James M. Enelow

The spatial theory of voting: an introduction.

Preface 1. Spatial voting models: the behavioural assumptions 2. The unidimensional spatial voting model 3. A two-dimensional spatial model 4. A general spatial model of candidate competition 5. The influence of candidate characteristics and abstention on election outcomes 6. Voting on budgets 7. Models of voter uncertainty 8. Institutions 9. Empirical testing of the spatial theory of elections 10. Concluding observations References Answers to selected problems Index.

A New Approach to Voter Uncertainty in the Downsian Spatial Model

A new model of voter uncertainty about candidate positions is presented in which voters simplify the issue positions of the candidate by representing them as a random variable on an underlying evaluative dimension. It is further assumed that the degree of voter uncertainty depends upon the mean location of this random variable. It is demonstrated that this type of spatially dependent uncertainty results in a shift of each voters ideal point on the underlying dimension. We discuss two types of shifts, one in which voter ideal points are shifted toward the extremes and the other in which they are shifted toward the center and comment on the consequences of these shifts for two-candidate electoral competition. Finally, we relate our model to earlier work on the subject by Downs (1957) and Shepsle (1972).

Nonspatial Candidate Characteristics and Electoral Competition

BASIC TO MODELS of electoral competition is the assumption that candidates adopt positions on policy issues as a means of attracting votes. However, candidates are also judged on the basis of human qualities and other attributes not related to the policies they espouse in a campaign. The spatial theory of electoral competition has, in the past, treated such attributes as part of the policy space over which candidates compete. However, certain difficulties attend such an interpretation. For example, it is difficult to view a candidates personality as something which can be altered to please the voters. The mistakes that an incumbent has committed in office are not things he can erase to compete more effectively for votes. A candidates religion cannot be abandoned because it is a political liability. In short, there are nonspatial attributes that affect voter evaluations of each candidate, which are beyond that candidates immediate control. It is the purpose of this paper to incorporate these nonspatial attributes into the spatial model of electoral competition to show how the policy outcome of two candidate electoral competition is af-

A general probabilistic spatial theory of elections

In this paper, we construct a general probabilistic spatial theory of elections and examine sufficient conditions for equilibrium in two-candidate contests with expected vote-maximizing candidates. Given strict concavity of the candidate objective function, a unique equilibrium exists and the candidates adopt the same set of policy positions. Prospective uncertainty, reduced policy salience, degree of concavity of voter utility functions, some degree of centrality in the feasible set of policy locations, and restrictions on the dimensionality of the policy space are all stabilizing factors in two-candidate elections.

Ideology, Issues, and the Spatial Theory of Elections

The purpose of this article is to explore the connection between ideology and issues in the minds of voters and the relationship between this connection and the electoral prospects of candidates engaged in two-candidate competition. Toward this end we examine the effects on electoral competition of either magnifying or collapsing the expected policy difference that voters associate with a fixed ideological difference. We find that magnifying this difference aids the incumbent, whereas collapsing it aids the challenger. We go on to point out how this second result provides an explanation for the electoral appeal of extremist candidates and an important insight into the question of state stability. The connection between political issues and ideology in the spatial theory of electoral competition is explored in this article. In a recent publication, Hinich and Pollard (1981) develop a model of elections in which voters estimate a candidates positions on a set of campaign issues on the basis of the candidates position on an underlying predictive dimension. Assuming this predictive dimension to be political ideology, each candidate is known to the voters by an ideological label, which denotes his position on this underlying pre

Probabilistic Voting and the Importance of Centrist Ideologies in Democratic Elections

This study indicates that a probabilistic voting model allowing voters to abstain from alienation or indifference leads to a transitive ordering over candidate ideologies. Further, a weighted form of the mean most preferred ideology of the voters is the optimal ideology for both candidates in a two-candidate election. Centrist ideologies are attractive to the major parties in a two-party system, and probabilistic voting provides an important part of the explanation.

Voting One Issue at a Time: The Question of Voter Forecasts

When issues (i.e., dimensions) are voted on one at a time, a voter whose preferences are not separable across issues must forecast the outcome of later issues in order to know how to vote in the present. This is the problem of expectations. In this article, we develop a general theory designed to handle this problem. Assuming that voters are risk averse and maximize expected utility, we demonstrate that a random variable forecast of how later issues will be decided reduces to a point forecast, which is the mean of the multidimensional random variable. We also show that single-peaked preferences are induced on each issue, and consequently there exists an equilibrium across issues.

An Empirical Evaluation of Alternative Spatial Models of Elections

In Enelow and Hinich (1982, 1984a), the spatial theory of elections is augmented to incorporate nonspatial candidate characteristics in the voters candidate evaluations. In this extension, nonpolicy characteristics are represented by an additive term independent of the policy portion of the voters evaluation. In Grofman (1985), an interactive voting model is introduced, in which nonpolicy characteristics affect the voters evaluation of the candidate only through the candidates policy positions. An empirical question is raised by these two contrasting approaches: do nonpolicy candidate qualities affect voter choice independently of candidate policies, interactively with candidate policies, or through both means? This paper is designed to answer that question. An extended form of the Enelow-Hinich model is specified with both main and interaction terms. The model is then used to predict voter choice in the 1972, 1976, and 1980 presidential elections. Statistical evidence for the existence of interaction effects is present in each election. But the importance of these effects for predicting voter choice is statistically nonsignificant. The simple additive Enelow-Hinich model is unsurpassed by an expanded form of the model with interaction effects or by Grofmans interactive model which excludes main effects, and is usually better than two simpler models that exclude either policy or nonpolicy variables.

A Comparison of Two Distance Metrics Through Regression Diagnostics of a Model of Relative Candidate Evaluation

Regression analysis is widely used to estimate the effects of relative policy proximity on relative candidate evaluations. Using the 1984 NES data, we show that the functional form for specifying distance between voter and candidate can lead to different results concerning which policy variables significantly affect relative candidate evaluations. Simple statistics do not allow us to choose the distance specification most consistent with least-squares assumptions. A series of diagnostic tests are offered to make this determination.

Voter Expectations in Multi-Stage Voting Systems: An Equilibrium Result

Recent work by Shepsle (1979) on structure-induced equilibrium has been challenged by Denzau and Mackay (1981), who show that voter expectations about the outcome of future votes can upset the stability induced by voting on issues one at a time. We show that under a politically informed model of voter expecations, risk aversion on each issue is necessary and sufficient for equilibrium under all voter forecasts when issues are voted on one at a time. This result gives an important insight into the role played by risk aversion in ensuring stability in real world voting systems.