John Duggan

A Bargaining Model of Collective Choice

We provide a general theory of collective decision making, one that relates social choices to the strategic incentives of individuals, by generalizing the Baron-Ferejohn (1989) model of bargaining to the multidimensional spatial model. We prove existence of stationary equilibria, upper hemicontinuity of equilibrium outcomes in structural and preference parameters, and equivalence of equilibrium outcomes and the core in certain environments, including the one-dimensional case. The model generates equilibrium predictions even when the core is empty, and it yields a “continuous” generalization of the core in some familiar environments in which the core is nonempty. As the description of institutional detail in the model is sparse, it applies to collective choice in relatively unstructured settings and provides a benchmark for the general analysis of legislative and parliamentary politics.

Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized

Abstract. The Gibbard-Satterthwaite Theorem on the manipulability of social-choice 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.

Probabilistic Voting in the Spatial Model of Elections: The Theory of Office-motivated Candidates

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 controverts 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.

Dynamic Legislative Policy Making

We prove existence of stationary Markov perfect equilibria in an infinite-horizon model of legislative policy making in which the policy outcome in one period determines the status quo for the next. We allow for a multidimensional policy space and arbitrary smooth stage utilities, and we assume preferences and the status quo are subject to arbitrarily small shocks. We prove that equilibrium continuation values are differentiable and that proposal strategies are continuous almost everywhere. We establish upper hemicontinuity of the equilibrium correspondence, and we provide weak conditions under which each equilibrium of our model determines an aperiodic transition probability over policies. We establish a convergence theorem giving conditions under which the invariant distributions generated by stationary equilibria must be close to the core in a canonical spatial model. Finally, we extend the analysis to sequential move stochastic games and to a version of the model in which the proposer and voting rule are determined by play of a finite, perfect information game.

Repeated Elections with Asymmetric Information

An infinite 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 payoff 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. Copyright Blackwell Publishers Ltd 2000.

Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections

We prove that the support of mixed strategy equilibria of two-player, symmetric, zero-sum games lies in the uncovered set, a concept originating in the theory of tournaments. and the spatial theory of politics. We allow for uncountably infinite strategy spaces, and as a special case. we obtain a long-standing claim to the same effect. due to R. McKelvey (Amer. J. Polit. Sci. 30 (1986), 283-314). in the political science literature. Further. we prove the nonemptiness of the uncovered set under quite general assumptions, and we establish. under various assumptions. the coanalyticity and measurability of this set. In the concluding section. we indicate how the inclusion result may be extended to multiplayer. non-zero-sum games

Virtual Bayesian implementation

Allowing for incomplete information, this paper characterizes the social choice functions that can be approximated by the equilibrium outcomes of a mechanism: incentive compatibility is necessary and almost sufficient for virtual Bayesian implementability. In conjunction with a second condition, Bayesian incentive consistency, incentive compatibility is also sufficient. This new condition is weak--under standard topological and informational assumptions it is satisfied by every social choice function. The type sets of the agents are taken to be arbitrary (possibly infinite) measurable spaces. An example shows that there are virtually (in fact, exactly) Bayesian implementable social choice functions that are not virtually implementable in iteratively undominated strategies.

Uniqueness of Stationary Equilibria in a one-Dimensional Model of Bargaining

Abstract We prove uniqueness of stationary equilibria in a one-dimensional model of bargaining with quadratic utilities, for an arbitrary common discount factor. For general concave utilities, we prove existence and uniqueness of a “minimal” stationary equilibrium and of a “maximal” stationary equilibrium. We provide an example of multiple stationary equilibria with concave (nonquadratic) utilities.

Social Choice and Electoral Competition in the General Spatial Model

This paper extends the theory of the core, the uncovered set, and the related undominated set to a general set of alternatives and an arbitrary measure space of voters. We investigate the properties of social preferences generated by simple games; we extend results on generic emptiness of the core; we prove the general nonemptiness of the uncovered and undominated sets; and we prove the upper hemicontinuity of these correspondences when the voters’ preferences are such that the core is nonempty and externally stable. Finally, we give conditions under which the undominated set is lower hemicontinuous.

Repeated Downsian electoral competition

We analyze an infinitely repeated version of the Downsian model of elections. The folk theorem suggests that a wide range of policy paths can be supported by subgame perfect equilibria when parties and voters are sufficiently patient. We go beyond this result by imposing several suitable refinements and by giving separate weak conditions on the patience of voters and the patience of parties under which every policy path can be supported. On the other hand, we show that only majority undominated policy paths can be supported in equilibrium for arbitrarily low voter discount factors: if the core is empty, the generic case in multiple dimensions, then voter impatience leads us back to the problem of non-existence of equilibrium. We extend this result to give conditions under which core equivalence holds for a non-trivial range of voter and party discount factors, providing a game-theoretic version of the Median Voter Theorem in a model of repeated Downsian elections.