IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v80y2013icp179-185.html

The equivalence between costly and probabilistic voting models

Author

Listed:
  • Kamada, Yuichiro
  • Kojima, Fuhito

Abstract

In costly voting models, voters abstain when a stochastic cost of voting exceeds the benefit from voting. In probabilistic voting models, they always vote for a candidate who generates the highest utility, which is subject to random shocks. We prove an equivalence result: In two-candidate elections, given any costly voting model, there exists a probabilistic voting model that generates winning probabilities identical to those in the former model for any policy announcements, and vice versa. Thus many predictions of interest established in one of the models hold in the other as well, providing robustness of the conclusions to model specifications.

Suggested Citation

  • Kamada, Yuichiro & Kojima, Fuhito, 2013. "The equivalence between costly and probabilistic voting models," Games and Economic Behavior, Elsevier, vol. 80(C), pages 179-185.
    • Handle: RePEc:eee:gamebe:v:80:y:2013:i:c:p:179-185
    DOI: 10.1016/j.geb.2013.03.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S089982561300033X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2013.03.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Martin J. Osborne, 1995. "Spatial Models of Political Competition under Plurality Rule: A Survey of Some Explanations of the Number of Candidates and the Positions They Take," Canadian Journal of Economics, Canadian Economics Association, vol. 28(2), pages 261-301, May.
    2. Edward L. Glaeser & Giacomo A. M. Ponzetto & Jesse M. Shapiro, 2005. "Strategic Extremism: Why Republicans and Democrats Divide on Religious Values," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(4), pages 1283-1330.
    3. Wittman, Donald, 1983. "Candidate Motivation: A Synthesis of Alternative Theories," American Political Science Review, Cambridge University Press, vol. 77(1), pages 142-157, March.
    4. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    5. Timothy J. Feddersen, 2004. "Rational Choice Theory and the Paradox of Not Voting," Journal of Economic Perspectives, American Economic Association, vol. 18(1), pages 99-112, Winter.
    6. Alexei Zakharov, 2012. "Probabilistic voting equilibria under nonlinear candidate payoffs," Journal of Theoretical Politics, , vol. 24(2), pages 235-247, April.
    7. Patty, John Wiggs, 2005. "Local equilibrium equivalence in probabilistic voting models," Games and Economic Behavior, Elsevier, vol. 51(2), pages 523-536, May.
    8. Patty, John W, 2002. "Equivalence of Objectives in Two Candidate Elections," Public Choice, Springer, vol. 112(1-2), pages 151-166, July.
    9. Harald Uhlig, 1996. "A law of large numbers for large economies (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 41-50.
    10. Jeffrey S. Banks & John Duggan, 2005. "Probabilistic Voting in the Spatial Model of Elections: The Theory of Office-motivated Candidates," Studies in Choice and Welfare, in: David Austen-Smith & John Duggan (ed.), Social Choice and Strategic Decisions, pages 15-56, Springer.
    11. McKelvey, Richard D. & Patty, John W., 2006. "A theory of voting in large elections," Games and Economic Behavior, Elsevier, vol. 57(1), pages 155-180, October.
    12. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    13. Palfrey, Thomas R. & Rosenthal, Howard, 1985. "Voter Participation and Strategic Uncertainty," American Political Science Review, Cambridge University Press, vol. 79(1), pages 62-78, March.
    14. repec:cup:apsrev:v:62:y:1968:i:01:p:25-42_11 is not listed on IDEAS
    15. repec:cup:apsrev:v:62:y:1968:i:1:p:25-42_1 is not listed on IDEAS
    16. John Ledyard, 1984. "The pure theory of large two-candidate elections," Public Choice, Springer, vol. 44(1), pages 7-41, January.
    17. Hinich, Melvin J., 1977. "Equilibrium in spatial voting: The median voter result is an artifact," Journal of Economic Theory, Elsevier, vol. 16(2), pages 208-219, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Brito, Duarte & Osório, António & Ribeiro, Ricardo & Vasconcelos, Helder, 2018. "Unilateral effects screens for partial horizontal acquisitions: The generalized HHI and GUPPI," International Journal of Industrial Organization, Elsevier, vol. 59(C), pages 127-189.
    2. Brito, Duarte & Ribeiro, Ricardo & Vasconcelos, Helder, 2018. "Quantifying the coordinated effects of partial horizontal acquisitions," European Economic Review, Elsevier, vol. 110(C), pages 108-149.
    3. Prummer, Anja, 2020. "Micro-targeting and polarization," Journal of Public Economics, Elsevier, vol. 188(C).

