Abstract
Early studies of voting behavior hypothesized that the degree to which an individual was “cross-pressured” might affect how she participates in politics. However, attention to this topic waned before returning in recent years, mainly within the narrower confines of social networks analysis. In an effort to encourage broader consideration of the role of cross-pressures in political behavior, we present a new approach to estimating cross-pressures that (1) is individual-specific, (2) reflects the cumulative cross-pressures faced by an individual from her many intersecting social strata and group memberships, irrespective of the mechanism by which those pressures are experienced, and (3) can be estimated using widely-available data in party systems of any size, thus making it easier to study the effect of cross-pressures cross-nationally and over time. We demonstrate that these estimates are robust to many estimation choices, correspond well to existing measures of cross-pressures, and are correlated with patterns of political engagement and participation predicted by extant theories.
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Notes
Some researchers have attempted to account for cross-pressures in such analyses by using indicators for cross-pressures brought on by specific combinations of demographics (Powell 1976), but this is only feasible for examining a handful of characteristics at a time, and requires substantial a priori assumptions about the cross-pressuredness of various groups.
These groups may be any collection of individuals recognizably defined by a common set of experiences, interests, or goals. With a focus on national politics, we are interested predominantly in larger social groups. These can not only include common demographic groups defined by religion, race, ethnicity, class, education, sex, sexual orientation, region, occupation, age (or generation), but also groups defined by more particular interests or experiences, such as parenthood, marital status, hobby (e.g., hunters, cyclists, gardeners), or possessions (e.g., homeownership, gun owners, stock market investors).
One could expand this categorization to include mass-mediated cues about the majority preferences of the collective social group itself, such as those reported in polls—what Mutz (1998) labels “impersonal influence.”
One’s family members, friends, co-workers, neighbors, and other acquaintances frequently belong to at least some different social groups than oneself. In some cases, a person may have few or no personal contacts with other members of a larger social group to which she belongs.
More detail about each step is provided in the next section, while Fig. A1 in the online appendix provides a graphical display of the algorithm, and Appendix 1 describes the precise steps used for each dataset.
Our models of party preferences exclude other common variables such as ideology. At best, these variables would improve the overall fit of the model yet leave the coefficients on demographics unchanged, but more likely the inclusion of such variables would have a detrimental effect. We do not control for variables such as ideology specifically because group memberships may affect party preferences by way of influencing such attitudinal variables; including these potential mediators would thus obscure rather than clarify the relationships of interest.
We use the term “variance” herein to refer to the variation in respondents’ probabilities of supporting each party, but that term is only used in the general sense. The exact way “variance” is quantified—which may or may not involve the calculation of variance in the statistical sense—is discussed later in the paper.
CP scores arise out of estimates in a predictive model (Step 1). Thus, when using CP scores in subsequent models to explain outcomes, researchers may wish to account for the uncertainty in the Step 1 process that generated the scores (cf. Treier and Jackman 2008). For the analyses that follow, we re-checked the results while accounting for this uncertainty. Specifically we used bootstrapping methods in the Step 1 estimation to compute a distribution of values rather than a single point estimate and then re-estimated the impact of cross-pressures using these CP scores with uncertainty. As one might expect the strength of the predicted relationship between CP scores and participatory outcomes was lessened somewhat, but the changes were modest and did not appreciably alter our confidence in the estimated effects. Researchers are advised to check their own analyses, especially when working with small datasets (e.g., several hundred respondents or less). Table A6 in the online appendix shows the results from a re-analysis of the U.S. data in Table 4 using CP scores with uncertainty.
These questions are most similar to the typology of measurement validation procedures proposed by Adcock and Collier (2001), but given that (as we discussed in the introduction) cross-pressure scores are indirect estimates of cross-pressures rather than direct measurements, their framework only partially matches the needs of this analysis.
We performed these same tests using data from countries that effectively had two, three, four, five, and six major parties, respectively. Our robustness checks yielded similar conclusions across all party system sizes. Given space constraints, we present here the results from a two-party case (U.S.) and a six-party case (Poland) for maximum contrast. The PNES dataset also contains extensive instrumentation not only on demographic characteristics and party preferences, but also on political engagement and participation (relative to, e.g., the CSES dataset).
The precise steps we used to calculate CP scores in each dataset are summarized in Online Appendix 1.
A fuller discussion of the trade-offs between using vote choice and partisanship as the dependent variable in the first regression is available from the authors upon request (cf. Brader and Tucker 2008).
