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Tests of formal models of legislative politics have become increasingly common, and have tended to draw confident and positive inferences about focal theories. This is not a particularly satisfactory development, however, inasmuch as the supposedly supported theories are quite different from one another, and the tests that generate the support tend overwhelmingly to focus on one theory rather than competing theories. We develop and employ a method of comparative theory-testing using estimates of cutpoints on final passage results. The findings are inconclusive in part because the theories, while substantively different, are often operationally nearly observationally equivalent.

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.

This article uses the notion of a “Local Nash Equilibrium” (LNE) to model a vote maximizing political game that incorporates valence (the electorally perceived quality of the political leaders). Formal stochastic voting models without valence typically conclude that all political agents (parties or candidates) will converge towards the electoral mean (the origin of the policy space). The main theorem presented here obtains the necessary and sufficient conditions for the validity of the “mean voter theorem” when valence is involved. Since a pure strategy Nash equilibrium (PNE), if it exists, must be a LNE the failure of the necessary condition for an LNE at the origin also implies that PNE cannot be at the origin. To further account for the non-convergent location of parties, the model is extended to include activist valence (the effect on party popularity due to the efforts of activist groups). These results suggest that it is very unlikely that Local Nash equilibria will be located at the electoral center. The theoretical conclusions appear to be borne out by empirical evidence from a number of countries. Genericity arguments demonstrate that LNE will exist for almost all parameters, when the policy space is compact, convex, without any restriction on the variance of the voter ideal points or on the party valence functions.

This paper examines competition in a spatial model of two-candidate elections, where one candidate enjoys a quality advantage over the other candidate. The candidates care about winning and also have policy preferences. There is two-dimensional private information. Candidate ideal points as well as their tradeoffs between policy preferences and winning are private information. The distribution of this two-dimensional type is common knowledge. The location of the median voter’s ideal point is uncertain, with a distribution that is commonly known by both candidates. Pure strategy equilibria always exist in this model. We characterize the effects of increased uncertainty about the median voter, the effect of candidate policy preferences, and the effects of changes in the distribution of private information. We prove that the distribution of candidate policies approaches the mixed equilibrium of Aragones and Palfrey [2], when both candidates’ weights on policy preferences go to zero.

In the “divide a dollar” framework of distributive politics among three pivotal groups of unequal size, the paper compares two variants of two-party competition, the objective of a party being the probability of winning (“majority tournament” game) or the expected number of votes (“plurality” game). At a mixedequilibrium, all individuals are, on expectation, treated alike in the plurality game while the tournament game favors individuals in small groups.

This chapter examines a number of extensions of the multi-armed bandit framework. We consider the possibility of an infinite number of available arms, we give conditions under which the Gittins index strategy is well-defined, and we examine the optimality of that strategy. We then consider some difficulties arising from “parallel search,” in which a decision-maker may pull more than one arm per period, and from the introduction of a cost of switching between arms.

We examine how a society chooses to divide a given budget among various regions, projects or individuals. In particular, we characterize the Banks set and the Uncovered Set in such problems. We show that the two sets can be proper subsets of the set of all alternatives, and at times are very pointed in their predictions. This contrasts with well-known “chaos theorems,” which suggest that majority voting does not lead to any meaningful predictions when the policy space is multidimensional.

We investigate the predictive success of the Baron-Ferejohn model of legislative bargaining in laboratory environments. In particular, we use a finite period version of the bargaining game under weighted majority rule where a fixed payoff is divided between three players. We find that our subjects’ behavior is not predicted well by the Baron-Ferejohn model. The model predicts hardly better than a coin flip which coalition partner is selected by the chosen proposer, and proposers allocate more money to other players than predicted. A sizable number of proposals are rejected in the first proposal periods, and subjects who vote to reject a proposal on average receive a higher payoff from the new proposal. We find that a simple equal sharing rule yields point predictions that can account for 2/1 to 4/3 of all accepted proposals.

This paper examines competition in a spatial model of two-candidate elections, where one candidate enjoys a quality advantage over the other candidate. The candidates care about winning and also have policy preferences. There is two-dimensional private information. Candidate ideal points as well as their tradeoffs between policy preferences and winning are private information. The distribution of this two-dimensional type is common knowledge. The location of the median voter’s ideal point is uncertain, with a distribution that is commonly known by both candidates. Pure strategy equilibria always exist in this model. We characterize the effects of increased uncertainty about the median voter, the effect of candidate policy preferences, and the effects of changes in the distribution of private information. We prove that the distribution of candidate policies approaches the mixed equilibrium of Aragones and Palfrey [2], when both candidates’ weights on policy preferences go to zero.

Tests of formal models of legislative politics have become increasingly common, and have tended to draw confident and positive inferences about focal theories. This is not a particularly satisfactory development, however, inasmuch as the supposedly supported theories are quite different from one another, and the tests that generate the support tend overwhelmingly to focus on one theory rather than competing theories. We develop and employ a method of comparative theory-testing using estimates of cutpoints on final passage results. The findings are inconclusive in part because the theories, while substantively different, are often operationally nearly observationally equivalent.