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

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  • Brams, S.J.
  • Kaplan, T.R.

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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Bibliographic Info

Paper provided by C.V. Starr Center for Applied Economics, New York University in its series Working Papers with number 02-06.

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Length: 43 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:cvs:starer:02-06

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Postal: C.V. Starr Center, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012
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Postal: C.V. Starr Center, Department of Economics, New York University, 19 W. 4th Street, 6th Floor, New York, NY 10012
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Related research

Keywords: APPORTIONMENT METHODS; CABINETS; SEQUENTIAL ALLOCATION; MECHANISM DESIGN; FAIRNESS;

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References

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  1. 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.
  2. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
  3. 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.
  4. Carmignani, Fabrizio, 2001. "Cabinet Formation in Coalition Systems," Scottish Journal of Political Economy, Scottish Economic Society, vol. 48(3), pages 313-29, August.
  5. 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.
  6. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.

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