Complexity and the geometry of voting

Mathematical and Computer Modelling

Volumn 48, Issue 9-10, 2008, Pages 1335-1356

  Saari, Donald G ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Complexity; Geometry of voting; Voting paradoxes

Indexed keywords

COMPLEXITY; GEOMETRIC APPROACHES; GEOMETRY OF VOTING; MONOTONICITY; STRATEGIC BEHAVIOR; VOTING PARADOXES;

CHLORINE COMPOUNDS;

EID: 53049087863     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2008.05.033     Document Type: Article

References (62)

1. Brams S., and Fishburn P. Approval Voting (1983), Birkhauser Verlag, New York
2. Saari D.G. Mathematics and voting. Notices of AMS (2008)
3. Saari D.G. Dethroning Dictators; Demystifying Voting Paradoxes (2008), Cambridge University Press, New York
4. Saari D.G. Basic Geometry of Voting (1995), Springer-Verlag, Heildelberg
5. Saari D.G., and Valognes F. Geometry, voting, and paradoxes. Mathematics Magazine 4 (1998) 243-259
6. Saari D.G., and Valognes F. The geometry of Black's single peakedness and related conditions. Journal of Mathematical Economics 32 (1999) 429-456
7. Saari D.G., and Sieberg K.K. The sum of the parts can violate the whole. American Political Science Review (2001) 415-433
8. Arrow K.J. Social Choice and Individual Values. 2nd ed. (1963), Wiley, New York
9. Saari D.G. Geometry of Voting (1994), Springer-Verlag, Heildelberg
10. Saari D.G. Chaotic Elections! A Mathematician Looks at Voting (2001), American Mathematical Society, Providence, RI
11. Nurmi H. Voting Paradoxes and How to Deal with Them (1999), Springer-Verlag, NY
12. H. Nurmi, Monotonicity and its cognates in the theory of choice, Department of Political Science, University of Turku, Turku, Finland, 2001
13. Nurmi H. Voting Procedures Under Uncertainty (2002), Springer-Verlag, NY
14. Tabarrok A. President Perot or fundamentals of voting theory illustrated with the 1992 election, or could Perot have won in 1992?. Public Choice 106 (2001) 275-297
15. Tabarrok A., and Spector L. Would the Borda count have avoided the civil war?. Journal of Theoretical Politics 11 (1999) 261-288
16. Saari D.G. Explaining all three-alternative voting outcomes. Journal of Economic Theory 87 (1999) 313-335
17. Saari D.G. Mathematical structure of voting paradoxes II: Positional voting. Economic Theory 15 (2000) 55-101
18. Black D. The Theory of Committees and Elections (1958), Cambridge University Press, London, New York
19. Ward B. Majority voting and alternative forms of public enterprises. In: Margolis J. (Ed). The Public Economy of Urban Expenditures (1965), John Hopkins Press, Baltimore
20. Saari D.G. The profile structure for Luce's choice axiom. Journal of Mathematical Psychology 49 (2005) 226-253
21. Anscombe G.E.M. On the frustration of the majority by fulfillment of the majority's will. Analysis 36 (1976) 161-168
22. Brams S., Kilgour D., and Zwicker W. The paradox of multiple elections. Social Choice & Welfare 15 (1998) 211-236
23. Saari D.G. Analyzing Pairwise Voting Rules. In: Wiberg M. (Ed). Reasoned Choices (2004), Finnish Political Science Association, Turku, Finland 318-342
24. Ostrogorski M. Democracy and the Organization of Political Parties vol. I, II (1970), Haskell House, New York
25. List C., and Pettit P. Aggregating sets of judgments: An impossibility result. Economics and Philosophy 18 (2002) 89-110
26. Saari D.G. Decisions and Elections; Explaining the Unexpected (2001), Cambridge University Press, NY
27. Sen A. The impossibility of a paretian liberal. Journal of Political Economy 78 (1970) 152-157
28. Saari D.G., and Petron A. Negative externalities and Sen's liberalism theorem. Economic Theory 28 (2006) 265-281
29. McGarvey D.C. A theorem on the construction of voting paradoxes. Econometrica 21 (1953) 608-610
