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We analyze sequential bargaining in general political and economic environments, where proposers are recognized according to a random recognition rule and a proposal is implemented if it passes under an arbitrary voting rule. We prove existence of stationary equilibria, upper hemicontinuity of equilibrium proposals in structural and preference parameters, and core equivalence under certain conditions.

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The Condorcet Jury Theorem states that majorities are more likely than any single individual to select the “better” of two alternatives when there exists uncertainty about which of the two alternatives is in fact preferred. Most extant proofs of this theorem implicitly make the behavioral assumption that individuals vote “sincerely” in the collective decision making, a seemingly innocuous assumption, given that individuals are taken to possess a common preference for selecting the better alternative. However, in the model analyzed here we find that sincere behavior by all individuals is not rational even when individuals have such a common preference. In particular, sincere voting does not constitute a Nash equilibrium. A satisfactory rational choice foundation for the claim that majorities invariably “do better” than individuals, therefore, has yet to be derived.