Collaborative Research on Multi-dimensional Models of Bargaining and Elections

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A theory of collective choice is developed to facilitate our understanding of group decisionmaking, particularly when the decision of a group affects all members, perhaps not equally. Such situations are rife with opportunities for negotiation, coalition formation, and other forms of complex strategic interaction. The theory abstracts for the procedural details of decisionmaking and is, therefore, quite general. Unfortunately, Arrow (1963), Plott (1967), Schofield (1983) and others have shown that "core" points -- points from which no coalition can force a profitable change -- often fail to exist. Moreover, McKelvey (1977, 1979) has shown that, when the core is empty, the social alternatives that can be reached by successive coalitional moves comprise the entire space of alternatives. This has prompted some (e.g., Riker (1980)) to draw the conclusion that collective decisionmaking is inherently unstable and unpredictable. In this proposal, we outline a research program on bargaining and elections with the goal of advancing our understanding of collective choice. Although our work has connections to the theory of collective choice, our approach is distinct: we explicitly model the institutional setting in which collective choices are made, such as the procedural rules of legislatures or elections. Once the institutional context of choice is clarified, the tools of non-cooperative game theory can be applied, and choices can be analyzed as the product of equilibrium behavior in non-cooperative games. Our models have several elements in common that permit a unified theoretical treatment: they are dynamic and multi-dimensional, and the primary mechamisn by which individual preferences are aggregated is voting. We attempt to develop a general theory that will lay the groundwork for future theoretical and applied work and, accordingly, our focus is primarily on the existence of stationary equilibria (equilibria of a particularly simple form) and on connections to the theory of collective choice. We believe that addressing these foundational issues will facilitate future analysis of more highly specified models, allowing sharper equilibrium characterizations, comparative statics analysis, computational analysis, and empirical testing. The proposal consists of two parts, presented in Sections 2 and 3. In Section 2, we propose five projects on the study of bargaining, as outlined below. The results of the first project are contained in Banks and Duggan (1998), and are near their final form.A Bargaining Model of Collective Choice: We establish existence and robustness of staionary equilibria in the basic model, and generalize past work on bargaining. We establish conditions under which our non-cooperative theory predicts precisely the core, thereby corroborating the theory of collective choice.A Multi-dimensional Model of Gridlock: We investigate the issue of the stability of the status quo in the basic model . Our model generalizes Kreshbiel's (1996, 1998) model of legislative gridlock and provides the following insight: in multi-dimensional settings, complete gridlock of the sort in Krehbiel's model is rare, although a partial type of gridlock is possible.Contemporaneous Bargaining: We extend our equilibrium existence result to a model of simultaneous bargaining with multiple groups. Applications include the study of federal systems of government, bicameral legislatures, decisions within separate firms, and decisions within separate national assemblies. Bargaining in Economic Environments: We capture bargaining in economic contexts, give decisionmakers endowments and property rights over them, and allow endowments to vary stochastically over time. We focus on equilibrium existence and core equivalence. Dynamic Collective Choice: We allow bargaining to continue after an agreement has been reached - the outcome of bargaining in one period becomes the status quo point for bargaining in the next. We attempt to overcome difficult technical problems in the analysis of equilibrium existence in models of "ongoing" collective choice. In Section 3, we propose to study repeated elections, and generalize Duggan (1997) by allowing for a multi-dimensional policy space and more general preferences. The model of elections is mathematically quite similar to our basic model of bargaining, and the techniques we have developed in our analysis of bargaining enable us to establish the existence of stationary electoral equilibria, to characterize them, and to clarify their connection to the core.