Skip to main content
SpringerLink
Log in

A new monotonicity condition for tournament solutions

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

We identify a new monotonicity condition (called cover monotonicity) for tournament solutions which allows a discrimination among main tournament solutions: The top-cycle, the iterated uncovered set, the minimal covering set, and the bipartisan set are cover monotonic while the uncovered set, Banks set, the Copeland rule, and the Slater rule fail to be so. As cover monotonic tournament solutions induce social choice rules which are Nash implementable in certain non-standard frameworks (such as those set by Bochet and Maniquet (CORE Discussion Paper No. 2006/84, 2006) or Özkal-Sanver and Sanver (Social Choice and Welfare, 26(3), 607–623, 2006), the discrimination generated by cover monotonicity becomes particularly notable when implementability is a concern.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abreu D., Sen A. (1991) Virtual implementation in Nash equilibrium. Econometrica 59: 997–1021

    Article  Google Scholar 

  • Arrow K. (1951) Social choice and individual values. Wiley, New York

    Google Scholar 

  • Banks J.S. (1985) Sophisticated voting outcomes and agenda control. Social Choice and Welfare 5: 295–306

    Article  Google Scholar 

  • Benoit J.P., Ok E.A. (2008) Nash implementation without no veto power. Games and Economic Behavior 64: 51–67

    Article  Google Scholar 

  • Black D. (1958) The theory of committees and elections. Cambridge University Press, Cambridge

    Google Scholar 

  • Bochet O. (2007) Nash implementation with lottery mechanisms. Social Choice and Welfare 28(1): 111–125

    Article  Google Scholar 

  • Bochet, O., & Maniquet, F. (2006). Virtual Nash implementation with admissible support. CORE Discussion Paper No. 2006/84.

  • Copeland, A. (1951). A reasonable social welfare function. University of Michigan seminar on the applications of mathematics to social sciences.

  • Dutta B. (1988) Covering sets and a new Condorcet social choice correspondence. Journal of Economic Theory 44: 63–80

    Article  Google Scholar 

  • Erdem O., Sanver M.R. (2005) Minimal monotonic extensions of scoring rules. Social Choice and Welfare 25: 31–42

    Article  Google Scholar 

  • Gibbard A. (1973) Manipulation of voting schemes: A general result. Econometrica 41: 587–601

    Article  Google Scholar 

  • Good I.J. (1971) A note on Condorcet sets. Public Choice 10: 97–101

    Article  Google Scholar 

  • Hurwicz L. (1972) On informationally decentralized systems. In: McGuire C.B., Radner R. (eds) Decision and organization. Amsterdam, North Holland

    Google Scholar 

  • Jackson M.O. (2001) A crash course in implementation theory. Social Choice and Welfare 18: 655–708

    Article  Google Scholar 

  • Laffond G., Laslier J.F., Le Breton M. (1993) The bipartisan set of a tournament game. Games and Economic Behavior 5: 182–201

    Article  Google Scholar 

  • Laslier J.F. (1997) Tournament solutions and majority voting. Springer-Verlag, Heidelberg

    Google Scholar 

  • Maskin E. (1999) Nash equilibrium and welfare optimality. Review of Economic Studies 66: 23–38

    Article  Google Scholar 

  • Matsushima H. (1988) A new approach to the implementation problem. Journal of Economic Theory 45: 128–144

    Article  Google Scholar 

  • Mc. Garvey D. (1953) A theorem on the construction of voting paradoxes. Econometrica 21: 608–610

    Article  Google Scholar 

  • Miller N.R. (1980) A new solution set for tournaments and majority voting: Further graph-theoretical approaches to the theory of voting. American Journal of Political Science 24: 68–96

    Article  Google Scholar 

  • Muller E., Satterthwaite M. (1977) The equivalence of strong positive association and incentive compatibility. Journal of Economic Theory 14: 412–418

    Article  Google Scholar 

  • Nanson, E. J. (1907). Methods of elections. British Government Blue Book Miscellaneous No. 3.

  • Özkal-Sanver İ., Sanver M.R. (2006) Nash implementation via hyperfunctions. Social Choice and Welfare 26(3): 607–623

    Article  Google Scholar 

  • Sanver M.R. (2006) Nash implementing non-monotonic social choice rules by awards. Economic Theory 28(2): 453–460

    Article  Google Scholar 

  • Satterthwaite M. (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

    Article  Google Scholar 

  • Schwartz T. (1972) Rationality and the myth of maximum. Nous 6: 97–117

    Google Scholar 

  • Slater P. (1961) Inconsistencies in a schedule of paired comparisons. Biometrica 48: 303–312

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, İstanbul Bilgi University, İstanbul, Turkey

    İpek Özkal-Sanver & M. Remzi Sanver

Authors
  1. İpek Özkal-Sanver
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Remzi Sanver
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to İpek Özkal-Sanver.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Özkal-Sanver, İ., Sanver, M.R. A new monotonicity condition for tournament solutions. Theory Decis 69, 439–452 (2010). https://doi.org/10.1007/s11238-009-9159-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11238-009-9159-x

Keywords

Search

Navigation