Disposing dictators, demystifying voting paradoxes: Social choice analysis

Disposing Dictators, Demystifying Voting Paradoxes: Social Choice Analysis

Volumn , Issue , 2008, Pages 1-240

  Saari, Donald G ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84926205475     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511754265     Document Type: Book

References (120)

1. Anscombe, G. E. M., 1976, On the frustration of the majority by fulfillment of the majority’s will, Analysis 36, 161–68.
2. Arrow, K., 1951 (2nd ed., 1963), Social Choice and Individual Values, Wiley, New York.
3. Baigent, N., To appear, Topological theories of social choice, to appear in Handbook of Social Choice and Welfare, vol. 2, K. Arrow, A. Sen, and K. Suzumura, eds.
4. Banks, J., 1995, Singularity theory and core existence in the spatial models, Journal of Mathematical Economics 24, 523–36.
5. Baker, K. M., 1975, Condorcet: From Natural Philosophy to Social Mathematics, University of Chicago Press, Chicago.
6. Borda, J. C., 1781, Mémoire sur les élections au scrutin, Histoire de l’Académie Royale des Sciences, Paris.
7. Black, D., 1958, The Theory of Committees and Elections, Cambridge University Press, London.
8. Block, C., 1999, Truth and probability – Ironies in the evolution of social choice theory, Washington University Law Quarterly 76, 975–1037.
9. Brams, S., and P. Fishburn, 1978, Approval Voting, Birkhauser, Boston.
10. Campbell, D. E., and J. S. Kelly, 1997, Sen’s theorem and externalities, Economica 64, 375–86.
11. Chichilnisky, G., 1982, The topological equivalence of the Pareto conditions and the existence of a dictator, Journal of Mathematical Economics 9, 223–33.
12. Condorcet, M., 1785, Éssai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Paris.
13. Copeland, A. H., 1951, A reasonable social welfare function, University of Michigan, Mimeo.
14. Debreu, G., 1974, Excess demand functions, Journal of Mathematical Economics 1, 15–23.
15. Duxbury, A. (6th ed., 2000), An Introduction to the World’s Oceans, McGraw Hill, New York.
16. Enelow, J., and M. J. Hinich, 1990, Advances in the Spatial Theory of Voting, Cambridge University Press, New York.
17. Fine, B., 1975, Individual liberalism in a Paretian society, Journal of Political Economy 83, 1277–81.
18. Fishburn, P., 1974, Paradoxes of voting, American Political Science Review 68, 537–46.
19. Fishburn, P., 1981, Inverted orders for monotone scoring rules, Discrete Applied Mathematics 3, 27–36.
20. Gehrlein, W., 2006, Condorcet’s Paradox, Springer-Verlag, New York.
21. Golubitsky, M., and V. Guillemin, 1973, Stable Mappings and Their Singularities, Springer-Verlag, New York.
22. Haunsperger, D., 1992, Dictionaries of paradoxes for statistical tests on k samples, Journal of the American Statistical Association 87, 149–55.
23. Kemeny J., 1959, Mathematics without numbers, Daedalus 88, 571–91.
24. Kronewetter, J., and D. G. Saari, 2006, From decision problems to dethroned dictators, Journal of Mathematical Economics. Available online 4 August 2006.
25. Laruelle, A., and V. Merlin, 2002, Different least square values, different rankings, Social Choice & Welfare 19, 533–50.
26. Le Breton, M., and M. Truchon, 1997, A Borda measure for social choice functions, Mathematical Social Science 34, 249–72.
27. Li, L., and D. G. Saari, 2004, Sen’s theorem: Geometric proof and new interpretations, IMBS discussion papers. Social Choice & Welfare. (Online 1 Jan 2008.)
28. List, C., and P. Pettit, 2002, Aggregating sets of judgments: An impossibility result, Economics and Philosophy 18, 89–110.
