Collectively rational voting rules for simple preferences
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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- 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.
- Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990.
"Voting by Committees,"
Cowles Foundation Discussion Papers
941, Cowles Foundation for Research in Economics, Yale University.
- Brams, Steven J. & Fishburn, Peter, 1998.
98-30, C.V. Starr Center for Applied Economics, New York University.
- 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.
- Brams, Steven J., 1994. "Voting procedures," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 30, pages 1055-1089 Elsevier.
- Jerry S. Kelly & Donald E. Campbell, 2000. "A simple characterization of majority rule," Economic Theory, Springer, vol. 15(3), pages 689-700.
- Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005.
"Collective choice under dichotomous preferences,"
Journal of Economic Theory,
Elsevier, vol. 122(2), pages 165-184, June.
- Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
- 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.
- Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
- Barbera, S. & Sonnenschein, H., 1988.
"Voting By Quota And Committee,"
UFAE and IAE Working Papers
95-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
- Aleskerov, Fuad & Duggan, John, 1993.
"Functional voting operators: the non-monotonic case,"
Mathematical Social Sciences,
Elsevier, vol. 26(2), pages 175-201, September.
- Aleskerov, Fuad & Duggan, John, 1993. "Functional Voting Operators: The Non-Monotonic Case," Working Papers 858, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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.
- Inada, Ken-Ichi, 1970. "Majority rule and rationality," Journal of Economic Theory, Elsevier, vol. 2(1), pages 27-40, March.
- 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.
- Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
- 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.
- 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..
- Anna Bogomolnaia & Herve Moulin, 2004.
"Random Matching Under Dichotomous Preferences,"
Econometric Society, vol. 72(1), pages 257-279, 01.
- Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
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