A dynamic model of democratic elections in multidimensional policy spaces

We propose a general model of repeated elections. In each period, a challenger is chosen from the electorate to run against an incumbent politician in a majority-rule election, and the winner then selects a policy from a multidimensional policy space. Individual policy preferences are private information, whereas policy choices are publicly observable. We prove existence and continuity of equilibria in "simple" voting and policy strategies; we provide examples to show the variety of possible equilibrium patterns in multiple dimensions; we analyze the effects of patience and office-holding benefits on the persistence of policies over time; and we identify relationships between equilibrium policies and the core of the underlying voting game. As a byproduct of our analysis, we show how equilibrium incentives maylead elected representatives to make policy compromises, even when binding commitments are unavailable. We provide an informational story for incumbency advantage. Finally, we give an asymptotic version of the median voter theorem for the one-dimensional model as voters become-arbitrarily patient

A General Bargaining Model of Legislative Policy-making

We present a general model of legislative bargaining in which the status quo is an arbitrary point in a multidimensional policy space. In contrast to other bargaining models, the status quo is not assumed to be bad for all legislators, and delay may be Pareto efficient. We prove existence of stationary equilibria. We show that if all legislators are risk averse or if even limited transfers are possible, then delay is only possible if the status quo lies in the core. Thus, we expect immediate agreement in multidimensional models, where the core is typically empty. In one dimension, delay is possible if and only if the status quo lies in the core of the voting rule, and then it is the only possible outcome. Our comparative statics analysis yield two noteworthy insights: moderate status quos imply moderate policy outcomes, and legislative patience implies policy moderation

Social choice theory, game theory, and positive political theory

We consider the relationships between the collective preference and non-cooperative game theory approaches to positive political theory. In particular, we show that an apparently decisive difference between the two approachesthat in sufficiently complex environments (e.g. high-dimensional choice spaces) direct preference aggregation models are incapable of generating any prediction at all, whereas non-cooperative game-theoretic models almost always generate predictionis indeed only an apparent difference. More generally, we argue that when modeling collective decisions there is a fundamental tension between insuring existence of well-defined predictions, a criterion of minimal democracy, and general applicability to complex environments; while any two of the three are compatible under either approach, neither collective preference nor non-cooperative game theory can support models that simultaneously satisfy all three desiderata

A Dynamic Model of Democratic Elections in Multidimensional Policy Spaces

We propose a general model of repeated elections. In each period, a challenger is chosen from the electorate to run against an incumbent politician in a majority-rule election, and the winner then selects a policy from a multidimensional policy space. Individual policy preferences are private information, whereas policy choices are publicly observable. We prove existence and continuity of equilibria in “simple” voting and policy strategies; we provide examples to show the variety of possible equilibrium patterns in multiple dimensions; we analyze the effects of patience and office-holding benefits on the persistence of policies over time; and we identify relationships between equilibrium policies and the core of the underlying voting game. As a byproduct of our analysis, we show how equilibrium incentives may lead elected representatives to make policy compromises, even when binding commitments are unavailable. We provide an informational story for incumbency advantage. Finally, we give an asymptotic version of the median voter theorem for the one-dimensional model as voters becomes arbitrarily patient.

Reviewed Work: Analytical Politics

Mathematical models of political processes have become increasingly sophisticated over the last few decades, with the lessons drawn from such models generating insights relevant for both political scientists and economists. In Analytical Politics, Professors Hinich and Munger present some of the primary building blocks of these models, show how they fit together, and describe some of the more fundamental conclusions established to date. The material is pitched to an audience of graduate and advanced undergraduate students in political science and economics (exercises are provided), as well as to scholars unfamiliar with the terrain. Most of the formal results are stated without proof, and no new results are presented

Equilibrium Behavior in Crisis Bargaining Games

This paper analyzes a general model of two-player bargaining in the shadow of war, where one player possesses private information concerning the expected benefits of war. I derive conclusions about equilibrium behavior by examining incentive compatibility constraints, where these constraints hold regardless of the game form; hence, the qualitative results are "game-free." I show that the higher the informed player's payoff from war, the higher is his or her equilibrium payoff from settling the dispute short of war, and the higher is the equilibrium probability of war. The latter result rationalizes the monotonicity assumption prevalent in numerous expected utility models of war. I then provide a general result concerning the equilibrium relationship between settlement payoffs and the probability of war

Toward a History of Game Theory [Reviews]

This collection of eleven essays examines the development of game theory from its inception in the 1920s to the 1950s and offers examples of games and solutions from the probabilists of the early 1700s. Four general topics are covered, and some chapters deal with more than one. The first concerns the work ofJohn von Neumann and Emile Borel in the 1920s on the minimax theorem, a theoretical result on equilibrium behavior in two-person, zero-sum games. Von Neumann was the first to prove this theorem, in a paper published in 1928. However his proof followed on the heels of notes by Borel establishing the result for three-strategy and five-strategy games. The ensuing debate as to which of these two mathematical giants had the rightful claim as "the inventor" of game theory was to turn nasty