29. Luce, R. D., 1959, Individual Choice Behavior, Wiley, New York. Republished 2005, Dover Publications, Mineloa, NY.
30. Mantel, R., 1972, On the characterization of aggregate excess demain, Journal of Economic Theory 7, 348.
31. Marcart, J., 1919, La vie et les travaux de chevalier Jean-Charles de Borda, Annales de l’Universite de Lyon 2.
32. McGann, A., 2006, The Logic of Democracy, Michigan Studies in Political Analysis, University of Michigan Press, Ann Arbor.
33. McGarvey, D. C., 1953, A theorem on the construction of voting paradoxes, Economectrica 21 (4), 608–10.
34. McKelvey, R., 1979, General conditions for global intransitivities in formal voting models, Econometrica 47, 1085–1112.
35. McKelvey, R., 1986, Structural instability of the core, Journal of Mathematical Economics 15, 179–98.
36. McKelvey, R., and N. Schofield, 1987, Generalized symmetry conditions at a core point, Econometrica 55, 923–34.
37. McLean, I., 2003, The reasonableness of independence: A conversation from Condorcet and Borda to Arrow and Saari, University of Oxford, Nuffield College Politics Working Paper 2003–W6.
38. McLean, I., and A. Urken, 1995, Classics of Social Choice, University of Michigan Press, Ann Arbor.
39. Merlin, V., and D. G. Saari, 1997, Copeland method II: Manipulation, monotonicity, and paradoxes, Journal of Economic Theory 72, 148–72.
40. Merlin, V., and D. G. Saari, 2000. Changes that cause changes, Social Choice & Welfare 17, 691–705. Ȯzkal-Sanver, [41] Merlin, V., Í. and R. Sanver, 2006, Properties of majoritarian compromise, efficient compromise and related compromise rules, Presentation at the Eighth International Meeting of the Society for Social Choice and Welfare, Istanbul, July.
41. Nanson, E. J., 1882, Methods of elections, Transactions and Proceedings of the Royal Society of Victoria 18, 197–240.
42. Nurmi, H., 1987, Comparing Voting Systems, D. Reidel, Dordrecht.
43. Nurmi, H., 1999, Voting Paradoxes and How To Deal with Them, Springer Verlag, New York.
44. Nurmi, H., 2002, Voting Procedures under Uncertainty, Springer, Heidelberg.
45. Pattanaik, P., 1996, On modelling individual rights: Some conceptual issues, pp. 100–28, in Social Choices Re-examined, K. Arrow, A. Sen, and K. Suzumura, eds., St. Martin’s Press, New York.
46. Plott, C., 1967, A notion of equilibrium and its possibility under majority rule, American Economic Review 57, 787–806.
47. Ratliff, T., 2001, A comparison of Dodgson’s method and Kemeny’s rule, Social Choice & Welfare 18, 79–89.
48. Ratliff, T., 2002, A comparison of Dodgson’s method and the Borda count, Economic Theory 20, 357–72.
49. Ratliff, T., 2003, Some startling paradoxes when electing committees, Social Choice & Welfare 21, 433–54.
50. Ratliff, T., 2006, Selecting committees, Public Choice 126, 343–55.
51. Richards, D., 1994. Intransitivities in multidimensional spatial voting, Social Choice & Welfare 11 (2), 109–19.
52. Riker, W. H., 1982, Liberalism against Populism, W. H. Freeman, San Francisco.
53. Saari, D. G., 1984, The ultimate of chaos resulting from weighted voting systems, Advances in Applied Mathematics 5, 286–308.
54. Saari, D. G., 1985, Iterative price mechanisms, Econometrica 53, 1117–33.
55. Saari, D. G., 1989, A dictionary for voting paradoxes, Journal of Economic Theory 48, 443–75.
56. Saari, D. G., 1990, Susceptibility to manipulation, Public Choice 64, 21–41.
57. Saari, D. G., 1990, The Borda dictionary, Social Choice & Welfare 7, 279– 317.
58. Saari, D. G., 1991, Relationship admitting families of candidates, Social Choice Welfare 8, 21–50.
59. Saari, D. G., 1992, Symmetry extensions of “neutrality”: I. Advantage to the Condorcet loser. Social Choice & Welfare 9, 307–36.
