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Level r Consensus and Stable Social Choice

Author

Listed:
  • Muhammad Mahajne
  • Shmuel Nitzan
  • Oscar Volij

Abstract

We propose the concept of level 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 consensus around a given preference relation, the associated majority relation is transitive. In addition, the majority relation coincides with the preference relation around which there is such consensus. Furthermore, if the level of consensus is sufficiently strong, the Condorcet winner is chosen by all the scoring rules. Level 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.

Suggested Citation

  • Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2014. "Level r Consensus and Stable Social Choice," CESifo Working Paper Series 4808, CESifo.
    • Handle: RePEc:ces:ceswps:_4808
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    References listed on IDEAS

    as
    1. Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, vol. 48(2), pages 443-475, August.
    2. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: an oriented survey," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00504974, HAL.
    3. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521731607, October.
    4. 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.
    5. Shmuel Nitzan, 1989. "More on the Preservation of Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(1), pages 187-190.
    6. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, vol. 47(5), pages 1305-1306, September.
    7. 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.
    8. 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.
    9. Nick Baigent, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(1), pages 161-169.
    10. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, number 9780521516051, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    social choice; unanimity; consensus; preference aggregation rules; transitivity; simple majority; scoring rules; invariance to rule selection;
    All these keywords.

    JEL classification:

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

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