Using party affiliation to study partisan strength (for example) is not as problematic as it may seem at first glance—CP scores use overall patterns rather than any individual’s party preferences, so do not substantially reflect the individual’s actual preference—but avoiding the appearance of potential endogeneity is still preferable if the researcher is indifferent between the two approaches.
We believe demographic variables are reasonable proxies for capturing both the psychological and social forces that may arise from belonging to a particular group. This is not limited to traditional “identity groups” like those defined by ethnicity or religion. For example, individuals can experience political pressures as a result of belonging to income groups (e.g., poor, working class, middle class, wealthy) and employment status groups (e.g., the unemployed, part-time workers). It is possible that, for some groups, the pressures arise more often by social or psychological means rather than both. Perhaps employment status-related pressures are experienced more often psychologically, such as when people think of themselves as part of the group “unemployed” and consider which party is best for people in that category, even though they are not particularly likely to come into regular contact with unemployed friends pressuring them to vote a particular way. In contrast, people in a particular region, like New England, may not spend much time self-consciously considering their political interests as members of that regional group, but, to the extent there is a distinctive political tilt to their region (controlling for other factors), they may experience corresponding political pressures from regular contact with their New English family, friends, neighbors, and co-workers.
The American Voter (Campbell et al. 1960) effected a revolution in the study of voting behavior by arguing for the need to move beyond an exclusive focus on social groups to consider a wide range of attitudes and other psychological predispositions.
If social groups in a particular time and place do not align with parties (cf. Dalton and Wattenberg 2000), this would have several implications: Step 1 regressions would suggest a weak impact of social attributes on party preferences. At Step 2, therefore, the predicted probabilities would converge toward equality across parties, because the model offers little added information to predict how people would vote. This results in lower variance across probabilities and thus higher CP scores. Unlike situations where high CP scores result from strong offsetting group signals, there would be far less differentiation in CP scores across the sample (in theory, converging to a constant) and any such differentiation would be mostly noise. When used to explain some aspect of behavior, this variable—on account of being close to a constant or mostly noise—should have little or no predictive power. One would conclude then that partisan cross-pressures rooted in social groups are playing little role in explaining behavior. In short, one would reach the correct conclusion for that time and place, but it would be a mistake to render a broader judgment about the relevance of cross-pressures generally from such data. How can one tell this situation from one where group-based cross-pressures exist but simply don’t have an effect on behavior? At Step 1, researchers should check to see that (1) some social attributes significantly predict party preferences, and (2) that social attributes jointly make a significant contribution to explaining party preferences (e.g., by examining fit statistics).
To illustrate how these decisions affect subsequent analyses using CP scores, we repeated the analysis of the expected effects of CP scores on political behavior (see below), this time using scores generated from only the “core” set of demographics (omitting country-specific variables such as race, region, religion, etc.) in the U.S. These results—presented in Table A4 of the online appendix—are meant for comparison with Table 4 below, and show that the effects of these “core” CP scores are in the same directions as those of their “best-available” cousins, but of a moderately-diminished magnitude (up to 50 %, in terms of coefficient size). As we would expect, scores generated less precisely are weaker predictors of behavior, but the consistency of the overall pattern across models demonstrates that our measure is not overly reliant on a particular specification or proxying for one or two especially-important demographics.
It is important to note that these expectations about CP scores should be observed on average across the subgroups, so there will still be substantial variation between respondents within each subgroup. In other words, while the average rural and poor respondent will have a higher CP score than the average urban and poor respondent, there should also be many rural poor with low CP scores and many urban poor with high scores. This reflects the limitations of the old pairwise approach to studying cross-pressures.
See Table A1 in the online appendix for results; comparable results for Poland are presented in Table A2. We include gender, age, education, employment status, occupation, income, union membership, race, immigrant (vs. native born), religion, gun ownership, urban residence, and others; the immense sample size of the NAES gives us the luxury of using something closer to a “kitchen sink” approach, employing as broad a range of demographics as possible. Note that Table A2 displays multinomial logit estimates, and therefore one can not judge whether social group membership significantly predicts party preferences from the statistical significance of individual coefficients. If you changed which political party serves as the base reference category, a different set of coefficients may appear as “significant.”
