The spatial theory of voting continues to be a growth industry in political science. From its modest beginnings in the papers of Hotelling (1929) and Smithies (1941), through the pioneer work of Black (1948, 1958) and Downs (1957) and the early work of Davis and Hinich (1966), spatial voting theory has mushroomed to the point where it can now be broken down into subfields, such as agenda theory and probabilistic election theory. While this growth is a healthy sign, it has made it difficult for the outside observer to obtain a good grasp of recent developments and areas of current research interest. This volume of eight essays by recognized scholars is intended to provide just such an overview of important topics in the spatial theory of voting. These essays are specially written for this book and have never before appeared in print.

It is useful to divide the spatial theory of voting into the spatial theory of committees and the spatial theory of elections. Duncan Black originally analyzed these two social choice problems with a single model, but these two areas of spatial theory are now quite distinct. In the spatial theory of committees, the voters are the key actors, voting over different policy alternatives, each of which is usually represented as a point in a Euclidean space. In contrast, the spatial theory of elections treats the candidates as the key actors, with the voters playing a fixed role. Results in the spatial theory of elections have analogues in the spatial theory of committees.

Enelow and Hinich (1990) have made it clear that the spatial theory of voting encompasses a large number of alternative models of committees and elections and deals with a large number of questions about these models. This particular essay is concerned with an important topic in the spatial theory of voting that has been addressed in a number of different references in the literature: the implications (for two-candidate elections) of candidate uncertainty about whom the individual voters in the electorate will vote for. More specifically, this chapter will concentrate on what has been learned about the implications of the presence of this type of uncertainty for the existence and location of an electoral equilibrium.

Spatial voting theorists have become interested in the implications of candidate uncertainty about voters' choices primarily because there are good empirical reasons for believing that actual candidates often are uncertain about the choices that voters are going to make on election day. First, candidates tend to rely on polls for information about how voters will vote, but “information from public opinion surveys is not error-free and is best represented as statistical” (Ordeshook 1986, p. 179). Second, even when economists and political scientists have developed sophisticated statistical models of voters' choices and have used appropriate data sets to estimate them, there has consistently been a residual amount of unexplained variation (see, for instance, Fiorina 1981; Enelow and Hinich 1984a, chap. 9; Enelow, Hinich, and Mendell 1986).

Introduction

Adam Smith began his Wealth of Nations with an examination of the internal works of a pin factory, but he soon turned his attention to other things: the coordination of a market system and the economics of growth and development. For more than a century and a half following the publication of Smith's masterpiece, the nature and internal organization of the firm received little attention in mainstream economic theory. At the same time the firm grew in size and complexity. McNulty (1984) describes how preoccupation with certain themes – with the macroeconomic distribution of income among rent, wages, and interest, or the logic of the competitive model and decentralized allocation of resources – pushed aside issues related to the firm and its internal organization:

Neoinstitutional Economics and the theory of production and exchange

We are concerned in this book with recent attempts to extend and generalize the theory of price and apply it to economic and political institutions. Our focus is on a certain propensity in human nature, which Adam Smith pointed out – “the propensity to truck, barter, and exchange one thing for another” – and on the consequences of these activities for the use of scarce resources and the creation of wealth.

The economic outcomes of production depend in an important way on the social and political rules that govern economic activity and society in general. In his pioneering contribution to economics, Adam Smith sought to demonstrate how one specific set of rules contributes more to the wealth of nations than any other. The structure that Adam Smith recommended was one whereby individuals have exclusive private rights to economic assets.

In the more than 200 years following Adam Smith's contribution, the mainstream of research in economics has involved primarily an examination of a single set of idealized rules governing market exchange. In spite of this simplification, the approach has been fruitful: In terms of both analytical power and empirical relevance it overshadows all other theoretical systems in economics and the social sciences. The theory of price (microeconomic theory) has provided valuable insights into the fundamental nature of exchange and resource allocation in decentralized markets and also tools that enable us to predict how equilibrium outcomes are affected by changes in the constraints that individual decision makers face.

