Conceptualizing voter choice for directional and discounting models of two-candidate spatial competition in terms of shadow candidates

In contrast to the traditional modeling of voter choice based on proximity, under directional models, selection of candidates is based on the direction and/or intensity of change from a status quo or neutral point. Voter choice can also be modeled as representing both approaches, e.g., as a directional model with proximity restraint, or alternatively, in terms of proximity to discounted positions. We provide a unified perspective for these seemingly disparate models in terms of what we call “shadow” positions. We demonstrate that voter choice in a variety of spatial models including directional components can be viewed as proximity-based choices. Voters choose the candidate whose shadow is nearer, where shadow locations are defined by a simple transformation. We apply this approach to equilibrium analysis, showing that results for a discounted proximity model can be carried over – via shadows – to a variety of directional models.     

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.     

Issues,the Spatial Theory of Voting,and British General Elections: A Comparison of Proximity and Directional Models

Competing spatial models of voter choiceare compared in the context ofparliamentary representatives selectedthrough single-member district, pluralityelections where party platforms areemphasized over individual candidates.Respondents of the 1987, 1992, and 1997British general election surveys ratepolitical parties on a series of issuescales. Ordered logistic regressions ofparty evaluations under proximity,directional, and mixed models reveal thatthe classic spatial model and thedirectional model perform equally well.Differences center on perceptions of thestatus quo, as voters appear to evaluatethe incumbent party (here, theConservatives) slightly differently thanminority parties (Labour and the LiberalDemocrats). The proximity model worksbetter for voter evaluations of governingparties while the directional model workswell for opposition parties.     

How I learned to stop worrying and love polarization

This paper presents theoretical and experimental evidence of increased voter satisfaction due to moderate candidate platform divergence. The formal model combines the traditional proximity treatment of voter satisfaction with a disutility stemming from the likelihood of “incorrect” voter decision-making. The result is a voter utility function for the candidate field which is non-monotonic in platform divergence. I confirm the main result of the formal model through a voter survey where hypothetical candidate positions were varied from very moderate to very partisan. Respondents preferred moderate policy divergence to both minimal and extreme divergence. In tandem, these results recast moderate ideological differentiation as a desirable, rather than pejorative, element of politics and campaigning.     

Party policy equilibrium for alternative spatial voting models: An application to the Norwegian storting

In recent years a lively debate has emerged concerning the empirical status of the traditional proximity spatial model versus a directional model of voter choice. The central reason for this scholarly interest concerns these models' contrasting implications for parties' policy positioning, with the directional model motivating parties to present extreme policies, but the proximity model promoting centrist positions. To this point, however, there exist no studies that compute parties' optimal strategies in historical elections, for these competing models. This article addresses this issue, by examining party policy strategies in a multiparty electorate for three different vote models: (a) the proximity model, (b) a directional model (c) a mixed model which combines proximity and directional components. Each model incorporates past voting history and the random effects of unmeasured variables. Using parameter estimates derived from analyses of survey data from the 1989 Norwegian Election Study we compute — for each of these vote models — the configuration of party policy positions that maximize each party's vote share in relation to those of the other parties. We find that for each model, such a vote–maximizing configuration exists, but — for the proximity model — represents an unrealistic, tightly clustered array. A mixed proximity–directional model, however, provides by far the most convincing account of parties' actual policy strategies with regard to dispersion and vote share.     

Party policy equilibrium for alternative spatial voting models: An application to the Norwegian Storting

Abstract In recent years a lively debate has emerged concerning the empirical status of the traditional proximity spatial model versus a directional model of voter choice. The central reason for this scholarly interest concerns these models' contrasting implications for parties' policy positioning, with the directional model motivating parties to present extreme policies, but the proximity model promoting centrist positions. To this point, however, there exist no studies that compute parties' optimal strategies in historical elections, for these competing models. This article addresses this issue, by examining party policy strategies in a multiparty electorate for three different vote models: (a) the proximity model, (b) a directional model (c) a mixed model which combines proximity and directional components. Each model incorporates past voting history and the random effects of unmeasured variables. Using parameter estimates derived from analyses of survey data from the 1989 Norwegian Election Study we compute — for each of these vote models — the configuration of party policy positions that maximize each party's vote share in relation to those of the other parties. We find that for each model, such a vote–maximizing configuration exists, but — for the proximity model — represents an unrealistic, tightly clustered array. A mixed proximity–directional model, however, provides by far the most convincing account of parties' actual policy strategies with regard to dispersion and vote share.     

