Skip to main content

Modeling the Outcomes of Vote-Casting in Actual Elections

  • Chapter
  • First Online:
Electoral Systems

Part of the book series: Studies in Choice and Welfare ((WELFARE))

Abstract

How often do events of interest to voting theorists occur in actual elections? For example, what is the probability of observing a voting cycle – an outcome in which no candidate beats all other candidates in pairwise comparison by majority rule? When there is a candidate who beats all others in such pairwise comparisons – a Condorcet winner – what is the probability that a voting method chooses this candidate?What is the probability that voters have an incentive to vote strategically – that is, cast their votes in ways that do not reflect their true preferences? Voting theorists have analyzed these questions in great detail, using a variety of statistical models that describe different distributions of candidate rankings.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brams, S.J., & Fishburn, P. (2001). A nail-biting election. Social Choice Welfare, 18, 409–414.

    Article  Google Scholar 

  2. Campbell, C., & Tullock, G. (1965). A measure of the importance of cyclical majorities. Economic Journal, 75, 300 & 853–857.

    Google Scholar 

  3. Cervone, D., Gehrlein, W.V., Zwicker, W. (2005). Which scoring rule maximizes Condorcet efficiency under IAC. Theory and Decision, 58 (2), 145–185.

    Article  Google Scholar 

  4. Chamberlin, J.R., & Featherston, F. (1986). Selecting a voting system. Journal of Politics, 48 (2), 347–369.

    Article  Google Scholar 

  5. Condorcet, M.JAN., Marquis de (1785). Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix (Paris).

    Google Scholar 

  6. Conitzer, V., & Sandholm, T. (2005). Common voting rules as maximum likelihood estimators. Proceedings of the 21st Annual Conference on Uncertainty in Artificial Intelligence (UAI-05) (pp. 145–152). UK: Edinburgh.

    Google Scholar 

  7. Davis, O.A., Hinich, M.J., Ordeshook, P.C. (1970). An expository development of a mathematical model of the electoral process. American Political Science Review, 44, 426–448.

    Google Scholar 

  8. DiDonato, A.R., & Hageman, R.K. (1980). Computation of the integral of the bivariate normal distribution over arbitrary polygons. Naval Surface Weapons Center, Government Accession Number ADA102466.

    Google Scholar 

  9. Enelow, J.M., & Hinich, M.J. (1984). The spatial theory of voting: An introduction. Cambridge University Press.

    Google Scholar 

  10. Enelow, J.M., & Hinich, M.J. (1990). Advances in the spatial theory of voting. Cambridge University Press.

    Google Scholar 

  11. Feld, S., & Grofman, B. (1990). Collectivities as actors. Rationality and Society, 2 (4), 429–448.

    Article  Google Scholar 

  12. Feld, S., & Grofman, B. (1992). Who’s afraid of the big bad cycle? Evidence from 36 elections. Journal of Theoretical Politics, 4 (2), 231–237.

    Article  Google Scholar 

  13. Felsenthal, D.S., Maoz, Z., Rapoport, A. (1993). An empirical evaluation of six voting procedures: do they really make any difference? British Journal of Political Science, 23 (1), 1–27.

    Article  Google Scholar 

  14. Felsenthal, D.S., & Machover, M. (1995). Who ought to be elected and who is actually elected? An empirical investigation of 92 Elections under three procedures. Electoral Studies, 14 (2), 143–169.

    Article  Google Scholar 

  15. Gehrlein, W.V., & Fishburn, P.C. (1976). Condorcet’s paradox and anonymous preference profiles. Public Choice, 26, 1–18.

    Article  Google Scholar 

  16. Gehrlein, W.V. (1978). Condorcet winners in dual cultures. Presented at the National Meeting of the Public Choice Society, New Orleans.

    Google Scholar 

  17. Gehrlein, W.V. (2002). Condorcet’s paradox and the likelihood of its occurrence: Different perspectives on balanced preferences. Theory and Decision, 52 (2), 171–199.

