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Level r Consensus and Stable Social Choice

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  • 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.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 4808.

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Date of creation: 2014
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Handle: RePEc:ces:ceswps:_4808

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Keywords: social choice; unanimity; consensus; preference aggregation rules; transitivity; simple majority; scoring rules; invariance to rule selection;

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  1. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521516051.
  2. Hannu Nurmi, 2004. "A Comparison of Some Distance-Based Choice Rules in Ranking Environments," Theory and Decision, Springer, Springer, vol. 57(1), pages 5-24, 08.
  3. Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, Elsevier, vol. 48(2), pages 443-475, August.
  4. Saari,Donald G., 2008. "Disposing Dictators, Demystifying Voting Paradoxes," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521731607.
  5. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, Econometric Society, vol. 47(5), pages 1305-06, September.
  6. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories : An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  7. Lerer, Ehud & Nitzan, Shmuel, 1985. "Some general results on the metric rationalization for social decision rules," Journal of Economic Theory, Elsevier, Elsevier, vol. 37(1), pages 191-201, October.
  8. Baigent, Nick, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 102(1), pages 161-69, February.
  9. Eyal Baharad & Shmuel Nitzan, 2006. "On the selection of the same winner by all scoring rules," Social Choice and Welfare, Springer, Springer, vol. 26(3), pages 597-601, June.
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