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Condorcet cycles? A model of intertemporal voting

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  • Kevin Roberts

Abstract

An intertemporal voting model is examined where, at each date, there is a pairwise majority vote between the existing chosen state and some other state, chosen randomly. Intertemporal voting simplifies the strategic issues and the agenda setting is as unrestricted as possible. The possibility of cycles is examined, both in the intertemporal extension to the Condorcet paradox and in more general examples. The set of possibilities is rich, as is demonstrated by an exhaustive study of a three person, three state world. Equilibrium in pure strategies may fail to exist but a weakening of the equilibrium concept to admit probabilistic voting allows a general existence result to be proved. The analysis leads to the development of a dominant state which extends the notion of a Condorcet winner.
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  • Kevin Roberts, 2007. "Condorcet cycles? A model of intertemporal voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 383-404, October.
    • Handle: RePEc:spr:sochwe:v:29:y:2007:i:3:p:383-404
    DOI: 10.1007/s00355-006-0211-2
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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. B. D. Bernheim & S. N. Slavov, 2009. "A Solution Concept for Majority Rule in Dynamic Settings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 33-62.
    3. Jeffrey Banks & John Duggan, 2001. "A Multidimensional Model of Repeated Elections," Wallis Working Papers WP24, University of Rochester - Wallis Institute of Political Economy.
    4. David Austen-Smith & Jeffrey S. Banks, 1999. "Cycling of simple rules in the spatial model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 663-672.
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    Cited by:

    1. Christian Roessler & Sandro Shelegia, 2012. "The Roman Metro Problem," Vienna Economics Papers 1202, University of Vienna, Department of Economics.
    2. , & , J., 2014. "Bargaining over an endogenous agenda," Theoretical Economics, Econometric Society, vol. 9(2), May.
    3. Christian Roessler & Sandro Shelegia & Bruno Strulovici, 2013. "The Roman Metro Problem: Dynamic Voting and the Limited Power of Commitment," Discussion Papers 1560, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Zapal, Jan, 2020. "Simple Markovian equilibria in dynamic spatial legislative bargaining," European Journal of Political Economy, Elsevier, vol. 63(C).
    5. B. D. Bernheim & S. N. Slavov, 2009. "A Solution Concept for Majority Rule in Dynamic Settings," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 33-62.
    6. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2021. "Simple collective equilibria in stopping games," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    7. Herings, P.J.J. & Predtetchinski, A., 2013. "Voting in collective stopping games," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).
    8. Hülya Eraslan & Kirill S. Evdokimov & Jan Zápal, 2022. "Dynamic Legislative Bargaining," Springer Books, in: Emin Karagözoğlu & Kyle B. Hyndman (ed.), Bargaining, chapter 0, pages 151-175, Springer.
    9. Elizabeth Maggie Penn, 2009. "A Model of Farsighted Voting," American Journal of Political Science, John Wiley & Sons, vol. 53(1), pages 36-54, January.
    10. Akira Okada & Ryoji Sawa, 2016. "An evolutionary approach to social choice problems with q-quota rules," KIER Working Papers 936, Kyoto University, Institute of Economic Research.
    11. Anesi, Vincent & Seidmann, Daniel J., 2014. "Bargaining over an endogenous agenda," Theoretical Economics, Econometric Society, vol. 9(2), May.

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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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