ABSTRACT

The Euclidean representation of political issues and alternative outcomes, and the associated representation of preferences as quasiconcave utility functions, is by now a staple of formal models of committees and elections. This theoretical development, moreover, is accompanied by a considerable body of experimental research. We can view that research in two ways: as a test of the basic propositions about equilibria in specific institutional settings, and as an attempt to gain insights into those aspects of political processes that are poorly understood or imperfectly modeled, such as the robustness of theoretical results with respect to procedural details and bargaining environments. This essay reviews that research so that we can gain some sense of its overall import.

A considerable body of political theory represents alternative outcomes or policies by a subset of n-dimensional Euclidean space, and assumes that we can represent individual preferences over these outcomes by quasiconcave utility functions with internal satiation points. By imposing this particular structure on alternatives and preferences, we can deduce a variety of substantively informative results, such as the Median Voter Theorem in elections, and the generic emptiness of cores in cooperative political games (cf. Plott 1967, Schofield 1983). Correspondingly, the special case of Euclidean preferences, introduced by Davis and Hinich (1966, 1968), form the basis for the most extensively developed models of two general classes of political institutions – elections and committees.

Political processes that involve voting are invariably subject to an element of agenda control. Predictions about the outcomes of these processes can be made only if we specify (a) the preferences of the agenda setters, (b) the preferences of the voters, (c) institutional constraints on the process—the rules of the game, (d) the behavioral rules used by voters (are they sincere-myopic or sophisticated—forward looking), and (e) the information structure of the game.

What has come to be known as the monopoly model or setter model (Romer and Rosenthal 1978, 1979a) puts enormous, restrictive structure on the political process. In this essay, I limit the discussion to this model and its extensions. The first part of the essay analyzes the case of a single issue (a budget) under complete (and perfect) information. Dynamic as well as static analysis is covered. The second part treats effects of both simple uncertainty and strategic uncertainty that allows for learning. The third part summarizes empirical evidence that bears on the model. The essay contains some new work on the dynamics of agenda setting with sophisticated voters in a complete information environment and on learning by agenda setters under incomplete information; the basic thrust, however, is directed at providing a review.

THE SETTER MODEL WITH COMPLETE INFORMATION

The setter model was developed in the context of budgeting decisions. Motivated by Niskanen (1971), Romer and Rosenthal made several simplifying assumptions. First, the agenda setter was assumed to be an individual whose goal is to maximize the total budget. Second, voter preferences were single-peaked over budget levels. Single-peaked preferences for three voters are illustrated in Figure 9.1. The top of a voter's curve represents the voter's ideal point.

Introduction

The state can affect the net wealth of a community by redefining the structure of property rights, and by providing public goods, such as standardized weights and measures, which reduce the costs of transacting. Neoinstitutional Economics suggests that the rules of the game, which in part are controlled by the state, have a fundamental role in determining whether an economy enters a path of growth and development or stagnation and decline. But why should any government lay down rules that retard the economy? Although little can be said a priori about the utility function of those who control the state, it is unreasonable to assume that, other things being equal, they either prefer or are indifferent to economic decline in their country. This conclusion should be independent of our model of the state, be it one assuming a contract state or a predatory state. For example, a ruler of a predatory state who seeks to maximize her wealth by taxing her subjects, will, other things being equal, attempt to maximize the tax base, the national income. An increase in the national income due to more clearly defined property rights and less dissipation of rent should be welcomed by both subjects and ruler, as it can be used to augment both tax revenues and general living standards.

What are the moving parts in the spatial model of politics?

The formal theorems about equilibrium reveal nothing about moving parts. Black's median voter theorem simply identifies the equilibrium, given single-peaked utility curves, as the ideal point of the median voter (Black 1948, 1958). Plott's multidimensional extension of this theorem identifies the equilibrium, given convex utility curves, as the ideal point of the voter at the multidimensional median (Plott 1967). These fundamental facts require no moving parts, mainly because they describe outcomes from the black box, not the processes that go on inside it.

