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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 153-170.
- Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990.
"Voting by Committees,"
Cowles Foundation Discussion Papers
941, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Jerry S. Kelly & Donald E. Campbell, 2000. "A simple characterization of majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 689-700.
- Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
- Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
- Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005.
"Collective choice under dichotomous preferences,"
Journal of Economic Theory,
Elsevier, vol. 122(2), pages 165-184, June.
- 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.
- 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.
- Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
- Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
- Brams, Steven J. & Fishburn, Peter C., 2002.
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
- 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.
- 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.
- Anna Bogomolnaia & Herve Moulin, 2004.
"Random Matching Under Dichotomous Preferences,"
Econometric Society, vol. 72(1), pages 257-279, 01.
- Toyotaka Sakai & Masaki Shimoji, 2006. "Dichotomous preferences and the possibility of Arrovian social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 435-445, June.
- Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
- 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.
- 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, 1970. "Majority rule and rationality," Journal of Economic Theory, Elsevier, vol. 2(1), pages 27-40, March.
When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:143-149. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.