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.

We take a game-theoretic approach to the analysis of juries by modelling voting as a game of incomplete information. Rather than the usual assumption of two possible signals (one indicating guilt, the other innocence), we allow jurors to perceive a full spectrum of signals. We o®er three main results. First, given any voting rule requiring ā xed fraction of votes to convict, we characterize the unique symmetric equilibrium of the game. Second, we obtain a condition under which unanimity rule exhibits a bias toward convicting the innocent. Third, we prove a \jury theorem" for the continuous signal model: as the size of the jury increases, the probability of making a mistaken judgment goes to zero for every voting rule, except unanimity rule; for unanimity rule, the probability of a mistake is bounded strictly above zero.

The Gibbard-Satterthwaite Theorem on the manipulability of socialchoice rules assumes resoluteness: there are no ties, no multi-member choice sets. Generalizations based on a familiar lottery idea allow ties but assume perfectly shared probabilistic beliefs about their resolution. We prove a more straightforward generalization that assumes almost no limit on ties or beliefs about them.

We unify and extend much of the literature on probabilistic voting in two-candidate elections. We give existence results for mixed and pure strategy equilibria of the electoral game. We prove general results on optimality of pure strategy equilibria vis-a-vis a weighted utilitarian social welfare function, and we derive the well-known "mean voter" result as a special case. We establish broad conditions under which pure strategy equilibria exhibit "policy coincidence," in the sense that candidates pick identical platforms. We establish the robustness of equilibria with respect to variations in demographic and informational parameters. We show that mixed and pure strategy equilibria of the game must be close to being in the majority rule core when the core is close to non-empty and voters are close to deterministic. This contraverts the notion that the median (in a one-dimensional model) is a mere "artifact." Using an equivalence between a class of models including the binary Luce model and a class including additive utility shock models, we then derive a general result on optimality vis-a-vis the Nash social welfare function.

An in®nite sequence of elections with no term limits is modelled. In each period a challenger with privately known preferences is randomly drawn from the electorate to run against the incumbent, and the winner chooses a policy outcome in a one-dimensional issue space. One theorem is that there exists an equilibrium in which the median voter is decisive: an incumbent wins re-election if and only if his most recent policy choice gives the median voter a payo at least as high as he would expect from a challenger. The equilibrium is symmetric, stationary, and the behavior of voters is consistent with both retrospective and prospective voting. A second theorem is that, in fact, it is the only equilibrium possessing the latter four conditions ± decisiveness of the median voter is implied by them.