IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2410.20476.html

Voting with Random Proposers: Two Rounds May Suffice

Author

Listed:
  • Hans Gersbach
  • Kremena Valkanova

Abstract

This paper introduces the Voting with Random Proposers (VRP) procedure to address the challenges of agenda manipulation in voting. In each round of VRP, a randomly selected proposer suggests an alternative that is voted on against the previous round's winner. In a framework with single-peaked preferences, we show that the VRP procedure guarantees that the Condorcet winner is implemented in a few rounds with truthful voting, and in just two rounds under sufficiently symmetric preference distributions or if status quo positions are not extreme. The results have applications for committee decisions, legislative decision-making, and the organization of citizens' assemblies and decentralized autonomous organizations.

Suggested Citation

  • Hans Gersbach & Kremena Valkanova, 2024. "Voting with Random Proposers: Two Rounds May Suffice," Papers 2410.20476, arXiv.org, revised Oct 2025.
    • Handle: RePEc:arx:papers:2410.20476
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2410.20476
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Callander, Steven, 2011. "Searching for Good Policies," American Political Science Review, Cambridge University Press, vol. 105(4), pages 643-662, November.
    2. Barberà, Salvador & Gerber, Anke, 2017. "Sequential voting and agenda manipulation," Theoretical Economics, Econometric Society, vol. 12(1), January.
    3. Banks, Jeffrey S., 2002. "Strategic aspects of political systems," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 59, pages 2203-2228, Elsevier.
    4. Salvador Barberà & Anke Gerber, 2022. "Deciding On What To Decide," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 37-61, February.
    5. Rubinstein, Ariel, 1979. "A Note about the "Nowhere Denseness" of Societies Having an Equilibrium under Majority Rule," Econometrica, Econometric Society, vol. 47(2), pages 511-514, March.
    6. Bettina Klaus & Panos Protopapas, 2020. "On strategy-proofness and single-peakedness: median-voting over intervals," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1059-1080, December.
    7. Austen-Smith, David, 1987. "Sophisticated Sincerity: Voting Over Endogenous Agendas," American Political Science Review, Cambridge University Press, vol. 81(4), pages 1323-1330, December.
    8. Horan, Sean Michael, 2021. "Agendas in legislative decision-making," Theoretical Economics, Econometric Society, vol. 16(1), January.
    9. S. Nageeb Ali & B. Douglas Bernheim & Alexander W. Bloedel & Silvia Console Battilana, 2023. "Who Controls the Agenda Controls the Legislature," American Economic Review, American Economic Association, vol. 113(11), pages 3090-3128, November.
    10. Rosenthal, Howard & Zame, William R., 2022. "Sequential referenda with sophisticated voters," Journal of Public Economics, Elsevier, vol. 212(C).
    11. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    12. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
    13. Norman Schofield, 1983. "Generic Instability of Majority Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 695-705.
    14. Baron David & Kalai Ehud, 1993. "The Simplest Equilibrium of a Majority-Rule Division Game," Journal of Economic Theory, Elsevier, vol. 61(2), pages 290-301, December.
    15. Bell, Colin E, 1981. "A Random Voting Graph Almost Surely Has a Hamiltonian Cycle When the Number of Alternatives Is Large," Econometrica, Econometric Society, vol. 49(6), pages 1597-1603, November.
    16. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hans Gersbach, 2025. "Propose or Vote: A Canonical Democratic Procedure," Papers 2506.05998, arXiv.org, revised Dec 2025.
    2. Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
    3. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    4. P. Jean-Jacques Herings & Harold Houba, 2010. "The Condorcet Paradox Revisited," Tinbergen Institute Discussion Papers 10-026/1, Tinbergen Institute.
    5. Crès, Hervé & Utku Ünver, M., 2017. "Toward a 50%-majority equilibrium when voters are symmetrically distributed," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 145-149.
    6. 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.
    7. Bettina Klaus & Panos Protopapas, 2020. "On strategy-proofness and single-peakedness: median-voting over intervals," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1059-1080, December.
    8. Adrian Fernández-Pérez & Marta Gómez-Puig & Simón Sosvilla-Rivero, 2025. "Hot Property: A Spatial Analysis of Temperature and Housing Prices in Spain," Documentos de Trabajo del ICAE 2025-04, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    9. 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.
    10. 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.
    11. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.
    12. Berga, Dolors & Serizawa, Shigehiro, 2000. "Maximal Domain for Strategy-Proof Rules with One Public Good," Journal of Economic Theory, Elsevier, vol. 90(1), pages 39-61, January.
    13. Fleckinger, Pierre, 2008. "Bayesian improvement of the phantom voters rule: An example of dichotomic communication," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 1-13, January.
    14. Bonifacio, Agustín G. & Massó, Jordi & Neme, Pablo, 2023. "Preference restrictions for simple and strategy-proof rules: Local and weakly single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    15. Régis Renault & Alain Trannoy, 2011. "Assessing the extent of strategic manipulation: the average vote example," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 497-513, December.
    16. Chatterjee, Swarnendu & Peters, Hans & Storcken, Ton, 2016. "Locating a public good on a sphere," Economics Letters, Elsevier, vol. 139(C), pages 46-48.
    17. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    18. Norman Schofield, 1986. "Existence of a ‘structurally stable’ equilibrium for a non-collegial voting rule," Public Choice, Springer, vol. 51(3), pages 267-284, January.
    19. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    20. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2410.20476. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.