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The Condorcet paradox revisited

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  • Herings, P.J.J.

    (Microeconomics & Public Economics)

  • Houba, H

Abstract

We analyze the Condorcet paradox within a strategic bargaining model with majority voting, exogenous recognition probabilities, and no discounting. Stationary subgame perfect equilibria (SSPE) exist whenever the geometric mean of the players' risk coefficients, ratios of utility differences between alternatives, is at most one. SSPEs ensure agreement within finite expected time. For generic parameter values, SSPEs are unique and exclude Condorcet cycles. In an SSPE, at least two players propose their best alternative and at most one player proposes his middle alternative with positive probability. Players never reject best alternatives, may reject middle alternatives with positive probability, and reject worst alternatives. Recognition probabilities represent bargaining power and drive expected delay. Irrespective of utilities, no delay occurs for suitable distributions of bargaining power, whereas expected delay goes to infinity in the limit where one player holds all bargaining power. Contrary to the case with unanimous approval, a player benefits from an increase in his risk aversion.

Suggested Citation

  • Herings, P.J.J. & Houba, H, 2013. "The Condorcet paradox revisited," Research Memorandum 021, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2013021
    DOI: 10.26481/umagsb.2013021
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    Cited by:

    1. Britz, V. & Herings, P.J.J. & Predtetchinski, A., 2012. "On the convergence to the Nash bargaining solution for endogenous bargaining protocols," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Houba, Harold & Wen, Quan, 2014. "Backward induction and unacceptable offers," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 151-156.
    3. Herings, P.J.J. & Houba, H, 2015. "Costless delay in negotiations," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).

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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary 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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