But if one wishes to get inside the black box to describe how the process moves toward equilibrium (or not, as the case may be), then it is necessary to assume something about the moving parts. In Downs's informal model of spatial competition, the candidates or parties position and reposition themselves, converging to the ideal of the median voter (Downs 1957). In McKelvey's agenda theorem, the agenda-controller moves motions in a trajectory toward his or her goal (McKelvey 1976, 1979). Something similar, but less well directed, occurs in Kramer's model of convergence to the minmax set (Kramer 1977). In the recent modifications of McKelvey's model (Ferejohn, McKelvey, and Packel 1984), as also in the models of Feld and Grofman (1988), the trajectories are confined to a central portion of the space, but still it is the motions that vary, not the voters.

Positive theories of the state

Positive theories of the state hold a central role in Neoinstitutional Economics because the state sets and enforces the fundamental rules that govern exchange. The enforcement of property rights depends on power, and economies of scale in the use of violence frequently give a single agent – the state – a monopoly over the legitimate use of violence. But the relationship between property rights and political structures is complex, and exclusive property rights are consistent with a range of alternative power structures. Consider the following three arrangements:

1. A community where there are no legislative or judicial bodies, no enforcement agencies, and no common rules

2. A society where there are common rules that specify exclusive rights, a law-making body, courts of law, but no police force or army and hence private enforcement of law

3. A community where the state sets the rules, arbitrates in disputes, and enforces exclusive rights

We would be surprised to find case 1, the private enforcement of private rules, in communities where productive assets such as land are scarce, where people live together in groups, practice the division of labor, and trade among themselves. In order to protect private property under case 1, a large share of the resources of each household would have to be allocated to the private protection of life, limb, and nonhuman assets and to efforts at forming coalitions with other individuals.

The classical spatial model, first formulated by Hotelling (1929), focused on competition between two agents (interpreted either as business firms or political parties). Although competition between more than two agents was considered soon thereafter (for example, Chamberlain 1933), only in the last decade or so has sustained attention been paid to the multiagent case. This essay surveys the results of this attention, especially as regards competition between political parties or candidates for political office.

Broadly speaking, the literature divides into two streams: those works analyzing multi-item agendas, and those works dealing with elections in which more than two candidates or parties are competing. I shall focus on the second topic: models of multicandidate (or multiparty) electoral competition.

An increasingly important distinction among such models is that some models attempt to endogenize the number of candidates, letting the model predict what the equilibrium number should be, while others take the number of competitors as exogeneously given. In other words, some models allow entry, while others do not. Because Chapter 2 by Shepsle and Cohen covers the question of entry, I shall focus here on no-entry models. Such models are of course necessary parts of the more elaborate entry models, but they are also of interest on their own: The no-entry assumption accurately describes the situation of candidates in a race after the filing deadline (for getting names onto the ballot) has passed. It is true that the possibility of write-in campaigns exists, but it is also true that such campaigns are usually of negligible importance. No-entry models should therefore be useful in investigating the incentives of candidates in the post-filing stage of the campaign.

INTRODUCTION

In An Economic Theory of Democracy, Anthony Downs characterized a political party as a team whose goal is to win the election. Although such an assumption concerning political parties is a reasonable first step, it is open to two important criticisms. The party may not be a team, and the goal of the party leaders may not be to win the election. Consider the latter criticism. It would be strange if the voters were interested in policy and not the members of the political party, especially so because government policy is a public good shared by all. Even if candidates were interested only in winning, the need to win election primaries would force the candidates to adopt positions more in line with the concerns of the median voter of the political party (or, more generally, of their constituencies). Since the party's median voter wants to maximize his/her expected utility from the election outcome, the political party's candidate would then adopt a position that maximized the party's median voter's expected utility from policy outcome. Treating the political party as a team also ignores the principal/agent problems that arise when monitoring is imperfect or when agreements are not completely enforceable. The winning candidate might enact policies that are more consistent with his/her own desires than those of the voters. In a nutshell, winning may be a means to enact policy, rather than policy being a means toward winning.

Here, we will assume that candidates maximize expected policy implementation. This approach not only has more realistic assumptions but, as will be shown in the following pages, also has a much richer set of empirical predictions.