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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
Brams, S.J.
Kaplan, T.R.

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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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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
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Handle: RePEc:cvs:starer:02-06

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

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Models of Political Processes: Rent-seeking, Elections, Legislatures, and Voting Behavior
H11 - Public Economics - - Structure and Scope of Government - - - Structure and Scope of Government

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  1. Brams, S. J. & Eldelman, P. H. & Fishburn, P. C., 2000. "Fair Division of Indivisible Items," Working Papers 00-15, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
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  2. Carmignani, Fabrizio, 2001. "Cabinet Formation in Coalition Systems," Scottish Journal of Political Economy, Scottish Economic Society, vol. 48(3), pages 313-29, August. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  4. Brams, S. J. & Eldelman, P. H. & Fishburn, P. C., 2000. "Paradoxes of Fair Division," Working Papers 00-13, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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