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, 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 \(r\) 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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References
Arrow KJ (2012) Social choice and individual values, vol 12. Yale University Press, New Haven
Baharad E, Nitzan S (2006) On the selection of the same winner by all scoring rules. Soc Choice Welf 26(3):597–601
Baigent N (1987) Preference proximity and anonymous social choice. Q J Econ 102(1):161–169
Campbell DE, Nitzan SI (1986) Social compromise and social metrics. Soc Choice Welf 3(1):1–16
Farkas D, Nitzan S (1979) The borda rule and pareto stability: a comment. Econometrica 47(5):1305–06
Fishburn PC (1974) Paradoxes of voting. Am Polit Sci Rev 68(2):537–546
Fishburn PC (1977) Condorcet social choice functions. SIAM J Appl Math 33(3):469–489
Fishburn PC (1981) Inverted orders for monotone scoring rules. Discret Appl Math 3(1):27–36
García-Lapresta JL, Pérez-Román D (2011) Measuring consensus in weak orders. Consensual processes. Springer, Berlin, pp 213–234
Kemeny JG (1959) Mathematics without numbers. Daedalus 88(4):577–591
Kemeny JG, Snell JL (1962) Mathematical models in the social sciences, vol 9. Ginn, Boston
Lerer E, Nitzan S (1985) Some general results on the metric rationalization for social decision rules. J Econ Theory 37(1):191–201
Mallows CL (1957) Non-null ranking models. i. Biometrika 44:114–130
Nitzan S (1981) Some measures of closeness to unanimity and their implications. Theory Decis 13(2):129–138
Nitzan S (1989) More on the preservation of preference proximity and anonymous social choice. Q J Econ 1:187–190
Nitzan S (2009) Collective preference and choice. Cambridge University Press, Cambridge
Nurmi H (2002) Voting procedures under uncertainty. Springer, Berlin
Nurmi H (2004) A comparison of some distance-based choice rules in ranking environments. Theory Decis 57(1):5–24
Saari DG (1984) The ultimate of chaos resulting from weighted voting systems. Adv Appl Math 5(3):286–308
Saari DG (1989) A dictionary for voting paradoxes. J Econ Theory 48(2):443–475
Saari DG (1999) Explaining all three-alternative voting outcomes. J Econ Theory 87(2):313–355
Saari DG (2000) Mathematical structure of voting paradoxes. Econ Theory 15(1):1–53
Saari DG (2001) Chaotic elections!: a mathematician looks at voting. American Mathematical Society, U.S.A
Sen A (1970) Collective choice and social welfare. Holden Day, San Francisco
Young HP (1988) Condorcet’s theory of voting. Am Polit Sci Rev 82(04):1231–1244
Acknowledgments
This paper is based on the first chapter of Mahajne’s PhD thesis. We thank an editor and two anonymous referees for their useful comments.
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Mahajne, M., Nitzan, S. & Volij, O. Level \(r\) consensus and stable social choice. Soc Choice Welf 45, 805–817 (2015). https://doi.org/10.1007/s00355-015-0882-7
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DOI: https://doi.org/10.1007/s00355-015-0882-7