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Collectively rational voting rules for simple preferences

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  • Ju, Biung-Ghi

Abstract

Abstract We offer a rationality foundation of majority voting on two restricted domains of individual preferences proposed by Inada (1964). One is the domain consisting of (dichotomous) preferences that have at most two indifference classes, and the other is the domain where any set of three alternatives is partitioned into two non-empty subsets and alternatives in one set are strictly preferred to alternatives in the other set. On these two domains, we investigate whether majority voting is the unique way of generating transitive, quasi-transitive, or acyclic social preferences. First of all, we rule out non-standard voting rules by imposing monotonicity, anonymity, and neutrality. Our main results show that majority rule is the unique voting rule satisfying transitivity, yet all other voting rules satisfy acyclicity (also quasi-transitivity on the second domain). Thus we find a very thin border dividing majority and other voting rules, namely, the gap between transitivity and acyclicity.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 2 (March)
Pages: 143-149

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Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:143-149

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Collective rationality Transitivity Quasi-transitivity Acyclicity Majority Voting rule Dichotomous preferences;

References

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  1. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
  2. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, 09.
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  4. Aleskerov, Fuad & Duggan, John, 1993. "Functional voting operators: the non-monotonic case," Mathematical Social Sciences, Elsevier, vol. 26(2), pages 175-201, September.
  5. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
  6. Brams, Steven J. & Fishburn, Peter C., 2002. "Voting procedures," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 4, pages 173-236 Elsevier.
  7. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
  8. Moulin, Herve & Bogomolnaia, Anna, 2001. "Random Matching under Dichotomous Preferences," Working Papers 2001-03, Rice University, Department of Economics.
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  10. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-57, Jan.-Feb..
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  12. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  13. Ferejohn, John A. & Fishburn, Peter C., 1979. "Representations of binary decision rules by generalized decisiveness structures," Journal of Economic Theory, Elsevier, vol. 21(1), pages 28-45, August.
  14. Toyotaka Sakai & Masaki Shimoji, 2006. "Dichotomous preferences and the possibility of Arrovian social choice," Social Choice and Welfare, Springer, vol. 26(3), pages 435-445, June.
  15. Jerry S. Kelly & Donald E. Campbell, 2000. "A simple characterization of majority rule," Economic Theory, Springer, vol. 15(3), pages 689-700.
  16. Aizerman, M. A. & Aleskerov, F. T., 1986. "Voting operators in the space of choice functions," Mathematical Social Sciences, Elsevier, vol. 11(3), pages 201-242, June.
  17. Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 153-70, January.
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Cited by:
  1. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2014. "Non-anonymous ballot aggregation: An axiomatic generalization of Approval Voting," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 69-78.
  2. Mongin, Philippe & Maniquet, François, 2011. "Approval voting and arrow's impossibility theorem," Les Cahiers de Recherche 954, HEC Paris.

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