Party Proximities in Voting Advice Applications – Identifying Structural Breaks in Data from the German Wahl-O-Mat

Felix Wieland

doi:10.1515/spp-2024-0009

Article

Party Proximities in Voting Advice Applications – Identifying Structural Breaks in Data from the German Wahl-O-Mat

Felix Wieland

Published/Copyright: August 28, 2024

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information

From the journal Statistics, Politics and Policy Volume 15 Issue 3

Abstract

Voting Advice Applications (VAAs), such as the German Wahl-O-Mat (WOM), have been examined extensively by researchers in various ways. Here, a subset of research uses data from the Wahl-O-Mat to investigate party relations. While these investigations focus on a limited number of WOM editions, I explicitly investigate the persistence of party relations in the WOM in a broad statistical analysis over 63 editions of the WOM in this exploratory research paper. At first glance, I find that intuitive differences in the overall proximities are observable. However, while many arguments exist that corroborate the suitability of the WOM data for the investigation of party relations, I identify statistically significant lower proximities for the six largest German parties in WOM editions from 2009 onward. Based on a review of changes in the design framework of the WOM and comparative data analyses based on the Chapel Hill Expert Survey and the Manifesto data set, these lower proximities are apparently linked to changes in the design of the WOM. As a result, I discuss the general ability of data from the WOM to give reliable insights into party relations. I argue that the WOM might roughly represent overall party relations but, due to a non-proportionality in the shift of the distances, potential design changes have distorting impacts on the relations between parties that make comparisons between different editions of the WOM problematic. This should be a starting point to investigate other VAAs for similar patterns to reevaluate the validity of data from VAAs for the examination of party relations in general.

Keywords: voting advice applications; Wahl-O-Mat; party proximities; proximity measures

Corresponding author: Felix Wieland, Department of Economics and Social Sciences, University of Cologne, Cologne, Germany, E-mail: contact@felixwieland.de

Acknowledgment

I want to thank Prof. Dr Dominik Wied for all his helpful advice for my research. Next, I want to thank Felix Boelte for his hints on existing literature as well as his comprehensive provision of WOM data. Further, I want to thank Prof. Dr Alexia Katsanidou, Prof. Dr Diego Garzia, as well as two anonymous peer reviewers for their constructive and helpful feedback.

Research funding: I did not receive any funding for this work.

Appendix A

A.1 Equality of Dummy-Variable Approach and Normed Manhattan Distance

If a measure of similarity fulfills 0 ≤ s(x_i, x_j) ≤ 1, it can easily be transformed into a measure of distance by 1 − s(x_i, x_j) = d(x_i, x_j) (Backhaus et al. 2016, p. 498). Since the matching coefficient obviously fulfills this condition, it can simply be converted into a measure of distance:

(8) 1 − s Mat * x i * , x j * = P ( K − 1 ) P ( K − 1 ) − m = * P ( K − 1 ) = m ≠ * P ( K − 1 )

Here, m ≠ * denotes the number of non-matching elements of the P(K − 1) dummy variables. If the number of non-matches for the K − 1 dummy variables that have been introduced for the variable p is given by m ≠ , p * , one obtain

(9) m ≠ * P ( K − 1 ) = ∑ p = 1 P m ≠ , p * P ( K − 1 )

Since the K − 1 dummy variables code the deviation of the reached expression level from the baseline in the variable p, m ≠ , p * can alternatively be interpreted as the difference in the expression levels of the variable p for two objects. Hence, m ≠ , p * = ( 0,1 , … , K − 1 ) is equal to the absolute deviation in the variable p. As a result, the normed Manhattan distance is obtained:

(10) ∑ p = 1 P m ≠ , p * P ( K − 1 ) = ∑ p = 1 P | x i p − x j p | P ( K − 1 )

A.2 Empirical Comparison of Proximity Measures

While discussing the proximity measures theoretically, I further test their performance on the WOM data in practice. As mentioned above, the Manhattan and Euclidean distances are normalized to enable a sensible comparison between the WOMs as well as between the proximity measures. To further enable a comparison, the matching coefficient is reformulated as a measure of distance via 1 − s_Mat(x_i, x_j) which I refer to as the non-matching coefficient. Since measurements based on the Manhattan distance are preferred from a theoretical perspective, it is considered to be the “gold standard”. Figure 4 illustrates the pairwise scatterplots for the three different measures.

Figure 4:

Plots of the pairwise distance measurements for the 788 pairwise distance measurements of the six parties. The colored lines represent the bisectrix.