    Article  Google Scholar 

  18. Gehrlein, W.V. (2004). Consistency in measures of social homogeneity: A connection with proximity to single-peaked preferences. Quality and Quantity, 38, 147–171.

    Article  Google Scholar 

  19. Gehrlein, W.V. (2006). Condorcet’s paradox. Berlin and Heidelberg: Springer.

    Google Scholar 

  20. Good, I.J., & Tideman, T.N. (1976). From individual to collective ordering through multidimensional attribute space. Proceedings of the Royal Society of London (Series A), 347, 371–385.

    Article  Google Scholar 

  21. Kemeny, J. (1959). Mathematics without numbers. Daedalus, 88, 571–91.

    Google Scholar 

  22. Kendall, M., & Gibbons, J.D. (1990). Rank correlation methods. New York: Oxford University Press.

    Google Scholar 

  23. Kotz, S., Balakrishnan, N., Johnson, N.L. (2000). Continuous multivariate distributions. New York: Wiley.

    Book  Google Scholar 

  24. Kuga, K., & Nagatani, H. (1974). Voter antagonism and the paradox of voting. Econometrica, 42, 1045–1067.

    Article  Google Scholar 

  25. Lepelley, D. (1995). Condorcet efficiency of positional voting rules with single-peaked preferences. Economic Design, 1, 289–299.

    Article  Google Scholar 

  26. Merrill, S. (1984). A comparison of efficiency of multicandidate electoral systems. American Journal of Political Science, 28, 23–48.

    Article  Google Scholar 

  27. Mosimann, J.E. (1962). On the compound multinomial distribution, the multivariate beta distribution, and correlations among proportions. Biometrika, 49, 65–82.

    Google Scholar 

  28. Regenwetter, M., Grofman, B., Marley, A.A.J. (2002). On the model dependence of majority preference relations reconstructed from ballot or survey data. Mathematical Social Sciences, 43, 451–466.

    Article  Google Scholar 

  29. Regenwetter, M., Marley, A.A.J., Grofman, B. (2003). General concepts of value restriction and preference majority. Social Choice Welfare, 21, 149–173.

    Article  Google Scholar 

  30. Regenwetter, M., Grofman, B., Marley, A.A.J., Tsetlin, I.M. (2006). Behavioral social choice: Probabilistic models, statistical inference, and applications. Cambridge University Press.

    Google Scholar 

  31. Saari, D.G. (1990). Susceptibility to manipulation. Public Choice, 64, 21–41.

    Article  Google Scholar 

  32. Saari, D.G. (2001). Analyzing a nail-biting election. Social Choice Welfare, 18, 415–430.

    Article  Google Scholar 

  33. Tideman, T.N., & Richardson, D. (2000). Better voting methods through technology: the refinement-manageability trade-off in the single transferable vote. Public Choice, 103 (1–2), 13–34.

    Article  Google Scholar 

  34. Tideman, T.N. (2006). Collective decisions and voting. Ashgate: Burlington VT.

    Google Scholar 

  35. Truchon, M. (2006). Borda and the maximum likelihood approach to vote aggregation. Mimeo.

    Google Scholar 

  36. Young, H.P. (1988). Condorcet’s theory of voting. American Political Science Review, 82 (4), 1231–1244.

    Article  Google Scholar 

  37. Google Scholar 

Download references

Acknowledgements

We express our gratitude to an anonymous referee, who read our paper with unusual care and pointed out several errors and omissions, as well as to Dan Felsenthal and Moshé Machover for their patience and persistence during the editing process. All remaining errors are ours.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Florenz Plassmann .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Tideman, T.N., Plassmann, F. (2012). Modeling the Outcomes of Vote-Casting in Actual Elections. In: Felsenthal, D., Machover, M. (eds) Electoral Systems. Studies in Choice and Welfare. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20441-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20441-8_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20440-1

  • Online ISBN: 978-3-642-20441-8

  • eBook Packages: Business and EconomicsEconomics and Finance (R0)

Publish with us

Policies and ethics