We analyze the Condorcet paradox within a strategic bargaining model with
majority voting. Consistent subgame perfect equilibria (CPE) exist whenever the
geometric mean of the players’ risk coefficients, ratios of utility differences between
alternatives, is at most one. CPEs are Pareto efficient and ensure agreement within
nite expected time. For generic parameter values, CPEs are unique and in a CPE
either all players propose their best alternative with probability one or two players
do so and the third player randomizes between proposing his best and middle
alternative. Agents accept best alternatives, may reject middle alternatives with
positive probability, and reject otherwise. Bargaining power as modeled by recognition
probabilities is a key factor in determining expected delay. Irrespective of the
utility functions, no delay occurs for a suitable choice of bargaining power, whereas
expected delay goes to infinity if one of the players has almost all the bargaining
power. For generic parameter values, Condorcet cycles do not occur. Contrary to
the case with unanimous approval, a player bene ts from an increase in his risk aversion.