I find the correlation of the normed Euclidean and the normed Manhattan approach with 0.99 to be the highest, the Manhattan and the non-matching coefficient to be correlated with 0.975, and I find a correlation of 0.949 for the normed Euclidean distance and the non-matching coefficient. While these correlations seem to be high at first glance, the inspection of the scatterplots reveals deviations in the measurements: For example, for a normed Manhattan distance of 0.5, the measurements of the normed Euclidean distance lie between approximately 0.62 and 0.70 while the measurements of the non-matching coefficient lie between 0.56 and 0.68. However, for a normed Euclidean distance of 0.5, we observe an even larger range for the measurements of the non-matching coefficient of approximately 0.22.

Further, it is possible to identify the discussed tendencies of the proximity measures. First, the (normed) Euclidean distance generally shows larger measurements than the (normed) Manhattan distance. This seems to be especially the case for measurements of the normed Manhattan distance below 0.4. While the distance measurements of the non-matching coefficient also show higher maximum distances, the deviations from the measurements based on the Manhattan distance are highly dispersed. This seems to be especially the case for an increasing normed Manhattan distance. For the sake of completeness, I also compare the normed Euclidean distance to the non-matching coefficient which reveals an even higher dispersion. It is salient that the measurements of the Euclidean distance tend to be higher for lower measurements of the non-matching coefficient, while the measurements tend to scatter around the bisectrix for higher measured distances.

This practical examination demonstrates the potential overweighting of larger deviations of the Euclidean distance and the overestimation of general distances by the (non-)matching coefficient. Hence, these results underline the theoretical considerations.

A.3 MWU Test-Statistic

For sizes of the pooled sample n > 50 and ties in the ranks, the test statistic and the respective (approximative) distribution under H₀ are given by

(11) U 1 = n 1 n 2 + n 1 ( n 1 + 1 ) 2 − R 1

(12) U 2 = n 1 n 2 + n 2 ( n 2 + 1 ) 2 − R 2

(13) U = min { U 1 , U 2 }

(14) U ∼ appr. N μ U = n 1 n 2 2 , σ U 2 = n 1 n 2 ( n 1 + n 2 + 1 ) 12

with R₁, R₂ denoting the rank sums of subsample 1 and 2 respectively.

A.4 Figures

Figure 5:

Boxplots of the distances for all party combinations.

Figure 6:

Depiction of the normed Manhattan distances for SPD/FDP (yellow) and SPD/Greens (green) over all 63 WOMs indicated by the date of the respective election.

References

Aggarwal, C. C., A. Hinneburg, and D. A. Keim. 2001. “On the Surprising Behavior of Distance Metrics in High Dimensional Space.” In Database Theory — ICDT 2001, edited by J. Van den Bussche, and V. Vianu, 420–34. Berlin: Springer Berlin Heidelberg.10.1007/3-540-44503-X_27Search in Google Scholar

Backhaus, K., B. Erichson, W. Plinke, and R. Weiber. 2016. Multivariate Analysemethoden, 16th ed. Berlin, Heidelberg: Springer.10.1007/978-3-662-46076-4Search in Google Scholar

Bolte, F. 2023. Qual-O-Mat-Data Repository. https://github.com/gockelhahn/qual-o-mat-data (accessed August 18, 2023).Search in Google Scholar

Bundeszentrale für politische Bildung. 2017. “Die Entstehung eines Wahl-O-Mat.” https://www.bpb.de/themen/wahl-o-mat/45292/die-entstehung-eines-wahl-o-mat/ (accessed August 18, 2023).Search in Google Scholar

Büning, H., and G. Trenkler. 1994. Nichtparametrische statistische Methoden. Berlin: De Gruyter.10.1515/9783110902990Search in Google Scholar

Cohen, J. 1992. “A Power Primer.” Psychological Bulletin 112 (1): 155–9. https://doi.org/10.1037/0033-2909.112.1.155.Search in Google Scholar

Dahl, D. B., D. Scott, C. Roosen, A. Magnusson, and J. Swinton. 2019. xtable: Export Tables to LaTeX or HTML. R package version 1.8-4. https://CRAN.R-project.org/package=xtable.Search in Google Scholar

Debus, M. 2009. “Analysing Party Politics in Germany with New Approaches for Estimating Policy Preferences of Political Actors.” German Politics 18 (3): 281–300. https://doi.org/10.1080/09644000903055773.Search in Google Scholar

Fahrmeir, L., A. Hamerle, and G. Tutz. 2018. Multivariate statistische Verfahren, 15th ed. Berlin, New York: Springer.Search in Google Scholar

