Nash equilibrium strategies in directional models of two- candidate spatial competition

The standard approach to two-party political competition in a multi-dimensional issue space models voters as voting for the alternative that is located closest to their own most preferred location. Another approach to understanding voter choice is based on preferred direction of change with respect to some specified neutral point (e.g., an origin or status quo point). For the two-dimensional Matthews directional model (Matthews, 1979), we provide geometric conditions in terms of the number of medians through the neutral point for there to be a Condorcet (undominated) direction. In this two-dimensional setting, the set of residual locations for which no Condorcet directions exist is identical to the null dual set (Schofield, 1978) and to the heart (Schofield, 1993). In two dimensions, for most locations of the origin/status quo point, a Condorcet direction exists and points toward the yolk, a geometric construct first identified by McKelvey (1986). We also provide some simulation results on the size of the null dual set in two dimensions when the underlying distribution of points is non-symmetric.     

The impact of scandal on candidate evaluations: An experimental test of the role of candidate traits

Correlational studies have found candidate traits to be an important determinant of vote preferences but cannot rule out reverse causality processes in explaining these findings. The present study demonstrates the independent impact of trait inferences on candidate evaluations using experimentally controlled candidate profiles of hypothetical U.S. congressmen. Using the scandal situation as a testing ground, this experiment examines whether task-relevant, competence traits actually have greater impact on political judgments than the more general, warmth-related trait qualities. Two types of scandals are considered (marital infidelity and tax evasion), both implying negative trustworthiness characteristics of the officeholder. Results demonstrate that trait inferences do have a causal impact on global evaluations. Consistent with past survey studies, competence qualities appear to be more important than warmth qualities but only for those with greater political information levels.     

A model of candidate location with endogenous valence

This work gives a theoretical explanation for the increase in campaign spending and party polarization in U.S. politics. I assume that the effectiveness of persuasive advertising, and of costly valence campaigning in general, positively depends on the share of nonpartisan voters. A decline in the number of partisan voters in a constituency results in greater campaign spending by the candidates. If the voters are risk-averse, the candidates who maximize their expected office rents minus the cost of campaigning will choose divergent policy platforms strategically in order to reduce the costs of subsequent campaign spending. The degree of policy divergence positively depends on the share of nonpartisan voters for a broad class of voter disutility and candidate cost of valence functions.     

A technique for estimating candidate and voter locations

This paper develops a simple technique for locating voters and candidates in two-party US elections. Such a procedure is attractive because it overcomes the limitations of existing techniques that fail to place incumbents, challengers, and constituents on the same scale. The method is demonstrated using data from the 1988 presidential and congressional elections. The new data are then used to reevaluate spatial theories of candidate competition.     

Voter turnout and candidate choice: A merged theory

An alternative approach to the explanation of voting behavior is offered, suggesting that the starting point of electoral decision making is individuals' recall of their behavior in the last similar situation. Whether or not this recall is accurate is irrelevant in our model, since the voters' reasoning proceeds from their belief about their earlier behavior, whether or not it is correct. Using this approach we are able to treat voting from a unified perspective, rather than adopting the current stance of treating the turnout decision as separate from and preceding the candidate choice decision.     

Black-box models of candidate evaluation

All contemporary models of candidate evaluation are memory-based models in that they treat the direction and strength of evaluation as a function of the mix of positively and negatively valued (valenced) information retrieved from memory. Yet, oddly enough, despite the assumption that memory mediates judgment, none of the major models looks at the processes involved in what information voters recall and how that evidence was integrated into a summary evaluation. In this sense then, political science models of vote choice are black-box models: They are silent about how voters actually go about interpreting information and integrating the evidence into a summary evaluation of the candidates. In this article we critique the major political science models, call attention to the implicit assumptions they make about what evidence is assumed to be in memory, and conclude with an argument for introducing process into our explanations of vote choice.     

Ideology and candidate evaluation

How does the expressed political ideology of voters influence their evaluation of presidential candidates? The classic answer to this question is provided by the spatial theory of electoral choice in which utility for a candidate is a function of the proximity between the voter and candidate positions on the liberal-conservative continuum. We have argued elsewhere that spatial theory, while intellectually appealing, is inadequate as an empirical model of mass behavior. We have developed a directional theory of issue voting that we believe provides a more realistic accounting of how specific policy issues influence utility for a candidate. Directional theory is based on the view that for most voters issues are understood as a dichotomous choice between two alternative positions. While ideology is widely understood as a continuum of positions, the directional model can be applied to the relationship between ideology and candidate evaluation. In this paper we compare the two theories using National Election Study data from 1972 to 1988. The results tend to favor the directional model over the traditional proximity model. We conclude by briefly tracing out the implications of this finding.     

A dynamic test of the marginality hypothesis

The marginality hypothesis is an attempt to relate the voting margins of members of Congress to their subsequent legislative behavior. A major corollary of the hypothesis is that members of Congress with small victory margins will be more responsive to constituents than those with large victory margins. This has been assumed to mean that electorally secure representatives can afford to be more loyal to their congressional parties, since they have less cause to worry about their chances for reelection. Previous empirical studies have produced mixed results. We ask the question in a different way: Do changes in marginality affect party voting within Congress? If so, major shifts in the electorate potentially can have a fundamental impact on the behavior of Congress itself. We find that this is not true. Electoral margin is simply not related to party loyalty.     

Political evocation and styles of candidate evaluation

Recent work in cognitive processing and individual decision making has emphasized that individuals vary in the criteria they bring to bear to evaluate political objects. In this paper we argue that individual differences are but one piece of the decision-making puzzle, and that environmental factors are also important. Of particular interest to us is the idea that different candidates evoke different evaluative criteria. Using data from a 1984 sample of undergraduates and the 1980 National Election Study, we find evidence that political evocation effects do exist. This result has implications for understanding both the decision calculus of individuals and the collective rationality of the electorate.     

Democracy as an equilibrium

Observation shows that while democracy is fragile in poor countries, it is impregnable in developed ones. To explain this pattern, I develop a model in which political parties propose redistributions of incomes, observe the result of an election, and decide whether to comply with the outcome or to launch a struggle for dictatorship. Democracy prevails in developed societies because too much is at stake in turning against it. More income can be redistributed in developed than in poor countries without threatening democracy. Limits on redistribution arise endogenously, so that constitutions are not necessary for democracy to endure. A democratic culture characterizes the equilibrium.     

Third parties in equilibrium

Under standard assumptions equilibria with three parties normally do not exist in spatial models of electoral competition. In this paper I show that such equilibria are possible if it is assumed that voters are uncertain about the exact policies parties will adopt once elected. Substantive predictions can be derived from the model, explaining some features of three-party competition. First, the least risk party will always take the most moderate position. Second, this position is also winning. Third, the two riskier parties are always on opposite sides of the median voter and also of the moderate party.     

Bicameralism and majoritarian equilibrium

Recent papers have established that bicameralism can support a non-empty core in majority voting games in two dimensional policy spaces. We generalise this result to the n-dimensional case, and provide a discussion of multi-cameralism. Bicameralism generates a core of potentially stable equilibria by institutionalising opposition between mutually oriented median voters, this provides a clear link with the standard median voter model and with more traditional analyses of bicameralism.An earlier version of this paper (Brennan and Hamlin, 1990), written in ignorance of the work of Hammond and Miller (1987, 1990), benefited from comments at the Public Choice Society meetings, Tucson; the European Public Choice Society meetings, Meersburg; the Center for Study of Public Choice, and the Universities of Chicago and Oxford. Hamlin is grateful for the support of visiting fellowships at ANU and All Souls College, Oxford.