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Bargaining Power and Majoritarian Allocations


  • McCain , Roger

    () (School of Economics LeBow College of Business Drexel University)


It seems that decisions in many voting bodies might be described by a two-stage decision in which the first stage is a bargaining process and the second is a vote that is often a formality. This does not mean that the voting is irrelevant, but, rather, that it limits the threats that may be made and so influences bargaining power at the first stage. We will explore a two-stage game in which the first stage is a bargaining process and the game terminates if there is an agreement, while at the second stage, if there is no agreement at the first stage, a contested election is held to determine the joint strategy of the body. Bargaining power at the first stage is attributed to minimum winning coalitions in the possible second stage election. In an idealization of such a two-stage game, majority groups have equal bargaining power, and nonmajority groups have none. This paper uses a recent extension of bargaining theory that attributes bargaining power to groups as well as individuals and assumes that a minimum winning voting bloc has bargaining power one and other groups and individuals have bargaining power zero. For TU games, this yields a striking rule for the bargaining solution: the surplus generated by the coalition is either distributed as equal payouts, or distributed among the members with lesser individual rationality constraints, so that their payouts are equal, while others get their individual rationality constraints. In the tradition of cooperative game theory, we assume that the bargaining is successful and explicitly consider only the bargaining stage. In a digression, a model of a business enterprise as a TU game is developed, and the voting model is applied to contrast decisions in a worker cooperative (which makes decisions on the basis of majority rule among the employee members) with for-profit corporations and other organizational forms.

Suggested Citation

  • McCain , Roger, 2013. "Bargaining Power and Majoritarian Allocations," School of Economics Working Paper Series 2013-9, LeBow College of Business, Drexel University.
  • Handle: RePEc:ris:drxlwp:2013_009

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    References listed on IDEAS

    1. Masahiko Aoki, 2013. "A Model of the Firm as a Stockholder-Employee Cooperative Game," Chapters,in: Comparative Institutional Analysis, chapter 9, pages 141-142 Edward Elgar Publishing.
    2. Feldman, Allan M, 1979. "Manipulating Voting Procedures," Economic Inquiry, Western Economic Association International, vol. 17(3), pages 452-474, July.
    3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. T. de Scitovszky, 1943. "A Note on Profit Maximisation and its Implications," Review of Economic Studies, Oxford University Press, vol. 11(1), pages 57-60.
    6. Howard R. Bowen, 1943. "The Interpretation of Voting in the Allocation of Economic Resources," The Quarterly Journal of Economics, Oxford University Press, vol. 58(1), pages 27-48.
    7. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, September.
    8. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    More about this item


    voting; cooperative games; bargaining;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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