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Level $$r$$ r consensus and stable social choice

Author

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  • Muhammad Mahajne
  • Shmuel Nitzan
  • Oscar Volij

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Abstract

We propose the concept of level $$r$$ r consensus as a useful property of a preference profile which considerably enhances the stability of social choice. This concept involves a weakening of unanimity, the most extreme form of consensus. It is shown that if a preference profile exhibits level $$r$$ r consensus around a given preference relation, there exists a Condorcet winner. In addition, if the number of individuals is odd the majority relation coincides with the preference relation around which there is such consensus and consequently it is transitive. Furthermore, if the level of consensus is sufficiently strong, the Condorcet winner is chosen by all the scoring rules. Level $$r$$ r consensus therefore ensures the Condorcet consistency of all scoring rules, thus eliminating the tension between decision rules inspired by ranking-based utilitarianism and the majority rule. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2015. "Level $$r$$ r consensus and stable social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 805-817, December.
  • Handle: RePEc:spr:sochwe:v:45:y:2015:i:4:p:805-817
    DOI: 10.1007/s00355-015-0882-7
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    File URL: http://hdl.handle.net/10.1007/s00355-015-0882-7
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    References listed on IDEAS

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    1. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, vol. 47(5), pages 1305-1306, September.
    2. Eyal Baharad & Shmuel Nitzan, 2006. "On the selection of the same winner by all scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 597-601, June.
    3. Hannu Nurmi, 2004. "A Comparison of Some Distance-Based Choice Rules in Ranking Environments," Theory and Decision, Springer, vol. 57(1), pages 5-24, August.
    4. Nitzan,Shmuel, 2009. "Collective Preference and Choice," Cambridge Books, Cambridge University Press, number 9780521722131.
    5. Nick Baigent, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 102(1), pages 161-169.
    6. Saari, Donald G., 1999. "Explaining All Three-Alternative Voting Outcomes," Journal of Economic Theory, Elsevier, vol. 87(2), pages 313-355, August.
    7. repec:cup:apsrev:v:68:y:1974:i:02:p:537-546_11 is not listed on IDEAS
    8. Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, vol. 48(2), pages 443-475, August.
    9. Lerer, Ehud & Nitzan, Shmuel, 1985. "Some general results on the metric rationalization for social decision rules," Journal of Economic Theory, Elsevier, vol. 37(1), pages 191-201, October.
    10. Shmuel Nitzan, 1989. "More on the Preservation of Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 104(1), pages 187-190.
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    More about this item

    Keywords

    D71;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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