Skip to main content
SpringerLink
Log in

The wasted vote phenomenon with uncertain voter population

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

Palfrey (A mathematical proof of Duvergers law, 1989) shows that in large electorates with deterministic voter population, the expected equilibrium vote share of the weakest party tends to zero asymptotically. We extend this result to the uncertain case where the number of valid votes is a random variable satisfying a mild condition. Special cases include the degenerate, Poisson, binomial, and negative binomial distributions. In particular, we demonstrate that no matter how the number of valid votes fluctuates, as the probability of having a large number of valid votes approaches one, the expected equilibrium vote shares of the weak parties are asymptotically negligible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Duverger M (1964) Political parties: their organization and activity in the modern state. Methuen, London

    Google Scholar 

  • Eguia JX (2007) Citizen candidates under uncertainty. Soc Choice Welf 29: 317–331

    Article  Google Scholar 

  • Kallenberg O. (1983) Random measures. Academic Press, London

    Google Scholar 

  • Milchtaich I. (2004) Random-player games. Game Econ Behav 47: 353–388

    Article  Google Scholar 

  • Milgrom PR, Weber RJ (1985) Distributional strategies for games with incomplete information. Math Oper Res 10: 619–632

    Article  Google Scholar 

  • Myerson RB (1993) Effectiveness of electoral systems for reducing government corruption: a game-theoretic analysis. Game Econ Behav 5: 118–132

    Article  Google Scholar 

  • Myerson RB (1998) Population uncertainty and Poisson games. Int J Game Theory 27: 375–392

    Article  Google Scholar 

  • Myerson RB (2000) Large Poisson games. J Econ Theory 94: 7–45

    Article  Google Scholar 

  • Myerson RB (2002) Comparison of scoring rules in Poisson voting games. J Econ Theory 103: 219–251

    Article  Google Scholar 

  • Palfrey TR (1989) A mathematical proof of Duvergeros law. In: Ordeshook PC (eds) Models of strategic choice in politics. University of Michigan Press, Ann Arbor, pp 69–91

    Google Scholar 

  • Rae DW (1971) The political consequences of electoral laws, 2nd edn. Yale University Press, New Haven

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Economics, University of Queensland, St Lucia, QLD, 4072, Australia

    Yuelan Chen

  2. Department of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, 3010, Australia

    Aihua Xia

Authors
  1. Yuelan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aihua Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuelan Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Y., Xia, A. The wasted vote phenomenon with uncertain voter population. Soc Choice Welf 37, 471–492 (2011). https://doi.org/10.1007/s00355-010-0500-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-010-0500-7

Keywords

Search

Navigation