A directional model of candidate evaluations in the 2016 presidential election

The 2016 U.S. presidential election provides an interesting setting for testing the directional theory of issue voting. But, when modeled using the standard approach, using the seven-point issue scales in the 2016 ANES, it is not clear whether the directional model provides any additional leverage over the more traditional proximity model. In order to get around this impasse, I examine candidate evaluations rather than issue scales. Doing so enables a direct test of directional theory against proximity theory. The empirical results show that the proximity model does not outperform the directional model. Instead, the latter outperforms the former because the directional model produces not only a succinct graphical representation of the electorate's candidate evaluations but also an explanation for the relative spatial positions of the candidates.     

No Evidence on Directional vs. Proximity Voting

The directional and proximity models offer dramatically differenttheories for how voters make decisions and fundamentally divergentviews of the supposed microfoundations on which vast bodiesof literature in theoretical rational choice and empirical politicalbehavior have been built. We demonstrate here that the empiricaltests in the large and growing body of literature on this subjectamount to theoretical debates about which statistical assumptionis right. The key statistical assumptions have not been empiricallytested and, indeed, turn out to be effectively untestable withexisting methods and data. Unfortunately, these assumptionsare also crucial since changing them leads to different conclusionsabout voter decision processes.     

Systemic polarisation and spatial voting

The controversy between proximity and directional models of issue voting has not been settled. Instead of appointing an ultimate winner, this article explores the conditioning impact of the level of systemic polarisation and provides evidence that proximity is a more relevant determinant of voter behaviour in less polarised systems, whereas there is a centrifugal and directional dynamic in more polarised contexts. By so doing, the article shows how a largely forgotten notion – namely Sartori's idea of the spatial elasticity of the political spectrum – leads to different spatial viewpoints. In distinguishing between party (supply side) and voter (demand side) polarisation, this framework provides a comprehensive picture about the conditions that turn a centripetal electoral dynamic into a purely centrifugal one.     

Voter Choice in the 1995 French Presidential Election

This study estimates a model of voter choice for the first and second ballots of the 1995 French Presidential election. Its objective is to characterize the relative importance of traditional bases of French voter choice such as social class relative to campaign issues and voter evaluations of the economy. The study also seeks to identify candidate-specific bases of voter choice. Multinomial logit analysis of voter choice among the four leading candidates reveals a stronger role for campaign issues than previous studies suggest. Voter-candidate ideological proximity is the strongest predictor of first and second ballot choice, followed by voter perceptions of candidate ability to address unemployment and political corruption. Demographic variables have limited explanatory power in both the first and second ballot models. The parameter estimates demonstrate considerable differences in the bases of voter choice across candidates, with the bases of voter choice for National Front leader Jean-Marie le Pen most distinct from those of the remaining candidates.     

Equilibrium in multicandidate probabilistic spatial voting

This paper presents a multicandidate spatial model of probabilistic voting in which voter utility functions contain a random element specific to each candidate. The model assumes no abstentions, sincere voting, and the maximization of expected vote by each candidate. We derive a sufficient condition for concavity of the candidate expected vote function with which the existence of equilibrium is related to the degree of voter uncertainty. We show that, under concavity, convergent equilibrium exists at a “minimum-sum point” at which total distances from all voter ideal points are minimized. We then discuss the location of convergent equilibrium for various measures of distance. In our examples, computer analysis indicates that non-convergent equilibria are only locally stable and disappear as voter uncertainty increases.     

Why candidate divergence should be expected to be just as great (or even greater) in competitive seats as in non-competitive ones

Basic Downsian theory predicts candidate convergence toward the views of the median voter in two-candidate elections. Common journalistic wisdom, moreover, leads us to expect these centripetal pressures to be strongest when elections are expected to be close. Yet, the available evidence from the US Congress disconfirms this prediction. To explain this counterintuitive result, we develop a spatial model that allows us to understand the complex interactions of political competition, partisan loyalties, and incentives for voter turnout that can lead office-seeking candidates, especially candidates in close elections, to emphasize policy appeals to their voter base rather than courting the median voter.     

Specification Issues in Proximity Models of Candidate Evaluation (with Issue Importance)

Bryce E. Corrigan Department of Political Science, University of Michigan, 5700 Haven Hall, 505 S. State Street, Ann Arbor, MI 48109-1045 e-mail: becorrig{at}umich.edu e-mail: grynaviski{at}uchicago.edu (corresponding author) The use of the proximity model to represent the relationshipbetween citizens' policy attitudes and the positions of candidateson the issues of the day has considerable appeal because itoffers a bridge between theoretical models of political behaviorand empirical work. However, there is little consensus amongapplied researchers about the appropriate representation ofvoter behavior with respect to the measurement of issue distance,candidate location, or whether to allow heterogeneity in theweight that each individual places on particular issues. Eachof these choices suggests a different, and reasonably complicated,nonlinear relationship between voter utility and candidate andvoter issue positions which may have a meaningful influenceon the substantive conclusions drawn by the researcher. Yet,little attention has been given to the best way to representthe proximity model in applied work. The purpose of this paperis to identify which forms of the proximity model work best,with particular consideration given to the identification offunctional forms that are invariant to the choice of scale forthe independent variables.     

