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Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System

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Author Info

  • Steven J. Brams

    (Department of Politics, New York University)

  • Todd R. Kaplan

    (Department of Economics, University of Exeter)

Abstract

Political parties in Northern Ireland recently used a divisor method of apportionment to choose, in sequence, ten cabinet ministries. If the parties have complete information about each others' preferences, we show that it may not be rational for them to act sincerely by choosing their most-preferred ministry that is available. One consequence of acting sophisticatedly is that the resulting allocation may not be Pareto-optimal, making all the parties worse off. Another is nonmonotonicty—choosing earlier may hurt rather than help a party. We introduce a mechanism that combines sequential choices with a structured form of trading that results in sincere choices for two parties. Although there are difficulties in extending this mechanism to more than two parties, other approaches are explored, such as permitting parties to making consecutive choices not prescribed by an apportionment method. But certain problems, such as eliminating envy, remain.

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File URL: http://people.exeter.ac.uk/cc371/RePEc/dpapers/DP0202.pdf
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Bibliographic Info

Paper provided by Exeter University, Department of Economics in its series Discussion Papers with number 0202.

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Date of creation: Sep 2002
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Handle: RePEc:exe:wpaper:0202

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Related research

Keywords: Proportional Representation; apportionment; divisor methods; Sincere and Sophisticated Choices; Envy Free Allocations; Sports Drafts;

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References

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  1. Dorothea Herreiner & Clemens Puppe, 2002. "A simple procedure for finding equitable allocations of indivisible goods," Social Choice and Welfare, Springer, vol. 19(2), pages 415-430, April.
  2. Carmignani, Fabrizio, 2001. "Cabinet Formation in Coalition Systems," Scottish Journal of Political Economy, Scottish Economic Society, vol. 48(3), pages 313-29, August.
  3. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446, October.
  4. Steven J. Brams & Paul H. Edelman & Peter C. Fishburn, 2003. "Fair Division Of Indivisible Items," Theory and Decision, Springer, vol. 55(2), pages 147-180, 09.
  5. Friedrich Pukelsheim & Albert W. Marshall & Ingram Olkin, 2002. "A majorization comparison of apportionment methods in proportional representation," Social Choice and Welfare, Springer, vol. 19(4), pages 885-900.
  6. Edelman, Paul & Fishburn, Peter, 2001. "Fair division of indivisible items among people with similar preferences," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 327-347, May.
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Cited by:
  1. Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2009. "The undercut procedure: an algorithm for the envy-free division of indivisible items," MPRA Paper 12774, University Library of Munich, Germany.
  2. Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2013. "Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm," MPRA Paper 47400, University Library of Munich, Germany.

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