Abstract
Plurality rule uniquely satisfies anonymity, monotonicity, neutrality, and tops-onlyness. However, it is not always able to produce resolute outcomes. We study singleton-valued refinements of plurality rule that satisfy all but one of these four axioms. Monotonicity is preserved by all refinements of plurality, whereas no refinement satisfies the remaining three except for a very limited case. We explore what dropping one of the three remaining axioms brings about towards singleton-valued refinements.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Campbell and Kelly (2015) find, inter alia that when the number of alternatives exceeds the smallest prime dividing the number of individuals, a resolute social choice rule is anonymous and neutral only if it chooses alternatives that are in the bottom half of preferences of all individuals.
So, given any distinct \(x,y\in A\) and \(P_i\in {\mathcal {L}}(A)\), precisely one of \(xP_iy\) and \(yP_ix\) holds. Moreover, \(xP_iy\) and \(yP_iz\) implies \(xP_iz\) for all \(x,y,z\in A\) and \(P_i\in {\mathcal {L}}(A)\). Finally, \(xP_ix\) does not hold for any \(x\in A\).
A choice function C satisfies the weak axiom of revealed preference (WARP) if for any \(a,b\in A\) and \(B\in {\mathcal {A}}\), having \(a,b\in B\) and \(a\in C(B)\) implies that if \(b\in B'\) and \(b\in C(B')\) for some \(B'\in {\mathcal {A}}\), we must have \(a\notin B'\). WARP is a consistency requirement on choice functions originated from the revealed preference theory.
References
Blais, A. (2008). To keep or to change first past the post?: The politics of electoral reform. Oxford University Press.
Calvao, A. M., Ramos, M., & Anteneodo, C. (2016). Role of the plurality rule in multiple choices. Journal of Statistical Mechanics: Theory and Experiment, 2016, 023405.
Campbell, D. E., & Kelly, J. S. (2015). The finer structure of resolute, neutral, and anonymous social choice correspondences. Economics Letters, 132, 109–111.
Ching, S. (1996). A simple characterization of plurality rule. Journal of Economic Theory, 71, 298–302.
Hartfield, D. J. (1978). A characterization result for the plurality rule. Journal of Economic Theory, 19, 548–550.
Ju, B.-G. (2005). An efficiency characterization of plurality social choice on simple preference domains. Economic Theory, 26, 115–128.
Kastiel, K., & Nili, Y. (2021). The corporate governance gap. Yale Law Journal, 131, 782.
Kelly, J. S., & Qi, S. (2016). Characterizing plurality rule on a fixed population. Economics Letters, 146, 39–41.
Miller, N. R. (2012). Why the Electoral College is good for political science (and public choice). Public Choice, 150, 1–25.
Moulin, H. (1980). Implementing efficient, anonymous and neutral social choice functions. Journal of Mathematical Economics, 7, 249–269.
Moulin, H. (1991). Axioms of cooperative decision making, number 15 in econometric society monographs. Cambridge University Press.
Ozkes, A. I., & Sanver, M. R. (2021). Anonymous, neutral, and resolute social choice revisited. Social Choice and Welfare, 57, 97–113.
Roberts, F. S. (1991). Characterizations of the plurality function. Mathematical Social Sciences, 21, 101–127.
Thurmon, M. A. (1992). When the court divides: Reconsidering the precedential value of supreme court plurality decisions. Duke Law Journal, 42, 419.
Tonello, M. (2020). Corporate board practices in the Russell 3000 and S &P 500, in HLS Corporate Governance Forum.
Yeh, C.-H. (2008). An efficiency characterization of plurality rule in collective choice problems. Economic Theory, 34, 575–583.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ozkes, A.I., Sanver, M.R. Axiomatization of plurality refinements. Public Choice (2024). https://doi.org/10.1007/s11127-024-01154-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11127-024-01154-4