Progressives, Never-Trumpers, and Brexiteers: Applying cPCA to US-UK Survey Data

• In Event: Measuring Political Preferences

Abstract

Recent public discourse and academic research have both discussed and attempted to examine divides within American political parties and the Brexit divide among British voters (Hobolt et al. 2020; Lewis et al. 2021). For the former, there has been much discussion surrounding the progressive and moderate divide in the Democratic Party, see Bernie Sanders and “The Squad’s” supporters versus Hillary Clinton and Joe Biden’s, and the more moderate anti-Trump and more extreme pro-Trump divisions within the Republican Party, see Mitt Romney and Pat Toomey’s supporters versus Ted Cruz and Lindsey Graham’s. For the latter, researchers have noted that pro- versus anti-brexit sentiment is the primary division in British politics above and beyond left-right ideology, existing within all three major parties.

However, actually identifying these respondents/voters in survey data has been relatively difficult when using standard unsupervised machine learning and scaling methods. We illustrate this phenomenon using principal component analysis (PCA), factor analysis, independent component analysis (ICA), and unfolding methods on voter surveys in California, the US, and the UK. These methods, while successful in identifying important ideological differences among entire samples, consistently fail to identify the subgroups mentioned above.

While these methods’ results seem to suggest that these groups do not meaningfully exist, we instead argue that this is due to the primary goals of these methods and thus their limitations. Specifically, this arises from the fact that these methods either focus on explaining the most variation occurring in the entire sample (PCA and ICA) or minimizing classification/prediction error (unfolding methods). In both scenarios important subgroup variation (e.g, progressives versus moderates in the Democratic Party) and/or latent, full-sample differences (anti- versus pro-Brexit attitudes in the UK) are obscured.

To address these shortcomings, we exploit an emerging analysis approach, contrastive learning, to effectively isolate and identify these subgroups using contrastive PCA (cPCA) (Abid et al. 2018). Contrastive learning, in this scenario, operates by adjusting PCA’s standard goal of identifying dimensions on which the data varies the most in the entire sample. This goal often leads to interesting subgroup variation being overwhelmed by more common dimensions, such as left-right ideology or demographic differences, as happened in our analyses. In contrast, cPCA instead identifies the dimensions on which one subset of the data (the target group) varies the most and the other subset of the data (the background group) varies the least, hence the contrastive of contrastive PCA. In short, cPCA removes the dimensions of high variance shared across these two groups, often ideology, and instead focuses on what differentiates the target group from the background group. Importantly, this method is agnostic to what these dimensions are: the researcher does not select which variables constitute which dimensions, but only selects the variable which denotes the target and background groups.

Applying cPCA to our data, we find that, in the US, we identify both the progressive versus moderate wings of the Democratic party, using Republicans as the background group, and the pro- versus anti-Trump wings of the Republican Party, using Democrats as the background group. In the United Kingdom, using American respondents of a US-UK survey as the background group, we identify pro- versus anti-Brexit sentiments across all three major parties. These examples not only directly identify these important differences in the US and UK but also highlight the general usefulness of cPCA for identifying both subgroups and latent divisions within entire populations. Furthermore, unsupervised methods like cPCA complement existing methodologies for studying public opinion in two major ways: first, it can identify dimensions that can be directly used in analyses as independent variables of interest; and second, cPCA can be used as an exploratory tool to identify hidden differences often overlooked by traditional methods. Overall, this paper’s primary contribution is extending the use of cPCA to voter surveys specifically and public opinion more generally and providing a foundation from which future work can build off of.


Citations:
Abid, Abubakar, Martin J. Zhang, Vivek K. Bagaria, and James Zou. “Exploring Patterns Enriched in a Dataset with Contrastive Principal Component Analysis.” Nature Communications 9, no. 1 (2018): 1-7.
Hobolt, Sara B., Thomas J. Leeper, and James Tilley. “Divided by the Vote: Affective Polarization in the Wake of the Brexit Referendum.” British Journal of Political Science (2020): https://doi.org/10.1017/S0007123420000125.
Lewis, Jeffrey B., Keith Poole, Howard Rosenthal, Adam Boche, Aaron Rudkin, and Luke Sonnet. “Voteview: Congressional Roll-Call Votes Database.” (2021) https://voteview.com/

Authors

• Samuel Fuller, University of California, Davis

• Tzu-Ping Liu