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

Author

Listed:
  • 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.

Suggested Citation

  • Steven J. Brams & Todd R. Kaplan, 2002. "Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System," Discussion Papers 0202, University of Exeter, Department of Economics.
    • Handle: RePEc:exe:wpaper:0202
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    File URL: https://exetereconomics.github.io/RePEc/dpapers/DP0202.pdf
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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. Harald Wiese, 2007. "Measuring The Power Of Parties Within Government Coalitions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 307-322.
    3. Haris Aziz, 2016. "A generalization of the AL method for fair allocation of indivisible objects," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 307-324, October.
    4. Alejandro Ecker & Thomas M. Meyer, 2019. "Fairness and qualitative portfolio allocation in multiparty governments," Public Choice, Springer, vol. 181(3), pages 309-330, December.
    5. Mithun Chakraborty & Ulrike Schmidt-Kraepelin & Warut Suksompong, 2021. "Picking Sequences and Monotonicity in Weighted Fair Division," Papers 2104.14347, arXiv.org, revised Aug 2021.

    More about this item

    Keywords

    Proportional Representation; apportionment; divisor methods; Sincere and Sophisticated Choices; Envy Free Allocations; Sports Drafts;
    All these keywords.

    JEL classification:

    • H00 - Public Economics - - General - - - General
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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