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Public Choice

, Volume 178, Issue 1–2, pp 53–65 | Cite as

The elimination paradox: apportionment in the Democratic Party

  • Michael A. Jones
  • David McCune
  • Jennifer WilsonEmail author
Article

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.

Keywords

Elimination paradox Democratic primary Population monotonicity 

Mathematics Subject Classification

91B32 91B12 91F10 

References

  1. 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
  2. Bradberry, B. A. (1992). A geometric view of some apportionment paradoxes. Mathematics Magazine, 65, 3–17.CrossRefGoogle Scholar
  3. Dančišin, V. (2017). No-show paradox in Slovak party-list proportional system. Human Affairs, 27, 15–21.Google Scholar
  4. Fishburn, P. C., & Brams, S. J. (1983). Paradoxes of preferential voting. Mathematics Magazine, 56(4), 207–214.CrossRefGoogle Scholar
  5. Geist, K., Jones, M. A., & Wilson, J. (2010). Apportionment in the democratic primary process. Mathematics Teacher, 104, 214–220.Google Scholar
  6. Jones, M. A., McCune, D., & Wilson, J. (2018). An iterative procedure for apportionment and its use in the Georgia Republican primary (Preprint).Google Scholar
  7. 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.Google Scholar
  8. Meredith, J. C. (1913). Proportional representation in Ireland. Dublin: E. Ponsonby.Google Scholar
  9. Moulin, H. (1988). Condorcet’s principle implies the no show paradox. Journal of Economic Theory, 45, 53–64.CrossRefGoogle Scholar
  10. The Royal Commission (1910) Report of the Royal Commission appointed to enquire into electoral systems. London: HMSO. Available at https://archive.org/details/reportofroyalco00grea.
  11. 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

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical ReviewsAnn ArborUSA
  2. 2.William Jewell CollegeLibertyUSA
  3. 3.Eugene Lang College, The New SchoolNew York CityUSA

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