30. Saari D.G. Mathematical structure of voting paradoxes I: Pairwise vote. Economic Theory 15 (2000) 1-53
31. Saari D.G., and Merlin V. Copeland method I: Dictionaries and relationships. Economic Theory 8 (1996) 51-76
32. Saari D.G., and Merlin V. A geometric examination of Kemeny's rule. Social Choice & Welfare 17 (2000) 403-438
33. Le Breton M., and Truchon M. A Borda measure for social choice functions. Mathematical Social Sciences 34 (1997) 249-272
34. Young H.P. Condorcet's theory of voting. American Political Science Review 82 (1988) 1231-1244
35. Young H.P., and Levenglick A. A consistent extension of Condorcet's election principle. SIAM Journal of Applied Mathematics 35 (1978) 285-300
36. Ratliff T. A comparison of Dodgson's method and Kemeny's rule. Social Choice and Welfare 18 (2001) 79-89
37. Ratliff T. A comparison of Dodgson's method and the Borda count. Economic Theory 20 (2002) 357-372
38. Ratliff T. Some startling paradoxes when electing committees. Social Choice & Welfare 21 (2003) 433-454
39. Saari D.G. Calculus and extensions of Arrow's theorem. Journal of Mathematical Economics 20 (1991) 271-306
40. Wilson R. Social choice theory without the Pareto principle. Journal of Economic Theory 5 (1972) 478-486
41. Kalai E., Muller E., and Satterthwaite M. Social welfare functions when preferences are convex, strictly monotonic, and continuous. Public Choice 34 (1979) 87-97
42. Saari D.G. Connecting and resolving Sen's and Arrow's theorems. Social Choice & Welfare 15 (1998) 239-261
43. Fishburn P., and Brams S. Paradoxes of preferential voting. Mathematics Magazine 56 (1983) 207-214
44. Gibbard A. Manipulation of voting schemes: A general result. Econometrica 41 (1973) 587-601
45. Satterthwaite M. Strategyproofness and Arrow's conditions. Journal of Economic Theory 10 (1975) 187-217
46. Saari D.G. Unsettling aspects of voting theory. Economic Theory 22 (2003) 529-556
47. Merlin V., and Saari D.G. Copeland method II: Manipulation, monotonicity, and paradoxes. Journal of Economic Theory 72 (1997) 148-172
48. Saari D.G. Susceptibility to manipulation. Public Choice 64 (1990) 21-41
49. Saari D.G., and Merlin V. Changes that cause changes. Social Choice & Welfare 17 (2000) 691-705
50. Saari D.G., and Van Newenhizen J. Is approval voting an "unmitigated evil?". Public Choice 59 (1988) 133-147
51. Saari D.G. Millions of election outcomes from a single profile. Social Choice & Welfare 9 (1992) 277-306
52. Saari D.G., and Tataru M. The likelihood of dubious election outcomes. Economic Theory 13 (1999) 345-363
53. Merlin V., Tataru M., and Valognes F. On the probability that all decision rules select the same winner. Journal of Mathematical Economics 33 (2000) 183-208
54. Merlin V., Tataru M., and Valognes F. The likelihood of Condorcet's profiles. Social Choice and Welfare 19 (2001) 193-206
55. Lepelley D., and Merlin V. Scoring runoff paradoxes for variable electorates. Economic Theory 17 (2001) 53-80
56. Tataru M., and Merlin V. On the relationships of the Condorcet winner and positional voting rules. Mathematical Social Sciences 34 (1997) 81-90
57. Saari D.G. Adopting a plurality vote perspective. Mathematics of Operations Research 27 (2002) 45-64
58. Sen A. A possibility theorem on majority decisions. Econometrica 34 (1966) 491-499
59. Zwicker W. The voters' paradox, spin, and the Borda count. Mathematical Social Sciences 22 (1991) 181-227
60. Saari D.G. Analyzing a "nail-biting" election. Social Choice & Welfare 18 (2001) 415-430
61. Saari D.G. A chaotic exploration of aggregation paradoxes. SIAM Review 37 (1995) 37-52
62. Saari D.G. A dictionary for voting paradoxes. Journal of Economic Theory 48 (1989) 443-475