60. Saari, D. G., 1993, Symmetry extensions of “neutrality”: II. Partial ordering of dictionaries, Social Choice & Welfare 10, 301–34.
61. Saari, D. G., 1992, Millions of election rankings from a single profile, Social Choice & Welfare 9, 277–306.
62. Saari, D. G., 1994, Geometry of Voting, Springer-Verlag, New York.
63. Saari, D. G., 1995, Basic Geometry of Voting, Springer-Verlag, New York.
64. Saari, D. G., 1995, A chaotic exploration of aggregation paradoxes, SIAM Review 37, 37–52.
65. Saari, D. G., 1996, Election relations and a partial ordering for positional voting, in N. Schofield (ed.), Collective Decision-Making: Social Choice and Political Economy, Kluwer.
66. Saari, D. G., 1997, Informational geometry of social choice, Social Choice & Welfare 14, 211–32.
67. Saari, D. G., 1997, The generic existence of a core for q-rules, Economic Theory 9, 219–60.
68. Saari, D. G., 1998, Connecting and resolving Sen’s and Arrow’s theorems, Social Choice & Welfare 15, 239–61.
69. Saari, D. G., 1999, Explaining all three-alternative voting outcomes, Journal of Economic Theory 87, 313–55.
70. Saari, D. G., 2000, Mathematical structure of voting paradoxes 1; Pairwise vote, Economic Theory 15, 1–53.
71. Saari, D. G., 2000, Mathematical structure of voting paradoxes 2; Positional voting, Economic Theory 15, 55–101.
72. Saari, D. G., 2001, Geometry of voting, UCI preprint. To appear: Mathematical and Computer Modelling.
73. Saari, D. G., 2001, Chaotic Elections!, American Mathematical Society, Providence, RI.
74. Saari, D. G., 2001, Decisions and Elections: Explaining the Unexpected, Cambridge University Press, New York.
75. Saari, D. G., 2001, Analyzing a “nail-biting” election, Social Choice & Welfare 18, 415–30.
76. Saari, D. G., 2002, Adopting a plurality vote perspective, Math of Operations Research 27, 45–64.
77. Saari, D. G., 2003, Disturbing aspects of voting theory, Economic Theory 22, 529–56.
78. Saari, D. G., 2004, Geometry of stable and chaotic discussion, American Mathematics Monthly 111, 377–93.
79. Saari, D. G., 2005, Collisions, Rings, and Other Newtonian N-Body Problems, American Mathematical Society, Providence, RI.
80. Saari, D. G., 2005, The profile structure for Luce’s choice axiom, Journal of Mathematical Psychology 49, 226–53.
81. Saari, D. G., 2006, Which is better: The Condorcet or Borda winner? Social Choice & Welfare 26, 107–30.
82. Saari, D. G., 2007, Hidden mathematical structures of voting, pp. 221–34, in Mathematics and Democracy: Recent Advances in Voting Systems and Collective Choice, B. Simeone and F. Pukelsheim, eds. Springer, New York.
83. Saari, D. G., and G. Asay, 2006, Finessing a point: Augmenting the core, UCI Institute for Mathematical Behavioral Sciences, Working Paper.
84. Saari, D. G., and S. Barney, 2003, Consequences of reversing preferences, Math Intelligencer 25, 17–31.
85. Saari, D. G., and V. Merlin, 1996, Copeland method: I. Dictionaries and relationships, Economic Theory 8, 51–76.
86. Saari, D. G., and V. Merlin, 2000, A geometric examination of Kemeny’s rule, Social Choice & Welfare 17, 403–38.
87. Saari, D. G., and A. Petron, 2006, Negative externalities and Sen’s liberalism theorem, Economic Theory 28, 265–81.
88. Saari, D. G., and K. Sieberg, 2001, The sum of the parts can violate the whole, American Political Science Review 95, 415–30.
89. Saari, D. G., and K. Sieberg, 2001, Some surprising properties of power indices, Games and Economic Behavior 36, 241–63.