For comparison, Fig. A2 in the online appendix shows the distribution of CP scores in Poland. There is considerable variation in CP scores, though fewer scores in the lower ranges than observed in the U.S. This is a logical consequence of the larger party system, as few Polish voters will find themselves attracted completely, on account of their social attributes, to one party and not at all attracted to the others. Nonetheless, given the parties on offer in 2001, some Poles found themselves much less cross-pressured than others. Making specific predictions for pairwise subgroups, as Lazarsfeld et al. (1944) did in the U.S. two-party system and as we do in Table 3, is not as simple where several parties compete for overlapping constituencies. Even so, the largest Polish parties in 2001 often drew support from voters with a distinctive cluster of social characteristics (see Markowski and Tucker 2010). Both the liberal Civic Platform and communist successor Democratic Left Alliance attracted voters who were young, urban, secular, educated, and financially well off. Anti-system parties such as Self-Defense and the League of Polish Families enjoyed support from older, rural, religious, less educated, and poorer citizens. When we compare voters who match these common profiles to those who do not, we find that the latter have higher CP scores (as expected): secular urban versus religious urban (0.62 vs. 082, p < 0.001), old religious versus young religious (0.79 vs. 0.83, p < 0.001), educated wealthy versus educated poor (0.62 vs. 0.84, p < 0.001). Although we observe similar patterns regardless of the version of CP scores used, the Top 3 version produced sharper distinctions than either the Top 2 or Full CP score versions.
It is worth reiterating that older methods of capturing cross-pressures through the use of dummy variables assume that all people with a particular demographic profile—e.g., evangelical union members—face the same cross pressures. Our method, in contrast, calculates a separate CP score for each individual, reflecting the fact that, for example, the population of evangelical union members still varies in terms of age, region, gender, and so forth.
Median respondents are presented here rather than subgroup means so that we can provide context by identifying these respondents’ locations in the overall distribution of scores.
Figure A3 in the online appendix shows the simple linear relationship between CP scores and each network measure.
Readers should not confuse this measure with calculating an issue-based CP score, which we are not estimating here.
Classifications as pro-Democrat, pro-Republican, or neutral made by authors; see Online Appendix 2.
Figure A4 in the online appendix shows the simple linear relationship between CP scores and each attitudinal conflict measure.
The specifications of each model are thus deliberately simple, only accounting for CP scores, the demographics used to create them, and a few other simple controls. We are not particularly concerned with omitted variable bias because, aside from our primary interest in the basic bivariate relationship, CP scores should be exogenous to most other variables typically included in these predictive models.
Given the incredulously high rate of reported turnout in the NAES, however, one might suspect a stronger relationship were turnout measured more accurately and less like a constant.
To provide additional context for these effect sizes, Table A5 of the online appendix presents comparable estimates for various levels of age, education, and income. We use these three variables because they are widely accepted to be among the most important predictors of participation, and while in most instances the effects of cross-pressure scores are smaller, they are still of a substantial magnitude.
With regard to indifference, the concept of individuals being unable to choose between candidates or parties has actually taken (at least) two forms in the relevant existing literature. In theories of behavior rooted in rational choice, the form of “indifference” used here has been most common, based on the relative evaluations of candidates/parties (with more similar evaluations indicating higher indifference). Among those concerned with social and political psychology, however, “ambivalence” (in which intensity of affect is also taken into account; those with strong but indifferent feelings are more ambivalent than those who are merely apathetic) has received more attention (see Lavine 2001 and Basinger and Lavine 2005). Given that indifference is easier to interpret, more readily quantified, and may be more correlated with participation (Yoo 2010), we focus on that variable.
Knowledge scales assign one point for being able to rate each of Bush, Kerry, Cheney, and Edwards on thermometer scales, and one point each for describing Bush as moderate or conservative and Kerry as moderate or liberal.
There are to date only a small number of studies of cross-pressures outside of the U.S. Among the most prominent, Powell (1976) examines the effects of cross-pressures on rates of partisanship in Austria, while Huckfeldt et al. (2005) look at political disagreement in social networks in three countries during the early 1990s.
When we applied this procedure to NAES data, it made a negligible difference in the resulting scores or their relationships to behavior, but with a smaller sample size it may prove more valuable.
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Acknowledgments
We thank Chris Achen, Larry Bartels, Will Bullock, Yanna Krupnikov, Dean Lacy, Adam Seth Levine, Devra Moehler, Jonathan Nagler, participants in the Center for the Study of Democratic Politics (Princeton) workshop, and especially the editors and anonymous reviewers, for their thoughtful feedback on earlier drafts. Therriault’s work on this project was supported in part by a research fellowship from the Center for the Study of Democratic Institutions at Vanderbilt University. All statistical analysis was conducted using the Stata and R software packages.
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Brader, T., Tucker, J.A. & Therriault, A. Cross Pressure Scores: An Individual-Level Measure of Cumulative Partisan Pressures Arising from Social Group Memberships. Polit Behav 36, 23–51 (2014). https://doi.org/10.1007/s11109-013-9222-8
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DOI: https://doi.org/10.1007/s11109-013-9222-8