Abstract
This paper studies the strategic foundation of the Representative Voter Theorem (Rothstein in: Pub Choice 72:193–212, 1991), also called the “second version” of the Median Voter Theorem. As a by-product, it also considers the existence of strategy-proof social choice functions over the domain of single-crossing preferences. The main result shows that single-crossing constitutes a domain restriction over the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median rule, which is found to be group strategic-proof over the full set of alternatives and over every nonempty subset. In addition, the paper also examines the relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median rule to prove that the outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism. This mechanism is a two-stage voting procedure in which, first, individuals select a representative among themselves, and then the winner chooses a policy to be implemented by the planner.
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References
Austen-Smith D, Banks J (1999) Positive political theory I: collective preference. The University of Michigan Press, Ann Arbor
Barberà S (2001) An introduction to strategy-proof social choice functions. Soc Choice Welfare 18:619–653
Barberà S, Jackson M (1994) A characterization of social choice functions for economies with pure public goods. Soc Choice Welfare 11:241–252
Berga D, Serizawa S (2000) Maximal domain for strategy-proof rules with one public good. J Econ Theory 90:39–61
Black D (1948) On the rationale of group decision-making. J Polit Econ 56:23–34
Campbell D, Kelly J (2003a) Are serial Condorcet rules strategy-proof? Rev Econ Design 7:385–410
Campbell D, Kelly J (2003b) A strategy-proofness characterization of majority rule. Econ Theory 22:557–568
Ching S (1997) Strategy-proofness and “median voters”. Int J Game Theory 26:473–490
Gans J, Smart M (1996) Majority voting with single-crossing preferences. J Publ Econ 59:219–237
Grandmont J (1978) Intermediate preferences and the majority rule. Econometrica 46:317–330
List C (2001) A possibility theorem on aggregation over multiple interconnected propositions. Math Soc Sci 45:1–13
Moulin H (1980) On strategy-proofness and single-peakedness. Pub Choice 35:437–455
Moulin H (1988) Axioms of cooperative decision making. Cambridge University Press, Cambridge
Myerson R (1996) Fundamentals of social choice theory. Discussion paper 1162 Math Center, Northwestern University
Persson T, Tabellini G (2000) Political economics: explaining economic policy. MIT Press, Cambridge, MA
Roberts K (1977) Voting over income tax schedules. J Publ Econ 8:329–340
Rothstein P (1990) Order-restricted preferences and majority rule. Soc Choice and Welfare 7:331–342
Rothstein P (1991) Representative voter theorems. Pub Choice 72:193–212
Saporiti A, Tohmé F (2004) Strategy-proofness and single-crossing. mimeo. Queen Mary, University of London
Sprumont Y (1995) Strategy-proof collective choice in economic and political environments. Can J Econ 28:68–107
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Saporiti, A., Tohmé, F. Single-Crossing, Strategic Voting and the Median Choice Rule. Soc Choice Welfare 26, 363–383 (2006). https://doi.org/10.1007/s00355-006-0098-y
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DOI: https://doi.org/10.1007/s00355-006-0098-y