The Condorcet paradox revisited
AbstractWe 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 InfoPaper provided by Maastricht University, Graduate School of Business and Economics (GSBE) in its series Research Memorandum with number 021.
Date of creation: 2013
Date of revision:
Stochastic and Dynamic Games; Evolutionary Games; Repeated Games; Bargaining Theory; Matching Theory; Political Processes: Rent-seeking; Lobbying; Elections; Legislatures; and Voting Behavior;
Other versions of this item:
- Herings P. Jean-Jacques & Houba Harold, 2010. "The Condercet Paradox Revisited," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- P. Jean-Jacques Herings & Harold Houba, 2010. "The Condorcet Paradox Revisited," Tinbergen Institute Discussion Papers 10-026/1, Tinbergen Institute.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2014-02-02 (All new papers)
- NEP-CDM-2014-02-02 (Collective Decision-Making)
- NEP-GTH-2014-02-02 (Game Theory)
- NEP-POL-2014-02-02 (Positive Political Economics)
- NEP-UPT-2014-02-02 (Utility Models & Prospect Theory)
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