Skip to main content
Log in

The elimination paradox: apportionment in the Democratic Party

  • Published:
Public Choice Aims and scope Submit manuscript

Abstract

To award delegates in their presidential primary elections, the US Democratic Party uses Hamilton’s method of apportionment after eliminating any candidates (and their votes) that receive less than 15% of the total votes cast. We illustrate how a remaining candidate may have his or her delegate total decline as a result of other candidates being eliminated; this leads to a new elimination paradox. We relate that paradox to the new states, no show, and population paradoxes and show that divisor methods are not susceptible to the elimination paradox. We conclude with instances in which the elimination paradox may occur in other contexts, including parliamentary systems.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Balinski, M., & Young, H. P. (2001). Fair representation: Meeting the ideal of one man, one vote (2nd ed.). New York: Brookings Institution Press.

    Google Scholar 

  • Bradberry, B. A. (1992). A geometric view of some apportionment paradoxes. Mathematics Magazine, 65, 3–17.

    Article  Google Scholar 

  • Dančišin, V. (2017). No-show paradox in Slovak party-list proportional system. Human Affairs, 27, 15–21.

    Google Scholar 

  • Fishburn, P. C., & Brams, S. J. (1983). Paradoxes of preferential voting. Mathematics Magazine, 56(4), 207–214.

    Article  Google Scholar 

  • Geist, K., Jones, M. A., & Wilson, J. (2010). Apportionment in the democratic primary process. Mathematics Teacher, 104, 214–220.

    Google Scholar 

  • Jones, M. A., McCune, D., & Wilson, J. (2018). An iterative procedure for apportionment and its use in the Georgia Republican primary (Preprint).

  • Lucas, W. F. (1983). The apportionment problem. In S. J. Brams, W. F. Lucas, & P. D. Straffin, Jr. (Eds.), Political and related models, Modules in Applied Mathematics (Vol. 2, Chapter 14, pp. 358–396). New York: Springer.

  • Meredith, J. C. (1913). Proportional representation in Ireland. Dublin: E. Ponsonby.

    Google Scholar 

  • Moulin, H. (1988). Condorcet’s principle implies the no show paradox. Journal of Economic Theory, 45, 53–64.

    Article  Google Scholar 

  • The Royal Commission (1910) Report of the Royal Commission appointed to enquire into electoral systems. London: HMSO. Available at https://archive.org/details/reportofroyalco00grea.

  • Thomson, W. (1995). Population monotonic allocation rules. In William A. Barnett, Hervé Moulin, Maurice Salles, & Norman J. Schofield (Eds.), Social choice, welfare, and ethics (pp. 79–124). Cambridge: Cambridge University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jennifer Wilson.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jones, M.A., McCune, D. & Wilson, J. The elimination paradox: apportionment in the Democratic Party. Public Choice 178, 53–65 (2019). https://doi.org/10.1007/s11127-018-0608-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11127-018-0608-3

Keywords

Mathematics Subject Classification

Navigation