1045-1067. · Zbl 0293.90020 · doi:10.2307/1914217
[73] Ludwin, W. G.: 1976, ?Voting Methods: A Simulation?, Public Choice 25, 19-30. · doi:10.1007/BF01726328
[74] Margolis, H.: 1977, ?Probability of a Tie Election?, Public Choice 31, 135-138. · doi:10.1007/BF01718979
[75] Marz, R. H., Casstevens, T. W., and Casstevens, H. T.: 1973, ?The Hunting of the Paradox?, Public Choice 15, 97-102. · doi:10.1007/BF01718845
[76] May, R. M.: 1971, ?Some Mathematical Remarks On the Paradox of Voting?, Behavioral Science 16, 143-151. · doi:10.1002/bs.3830160204
[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. · Zbl 0193.14103
[78] Niemi, R. G.: 1970, ?The Occurrence of the Paradox of Voting in University Elections?, Public Choice 8, 91-100. · doi:10.1007/BF01718507
[79] Niemi, R. G. and Riker, W. H.: 1976, ?The Choice of Voting Systems?, Scientific American 234, 21-27. · doi:10.1038/scientificamerican0676-21
[80] Niemi, R. G. and Weisberg, H. F.: ?A Mathematical Solution for the Probability of the Paradox of Voting?, Behavioral Science 13, 317-323.
[81] Paris, D. C.: 1975, ?Plurality Distortion and Majority Rule?, Behavioral Science 20, 125-133.
[82] Pomeranz, J. E. and Weil, R. L.: 1970, ?The Cyclical Majority Problem?, Communications of the ACM 13, 251-254. · Zbl 0195.03103 · doi:10.1145/362258.362282
[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. · doi:10.2307/1952537
[84] Riker, W. H.: 1958, ?The Paradox of Voting and Congressional Rules for Voting on Amendments?, American Political Science Review 52, 349-366. · doi:10.2307/1952321
[85] Rosenthal, R. W.: 1975, ?Voting Majority Sizes?, Econometrica 43, 293-299. · Zbl 0325.90004 · doi:10.2307/1913586
[86] Ruben, H.: 1954, ?On the Moments of Order Statistics in Samples from Normal Populations?, Biometrika 41, 200-227. · Zbl 0055.12803
[87] Sen, A.: 1970, Collective Choice and Social Welfare, Holden-Day, San Francisco. · Zbl 0227.90011
[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.
[89] Srivastava, M. S. and Khatri, C. G.: 1979, An Introduction to Multivariate Statistics, North Holland Publishing, New York. · Zbl 0421.62034
[90] Steck, G. P.: 1962, ?Orthant Probabilities for the Equicorrelated Multivariate Normal Distribution?, Biometrika 49, 433-445. · Zbl 0114.10606
[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. · doi:10.1007/BF01726329
[92] Tullock, G.: 1959, ?Problems of Majority Voting?, Journal of Political Economy 67, 57-79. · doi:10.1086/258244
[93] Tullock, G.: 1967, ?The General Irrelevance of the General Impossibility Theorem?, Quarterly Journal of Economics 81, 256-270. · doi:10.2307/1879585
[94] Tullock, G. and Campbell, C. D.: 1979, ?Computer Simulation of a Small Voting System?, Economic Journal 80, 97-104. · doi:10.2307/2230441
[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.
[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. · doi:10.1002/bs.3830180204
[97] Williamson, O. E. and Sargent, T. J.: 1967, ?Social Choice: A Probabilistic Approach?, Economic Journal 77, 797-813. · doi:10.2307/2229568
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.