Keeping the other candidate guessing: Electoral competition when preferences are private information

We analyze a, model of two candidate competition in which candidate and voter preferences are private information. If candidates simultaneously commit to policy platforms the uncertainty about candidate preferences reinforces the incentive for platform divergence. After a candidate observes the other candidate’s stance but before she learns about voter preferences she may face regret about her choice. This ex post irrationality suggests that a 1 period model may not capture the relevant incentives. In a multi-period proposal game in which candidates first make non-binding public proposals and then they make binding public proposals (similar to Ledyard, 1989) we find that candidates are uninformative during the first stage, as they have a disincentive to reveal their preferences to the opposing candidate. This finding offers an explanation for candidate ambiguity or inconsistency early in an election which does not involve efforts to deceive voters. Candidates may be trying to keep their opponent guessing. With a strong pre-election commitment technology, candidates can only be deterred from this type of behavior if they anticipate that a sizeable number of voters (more than a majority) will vote contrary to their preferences over policy.     

Distant allies and proximate enemies in issue voting: Myth or reality?

The purpose of this paper is to offer an explanation as to why Euclidean distance serves as a reasonably good approximation of reality when it does not incorporate explicity a consideration of the sides of the issue taken by the voter and candidate. The empirical evidence indicates quite clearly that Euclidean distance and side of issue are extremely highly correlated. Two general classes of explanation are offered. First, this powerful association can be seen as a function of the mathematical difficulty of actually being in close proximity to a preferred party while being on the opposite side of an issue on a 7-point scale. Second, even after this mathematical artifact is taken into account, the combined effects of assimilation, contrast, and negativity may bring favored candidates closer to the voter and drive the opposition further away, resulting in a strong correlation of Euclidean distance and side of the issue.     

The distorting effects of racial animus on proximity voting in the 2016 elections

While the use of racial appeals by the 2016 Trump campaign is indisputable, researchers are actively debating their precise role in influencing voter behavior in the election. We seek to expand upon existing research which finds that racial animus electorally benefited the Trump campaign. We examine to what extent those benefits also materialized for GOP candidates down-ballot and whether racial animus distorted ideological proximity voting in the 2016 election. We find that racial animus among voters helped Republicans at multiple ballot levels and that higher levels of racial animus distorted spatial voting among voters ideologically closest to the Democratic candidate.     

The proximity and the directional theories of issue voting: Comparative results for the USA and Germany

In several recent studies George Rabinowitz and his co–authors challenge the 'classical' spatial model of issue voting, the proximity model, by introducing a directional model. In this article we examine whether different measurement of perceived issue positions of candidates or parties leads to diverging judgments about the predictive power of the directional model (which is claimed to be empirically superior), as compared to the proximity model, using data from the USA and Germany. The results demonstrate that the measurement preferred by Rabinowitz et al. tends to bias empirical findings in favour of directional theory. If we use a more plausible operational definition of issue positions of candidates and parties the directional model in both countries fails to turn out superior.     

The proximity and the directional theories of issue voting: Comparative results for the USA and Germany

Abstract In several recent studies George Rabinowitz and his co–authors challenge the 'classical' spatial model of issue voting, the proximity model, by introducing a directional model. In this article we examine whether different measurement of perceived issue positions of candidates or parties leads to diverging judgments about the predictive power of the directional model (which is claimed to be empirically superior), as compared to the proximity model, using data from the USA and Germany. The results demonstrate that the measurement preferred by Rabinowitz et al. tends to bias empirical findings in favour of directional theory. If we use a more plausible operational definition of issue positions of candidates and parties the directional model in both countries fails to turn out superior.     

Bestimmungsfaktoren des Wahlverhaltens in Deutschland bei den Bundestagswahlen 1987, 1998 und 2002: Eine Anwendung des Modells von Adams, Merrill und Grofman

According to theories of voting behaviour, a number of factors can influence a voter’s decision. This is, first, the affiliation of a voter to a specific social group. Second, the existence of a subjective closeness to a political party can determine voting behaviour. A third and fourth account focus on the ideological or policy-area specific position of voters and political parties and the problem-solving competence of a political party, respectively. Fifth, voting behaviour could be candidate-driven so that a voter chooses the party that nominates his favorite candidate. Finally, the felt economic situation by the voters could affect their behaviour at the polls. This paper shows that party identification, problem-solving capacity, the belonging to social groups and the preference for a chancellor candidate are decisive factors for the explanation of voting behaviour in Germany. The analysis extends a model developed by Adams, Merrill and Grofman (2005) and uses data from the German national election studies of 1987, 1998 and 2002.