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A Social Choice Lemma on Voting over Lotteries with Applications to a Class of Dynamic Games

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  • Banks, Jeffrey S.
  • Duggan, John

Abstract

We prove a lemma characterizing majority preferences over lotteries on a subset of Euclidean space. Assuming voters have quadratic von Neumann-Morgenstern utility representations, and assuming existence of a majority undominated (or "core") point, the core voter is decisive: one lottery is majority-preferred to another if and only if this is the preference of the core voter. Several applications of this result to dynamic voting games are discussed.

Suggested Citation

  • Banks, Jeffrey S. & Duggan, John, 2003. "A Social Choice Lemma on Voting over Lotteries with Applications to a Class of Dynamic Games," Working Papers 1163, California Institute of Technology, Division of the Humanities and Social Sciences.
    • Handle: RePEc:clt:sswopa:1163
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    1. Cho, Seok-ju & Duggan, John, 2003. "Uniqueness of stationary equilibria in a one-dimensional model of bargaining," Journal of Economic Theory, Elsevier, vol. 113(1), pages 118-130, November.
    2. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
    3. Duggan, John & Fey, Mark, 2005. "Electoral competition with policy-motivated candidates," Games and Economic Behavior, Elsevier, vol. 51(2), pages 490-522, May.
    4. Banks, Jeffrey s. & Duggan, John, 2000. "A Bargaining Model of Collective Choice," American Political Science Review, Cambridge University Press, vol. 94(1), pages 73-88, March.
    5. Bernhardt, Dan & Dubey, Sangita & Hughson, Eric, 2004. "Term limits and pork barrel politics," Journal of Public Economics, Elsevier, vol. 88(12), pages 2383-2422, December.
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    Cited by:

    1. Meirowitz, Adam, 2005. "Communication and Bargaining in the Spatial Model," Papers 09-20-2005, Princeton University, Research Program in Political Economy.
    2. Zapal, Jan, 2016. "Markovian equilibria in dynamic spatial legislative bargaining: Existence with three players," Games and Economic Behavior, Elsevier, vol. 98(C), pages 235-242.
    3. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
    4. Haifeng Huang, 2010. "Electoral Competition When Some Candidates Lie and Others Pander," Journal of Theoretical Politics, , vol. 22(3), pages 333-358, July.
    5. Câmara, Odilon & Bernhardt, Dan, 2015. "Learning about challengers," Games and Economic Behavior, Elsevier, vol. 90(C), pages 181-206.
    6. Zapal, Jan, 2020. "Simple Markovian equilibria in dynamic spatial legislative bargaining," European Journal of Political Economy, Elsevier, vol. 63(C).
    7. Roger Lagunoff, 2004. "The Dynamic Reform of Political Institutions," Econometric Society 2004 Latin American Meetings 47, Econometric Society.
    8. Roberti, Paolo, 2019. "Citizens or lobbies: Who controls policy?," Games and Economic Behavior, Elsevier, vol. 113(C), pages 497-514.
    9. Forand, Jean Guillaume, 2014. "Two-party competition with persistent policies," Journal of Economic Theory, Elsevier, vol. 152(C), pages 64-91.
    10. David Hugh-Jones, 2008. "Explaining Institutional Change: Why Elected Politicians Implement Direct Democracy," Jena Economics Research Papers 2008-085, Friedrich-Schiller-University Jena.
    11. 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.
    12. Roger Lagunoff, 2005. "Markov Equilibrium in Models of Dynamic Endogenous Political Institutions," Game Theory and Information 0501003, University Library of Munich, Germany.
    13. John Duggan, 2014. "Majority Voting Over Lotteries: Conditions for Existence of a Decisive Voter," Economics Bulletin, AccessEcon, vol. 34(1), pages 263-270.
    14. Banks, Jeffrey S. & Duggan, John, 2008. "A Dynamic Model of Democratic Elections in Multidimensional Policy Spaces," Quarterly Journal of Political Science, now publishers, vol. 3(3), pages 269-299, October.
    15. Jean Guillaume Forand & John Duggan, 2013. "Markovian Elections," Working Papers 1305, University of Waterloo, Department of Economics, revised Oct 2013.
    16. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    17. Pech, Gerald, 2012. "Intra-party decision making, party formation, and moderation in multiparty systems," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 14-22.
    18. 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.
    19. Mohammad Mirhosseini, 2015. "Primaries with strategic voters: trading off electability and ideology," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 457-471, March.
    20. Nunnari, Salvatore & Zápal, Jan, 2017. "Dynamic Elections and Ideological Polarization," Political Analysis, Cambridge University Press, vol. 25(4), pages 505-534, October.
    21. Haomiao Yu, 2012. "Point-Rationalizability in Large Games," Working Papers 030, Ryerson University, Department of Economics.
    22. Kent Grote & Victor Matheson, 2011. "The Economics of Lotteries: An Annotated Bibliography," Working Papers 1110, College of the Holy Cross, Department of Economics.
    23. Keith E. Schnakenberg, 2017. "The downsides of information transmission and voting," Public Choice, Springer, vol. 173(1), pages 43-59, October.
    24. Navin Kartik & SangMok Lee & Daniel Rappoport, 2022. "Single-Crossing Differences in Convex Environments," Papers 2212.12009, arXiv.org, revised Jun 2023.

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    Keywords

    lotteries; dynamic games; representative voter; decisive voter;
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