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The Condorcet paradox revisited

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  • Herings P.J.J.
  • Houba H

    (GSBE)

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.

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Bibliographic Info

Paper provided by Maastricht University, Graduate School of Business and Economics (GSBE) in its series Research Memorandum with number 021.

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Date of creation: 2013
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Handle: RePEc:unm:umagsb:2013021

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Keywords: Stochastic and Dynamic Games; Evolutionary Games; Repeated Games; Bargaining Theory; Matching Theory; Political Processes: Rent-seeking; Lobbying; Elections; Legislatures; and Voting Behavior;

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  1. Herings,P. Jean-Jacques & Peeters,Ronald J.A.P, 2000. "Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, Elsevier, vol. 100(2), pages 191-219, October.
  3. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  4. Hans Haller & Roger Lagunoff, 2000. "Genericity and Markovian Behavior in Stochastic Games," Econometrica, Econometric Society, Econometric Society, vol. 68(5), pages 1231-1248, September.
  5. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 90-123, May.
  6. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, Elsevier, vol. 12(3), pages 472-482, June.
  7. Safra, Zvi & Zhou, Lin & Zilcha, Itzhak, 1990. "Risk Aversion in the Nash Bargaining Problem with Risky Outcomes and Risky Disagreement Points," Econometrica, Econometric Society, Econometric Society, vol. 58(4), pages 961-65, July.
  8. Chatterjee, Kalyan & Bhaskar Dutta & Debraj Ray & Kunal Sengupta, 1993. "A Noncooperative Theory of Coalitional Bargaining," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 60(2), pages 463-77, April.
  9. Houba, Harold, 2008. "On continuous-time Markov processes in bargaining," Economics Letters, Elsevier, Elsevier, vol. 100(2), pages 280-283, August.
  10. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, Econometric Society, vol. 47(5), pages 1085-1112, September.
  11. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
  12. Roth, Alvin E, 1985. "A Note on Risk Aversion in a Perfect Equilibrium Model of Bargaining," Econometrica, Econometric Society, Econometric Society, vol. 53(1), pages 207-11, January.
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