Advertisement

Distance from Consensus: A Theme and Variations

  • Tommi Meskanen
  • Hannu Nurmi
Part of the Studies in Choice and Welfare book series (WELFARE)

Abstract

Social choice theory deals with aggregating individual opinions into social choices. Over the past decades a large number of choice methods have been evaluated in terms of various criteria of performance. We focus on methods that can be viewed as distance minimizing ones in the sense that they can be analyzed in terms of a goal state of consensus and the methods themselves can be seen as minimizing the distance of the observed profile from that consensus. The methods, thus, provide a way of measuring the degree of disagreement prevailing in the profile.

Keywords

Voting systems metrics consensus outranking tournament 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baigent, N. (1987a) Preference proximity and anonymous social choice. The Quarterly Journal of Economics 102, 161–169.CrossRefMathSciNetGoogle Scholar
  2. Baigent, N. (1987b) Metric rationalization of social choice functions according to principles of social choice. Mathematical Social Sciences 13, 59–65.CrossRefMathSciNetGoogle Scholar
  3. Bury, H. and Wagner, D. (2003) Use of preference vectors in group judgement: the median of Litvak. In Kacprzyk, J. and Wagner, D. (eds), Group Decisions and Voting. Exit, Warszawa.Google Scholar
  4. Copeland, A. H. (1951) A ‘reasonable’ social welfare function. Mimeo. University of Michigan, Seminar on Applications of Mathematics to the Social Sciences. Ann Arbor.Google Scholar
  5. Farkas, D. and Nitzan, S. (1979) The Borda rule and Pareto stability: A comment. Econometrica 47, 1305–1306.CrossRefMathSciNetGoogle Scholar
  6. Kemeny, J. (1959) Mathematics without numbers. Daedalus 88, 571–591.Google Scholar
  7. Klamler, Chr. (2005) Copeland’s rule and Condorcet’s principle. Economic Theory 25, 745–749.CrossRefMathSciNetGoogle Scholar
  8. Litvak, B. G. (1982), Information Given by the Experts. Methods of Acquisition and Analysis. Radio and Communication, Moscow (in Russian).Google Scholar
  9. Maskin, E.S. (1985) The theory of implementation in Nash equilibrium. In: Hurwicz, L., Schmeidler, D., Sonnenschein, H. (eds) Social Goals and Social Organization: Essays in Memory of Elisha Pazner. Cambridge University Press, Cambridge.Google Scholar
  10. McLean, I. and Urken, A. B. (1995), General introduction. In:McLean, I. and Urken, A.B. (eds) Classics of Social Choice. The University of Michigan Press, Ann Arbor.Google Scholar
  11. Michaud, P. (1985) Hommage a Condorcet. Centre Scientifique IBM France, Report No F-094, November.Google Scholar
  12. Nitzan, S. (1981) Some measures of closeness to unanimity and their implications, Theory and Decision 13, 129–138.CrossRefMathSciNetGoogle Scholar
  13. Nurmi, H. (2002) Measuring disagreement in group choice settings. In: Holler, M. J., Kliemt, H., Schmidtchen and Streit, M. E. (eds) Power and Fairness. Jahrbuch für Neue Politische Ökonomie, Band 20. Mohr Siebeck, Tübingen.Google Scholar
  14. Nurmi, H. (2004) A comparison of some distance-based choice rules in ranking environments. Theory and Decision 57, 5–24.CrossRefMathSciNetGoogle Scholar
  15. Nurmi, H. (2005) A responsive voting system. Economics of Governance 6, 63–74.CrossRefGoogle Scholar
  16. Pérez, J. (2001) The strong no show paradoxes are common flaw in Condorcet voting correspondences. Social Choice and Welfare 18, 601–616.CrossRefMathSciNetGoogle Scholar
  17. Schulze, M. (2003) A new monotonic and clone-independent single-winner election method. Voting Matters 17, 9–19.Google Scholar
  18. Slater, P. (1961) Inconsistencies in a schedule of paired comparisons. Biometrika 48, 303–312.Google Scholar
  19. Smith, W. D. (2005) Descriptions of voting systems. Typescript.Google Scholar
  20. Tideman, N. (1987) Independence of clones as a criterion for voting rules. Social Choice and Welfare 4, 185–206.CrossRefMathSciNetGoogle Scholar
  21. Young, H. P. (1988) Condorcet’s theory of voting. American Political Science Review 82, 1231–1244.CrossRefGoogle Scholar
  22. Zavist, B. T. and Tideman, N. (1989) Complete independence of clones in the ranked pairs rule. Social Choice and Welfare 6, 167–173.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Berlin · Heidelberg 2006

Authors and Affiliations

  • Tommi Meskanen
    • 1
  • Hannu Nurmi
    • 2
  1. 1.Department of MathematicsUniversity of TurkuTurku
  2. 2.Department of Political ScienceUniversity of TurkuTurku

Personalised recommendations