    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. Krasa, Stefan & Polborn, Mattias K., 2012. "Political competition between differentiated candidates," Games and Economic Behavior, Elsevier, vol. 76(1), pages 249-271.
    2. Sorokin, Constantine & Zakharov, Alexei, 2018. "Vote-motivated candidates," Journal of Economic Theory, Elsevier, vol. 176(C), pages 232-254.
    3. Alexei Zakharov & Constantine Sorokin, 2014. "Policy convergence in a two-candidate probabilistic voting model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 429-446, August.
    4. McKelvey, Richard D. & Patty, John W., 2006. "A theory of voting in large elections," Games and Economic Behavior, Elsevier, vol. 57(1), pages 155-180, October.
    5. Michael Peress, 2011. "Securing the base: electoral competition under variable turnout," Public Choice, Springer, vol. 148(1), pages 87-104, July.
    6. Alexei Zakharov, 2012. "Probabilistic voting equilibria under nonlinear candidate payoffs," Journal of Theoretical Politics, , vol. 24(2), pages 235-247, April.
    7. Justin Mattias Valasek, 2012. "Get Out The Vote: How Encouraging Voting Changes Political Outcomes," Economics and Politics, Wiley Blackwell, vol. 24(3), pages 346-373, November.
    8. Alastair Smith & Bruce Bueno de Mesquita & Tom LaGatta, 2017. "Group incentives and rational voting1," Journal of Theoretical Politics, , vol. 29(2), pages 299-326, April.
    9. Antonio Merlo, 2005. "Whither Political Economy? Theories, Facts and Issues," PIER Working Paper Archive 05-033, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Dec 2005.
    10. Serge Blondel & Louis Lévy-garboua, 2011. "Can non-expected utility theories explain the paradox of not voting?," Economics Bulletin, AccessEcon, vol. 31(4), pages 3158-3168.
    11. repec:ehu:ikerla:6417 is not listed on IDEAS
    12. Taylor, Curtis R. & Yildirim, Huseyin, 2010. "A unified analysis of rational voting with private values and group-specific costs," Games and Economic Behavior, Elsevier, vol. 70(2), pages 457-471, November.
    13. Louis Kaplow & Scott Duke Kominers, 2024. "On the Representativeness of Voter Turnout," Journal of Law and Economics, University of Chicago Press, vol. 67(4), pages 879-904.
    14. Cameron Guage & Feng Fu, 2021. "Asymmetric Partisan Voter Turnout Games," Dynamic Games and Applications, Springer, vol. 11(4), pages 738-758, December.
    15. Mariam Arzumanyan, 2025. "Exploring voter turnout dynamics in polarized elections: A group-rule utilitarian framework," Rationality and Society, , vol. 37(2), pages 230-263, May.
    16. Helios Herrera & Andrea Mattozzi, 2006. "Turnout and Quorum in Referenda," Levine's Bibliography 321307000000000230, UCLA Department of Economics.
    17. Gábor Virág, 2008. "Playing for Your Own Audience: Extremism in Two‐Party Elections," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(5), pages 891-922, October.
    18. Matthew I. Jones & Antonio D. Sirianni & Feng Fu, 2022. "Polarization, abstention, and the median voter theorem," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 9(1), pages 1-12, December.
    19. Patty, John Wiggs, 2005. "Local equilibrium equivalence in probabilistic voting models," Games and Economic Behavior, Elsevier, vol. 51(2), pages 523-536, May.
    20. Konstantinou, Panagiotis Th. & Panagiotidis, Theodore & Roumanias, Costas, 2021. "State-dependent effect on voter turnout: The case of US House elections," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 753-765.
    21. Ozgur Evren, 2009. "Altruism, Turnout and Strategic Voting Behavior," Levine's Working Paper Archive 814577000000000309, David K. Levine.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

    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:eee:gamebe:v:80:y:2013:i:c:p:179-185. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.