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Group Decision and Negotiation

, Volume 15, Issue 1, pp 77–107 | Cite as

Exploratory Analysis of Similarities Between Social Choice Rules

  • John C. McCabe-Dansted
  • Arkadii SlinkoEmail author
Article

Abstract

Nurmi (1987) investigated the relationship between voting rules by determining the frequency that two rules pick the same winner. We use statistical techniques such as hierarchical clustering and multidimensional scaling to further understand the relationships between rules. We use the urn model with a parameter representing contagion to model the presence of social homogeneity within the group of agents and investigate how the classification tree of the rules changes when the homogeneity of the voting population is increased. We discovered that the topology of the classification tree changes quite substantially when the parameter of homogeneity is increased from 0 to 1. We describe the most interesting changes and explain some of them. Most common social choice rules are included, 26 in total.

Keywords

voting rule social choice rule social homogeneity Condorcet efficiency Pólya-Eggenberger distribution cluster analysis 

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References

  1. Arrow, K. J. (1951, 1963). Social Choice and Individual Values. New York: Wiley.Google Scholar
  2. Bartholdi, J. J., III, C. A. Tovey, and M. A. Trick. (1989). “Voting Schemes for which It Can be Difficult to Tell Who Won the Election,” Social Choice and Welfare 6, 157–165.Google Scholar
  3. Berg, S. (1985). “Paradox of Voting Under an Urn Model: The effect of homogeneity,” Public Choice 47, 377–387.CrossRefGoogle Scholar
  4. Black, D. (1958). Theory of Commitees and Elections. Cambridge: Cambridge University Press.Google Scholar
  5. Bordley, R. (1983). “A Pragmatic Method of Evaluating Election Schemes through Simulation”, The American Political Science Review 77, 123–141.Google Scholar
  6. Brams, S. and P. Fishburn. (1982). Approval Voting. Birkhauser.Google Scholar
  7. Brams, S. J. and P. C. Fishburn. (2002). “Voting Procedures,” Handbook of Social Choice and Welfare 77(1), 123–141. Elsevier.Google Scholar
  8. Creer, S., A. Malhotra, R. S. Thorpe, and W.-H. Chou. (2001). “Multiple Causation of Phylogeographical Pattern as Revealed by Nested Clade Analysis of the Bamboo Viper (Trimeresurus Stejnegeri) within Taiwan,” Molecular Ecology 10, 1967–1981.CrossRefPubMedGoogle Scholar
  9. Duda, R. O., P. E. Hart, and D. G. Stork. (2001). Pattern Classification. 2nd edition New York, Wiley.Google Scholar
  10. Fishburn, P. C. (1977). “Condorcet Social Choice Functions,” SIAM Journal on Applied Mathematics 33(3), 469–489.CrossRefGoogle Scholar
  11. Garman, M. and M. Kamien. (1968). “The Paradox of Voting: Probability Calculations,” Behavioral Science 13, 306–316.PubMedGoogle Scholar
  12. Gehrlein, W. V. (1987). “A Comparative Analysis of Measures of Social Homogeneity,” Quality and Quantity 21, 219–231.CrossRefGoogle Scholar
  13. Gehrlein, W. V. and D. Lepelley. (2000). “The Probability that all Weighted Scoring Rules Elect the Same Winner,” Economic Letters 66, 191–197.CrossRefGoogle Scholar
  14. Gibbard, A. (1973). “Manipulation of Voting Schemes: A General Result,” Econometrica 41, 587–601.Google Scholar
  15. Gower, J. C. (1966). “Some Distance Properties of Latent Root and Vector Methods used in Multivariate Analysis,” Biometrika 53, 325–328.Google Scholar
  16. Johnson, N. L. and S. Katz. (1969). Discrete Distributions. Boston: Houghton Mifflin.Google Scholar
  17. Kemeny, J. (1959). “Mathematics Without Numbers,” Daedalus 88, 577–591.Google Scholar
  18. Lansdowne, Z. F. (1997). “Outranking Methods for multicriterion Decision Making: Arrow's and Raynaud's Conjecture’. Social Choice and Welfare 14, 125–128.CrossRefGoogle Scholar
  19. Laslier, J.-F. (1997). Tournament Solutions and Majority Voting. Berlin - New York: Springer.Google Scholar
  20. Leung, W. (2001). “A Statistical Investigation of Social Choice Rules’. Master's thesis, Auckland University.Google Scholar
  21. Merlin, V., M. Tataru, and F. Valognes. (2000). “On the Probability that all Decision Rules Select the Same Winner,” Journal of Mathematical Economics 33, 183–207.CrossRefGoogle Scholar
  22. Milligan, G. W. (1980). “An Examination of the Effect of Six Types of Error Perturbation on Fifteen Clustering Algorithms,” Psychometrika 45, 325–342.CrossRefGoogle Scholar
  23. Nurmi, H. (1987). Comparing Voting Systems. Reidel.Google Scholar
  24. Nurmi, H. (1990). “Computer Simulation of Voting Systems,” Contemporary Issues in Decision Making 77(1), 391–405. Elsevier.Google Scholar
  25. Pritchard, G. and A. Slinko. (2003). “On the Average Minimum Size of a Manipulating Coalition’, Social Choice and Welfare, forthcoming. Available http://www.math.auckland.ac.nz/deptdb/dept_reports/507.pdf.
  26. Richelson, J. T. (1981). “A Comparative Analysis of Social Choice Functions IV’, Behavioral Science 26, 346–353.Google Scholar
  27. Satterthwaite, M. A. (1975). “Strategy-Proofness and Arrow's Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions,” Journal of Economic Theory 10, 187–217.CrossRefGoogle Scholar
  28. Sertel, M. R. and B. Yilmaz. (1999). “The Majoritarian Compromise is Majoritarian-Optimal and Subgame-Perfect Implementable,” Social Choice and Welfare 16, 615–627.CrossRefGoogle Scholar
  29. Shah, R. (2003). “Statistical Mappings of Social Choice Rules’, Master's thesis, Stanford University.Google Scholar
  30. Slinko, A. (2002). “The Majoritarian Compromise in Large Societies,” Review of Economics Design 7(3), 343–350.Google Scholar
  31. Slinko, A. and W. Leung. (2003). “Exploratory Data Analysis of Common Social Choice Functions’, II International Conference on the Problems of Control (17–19 June, 2003), Vol. 1, 224–228. Moscow.Google Scholar
  32. Tideman, T. N. (1987). “Independence of Clones as a Criterion for Voting Rules’. Social Choice and Welfare 4, 185–206.CrossRefGoogle Scholar
  33. Young, F. W. and R. M. Hamer: (1987). Multidimensional Scaling — History, Theory, and Applications. Hillsdale, N.J.: L. Erlbaum Associates.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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