90. Saari, D. G., and K. Sieberg, 2004. Are part wise comparisons reliable? Research in Engineering Design 15, 62–71.
91. Saari, D. G., and C. P. Simon, 1977, Singularity theory of utility mappings I: Degenerate maxima and pareto optima, Journal of Mathematical Economics 4, 217–51.
92. Saari, D. G., and J. Van Newenhizen, 1988, The problem of indeterminacy in approval, multiple, and truncated voting systems, Public Choice 59, 101–20.
93. Saari, D. G., and J. Van Newenhizen, 1988, Is approval voting an “unmitigated evil?”, Public Choice 59, 133–47.
94. Saari, D. G., and M. Tataru, 1999, The likelihood of dubious election outcomes, Economic Theory 13, 345–63.
95. Salles, M., 1997, On modelling individual rights: Some conceptual issues: Discussion, pp. 129–33, in Social Choice Re-Examined, vol. 2, Ed. by K. J. Arrow, A. K. Sen, and K. Suzumura, St. Martin’s Press, New York.
96. Salles, M., 2000. Amartya Sen: Droits et choix social, Revue Economique 51, 445–57.
97. Schofield, N., 1983, General instability of majority rule, Review of Economic Studies 50, 695–705.
98. Seidl, C., 1975, On liberal values, Journal of Economics 35, 257–92.
99. Seidl, C., 1990, On the impossibility of a generalization of the libertarian resolution of the liberal paradox, Journal of Economics 51, 71–88.
100. Sen, A., 1970, The impossibility of a Paretian liberal. Journal of Political Economy 78, 152–57.
101. Sen, A., 1970, Collective Choice and Social Welfare, Holden Day, San Francisco.
102. Sen, A. K., 1970, The impossibility of a Paretian liberal. Journal of Political Economy 78 (1), 152–57.
103. Sen, A. K., 1976, Liberty, unanimity and rights, Economica 43 (171), 217–45.
104. Sen, A., 1983, Liberty and social choice, Journal of Philosophy 80, 5–28.
105. Sen, A., 1987, On Ethics and Economics, Basil Blackwell, Oxford.
106. Sen, A. K., 1992, Minimal liberty, Economica 59 (234), 139–60.
107. Sen, A. K., 1999, The possibility of social choice, American Economic Review 89 (3), 349–78.
108. Sieberg, K., 2001 (2nd ed., 2005), Criminal Dilemmas, Springer-Verlag, New York.
109. Sieberg, K., and M. D. McDonald, 2007, Probability and plausibility of cycles in three-party systems: A mathematical formulation and applications, Department of Political Science, Binghamton University, Binghamton, NY, preprint.
110. Sonnenschein, H., 1972, Market excess demand functions, Econometrica, 40, 549–63.
111. Sugden, R., 1978, Social choice and individual liberty, in Contemporary Economic Analysis, M. Martis and A. Norbay, eds., Croom Helm, London.
112. Sugden, R., 1985, Liberty, preference and choice, Economics and Philosophy 1, 213–19.
113. Tabarrok, A., 2001, Fundamentals of voting theory illustrated with the 1992 election, or could Perot have won in 1992? Public Choice 106, 275–97.
114. Tabarrok, A., and L. Spector, 1999, Would the Borda count have avoided the civil war? Journal of Theoretical Politics 11, 261–88.
115. Tataru, M., 1996, Growth Rates in Multidimensional Spatial Voting, Ph.D. Dissertation, Northwestern University.
116. Tataru, M., 1999, Growth rates in multidimensional spatial voting, Mathematical Social Sciences 37, 253–63.
117. Wuffle, A., S. Feld, G. Owen, and B. Grofman, 1989, Finagle’s law and the Finagle point, a new solution concept for two-candidate competition in spatial voting games without a core, American Journal of Political Science 33, 348–75.
118. Young, P., 1975, Social choice scoring functions, SIAM Journal of Applied Mathematics 28, 824–38.
119. Young, P., and A. Levenglick, 1978, A consistent extension of Condorcet’s election principle, SIAM Journal of Applied Mathematics 35, 285–300.
120. Young, P., 1995, Optimal voting rules, The Journal of Economic Perspectives 9, 51–64.