GLES. 2019. “Vor- und nachwahl-querschnitt (kumulation) (gles 2013).” GESIS Datenarchiv. ZA5702 Datenfile Version 4.0.1.Search in Google Scholar

Graichen, R. 2019. Populismus und Demokratie, volume 37 of Extremismus und Demokratie, 1st ed. Baden-Baden: Nomos.Search in Google Scholar

Jolly, S., R. Bakker, L. Hooghe, G. Marks, J. Polk, J. Rovny, M. Steenbergen, and M. A. Vachudova. 2022a. “Chapel Hill Expert Survey Trend File, 1999–2019.” Electoral Studies 75: 102420. https://doi.org/10.1016/j.electstud.2021.102420.Search in Google Scholar

Jolly, S., R. Bakker, L. Hooghe, G. Marks, J. Polk, J. Rovny, M. Steenbergen, and M. A. Vachudova. 2022b. “Chapel Hill Expert Survey Trend File, 1999–2019.” Electoral Studies 75: 102420. https://doi.org/10.1016/j.electstud.2021.102420.Search in Google Scholar

Koh, A., D. Boey, and H. Béchara. 2021. “Predicting Policy Domains from Party Manifestos with Bert and Convolutional Neural Networks.” SocArXiv. https://doi.org/10.31235/osf.io/fjh4q.Search in Google Scholar

König, P. D., and D. Nyhuis. 2020. “Assessing the Applicability of Vote Advice Applications for Estimating Party Positions.” Party Politics 26 (4): 448–58.Search in Google Scholar

Lefevere, J., and S. Walgrave. 2014. “A Perfect Match? The Impact of Statement Selection on Voting Advice Applications’ Ability to Match Voters and Parties.” Electoral Studies 36: 252–62. https://doi.org/10.1016/j.electstud.2014.04.002.Search in Google Scholar

Lehmann, P., S. Franzmann, D. Al-Gaddooa, T. Burst, C. Ivanusch, S. Regel, F. Riethmüller, A. Volkens, B. Weißels, and L. Zehnter. 2024. “The Manifesto Data Collection. Manifesto Project (mrg/cmp/marpor). Version 2024a.” Berlin: Wissenschaftszentrum Berlin für Sozialforschung (WZB). Göttingen: Institut für Demokratieforschung (IfDem) Version 2024a, https://doi.org/10.25522/manifesto.mpds.2024a.Search in Google Scholar

Linhart, E. 2017. “Politische Positionen der AfD auf Landesebene: Eine Analyse auf Basis von Wahl-O-Wat-Daten.” Zeitschrift für Parlamentsfragen 48 (1): 102–23, https://doi.org/10.5771/0340-1758-2017-1-102.Search in Google Scholar

Louwerse, T., and M. Rosema. 2013. “The Design Effects of Voting Advice Applications: Comparing Methods of Calculating Results.” Acta Politica 49: 1–27. https://doi.org/10.1057/ap.2013.30.Search in Google Scholar

Mann, H. B., and D. R. Whitney. 1947. “On a Test of Whether One of Two Random Variables is Stochastically Larger than the Other.” The Annals of Mathematical Statistics 18 (1): 50–60. https://doi.org/10.1214/aoms/1177730491.Search in Google Scholar

Marschall, S. 2009. “Der Wahl-O-Mat als Instrument der Gesellschaftsberatung – Potenziale und Grenzen.” Zeitschrift für Politikberatung 2 (3): 485–92, https://doi.org/10.1007/s12392-009-0202-7.Search in Google Scholar

Marschall, S. 2011. “Nutzer und Nutzen – der Wahl-O-Mat zur Bundestagswahl 2009.” In Das Internet im Wahlkampf, 136–53. VS Verlag für Sozialwissenschaften.10.1007/978-3-531-92853-1_5Search in Google Scholar

Marschall, S., and C. K. Schmidt. 2008. “Preaching to the Converted or Making a Difference? Mobilizing Effects of an Internet Application at the German General Election 2005.” In Non-Party Actors in Electoral Politics: The Role of Interest Groups and Independent Citizens in Contemporary Election Campaigns, volume 8 of Studien zur Wahl- und Einstellungsforschung. 1st ed, edited by D. Farrell, and R. Schmitt-Beck, 259–78. Baden-Baden: Nomos. chapter 11.10.5771/9783845206639-259Search in Google Scholar

Marschall, S., and M. Schultze. 2012. “Voting Advice Applications and Their Effect on Voter Turnout: The Case of the German Wahl-O-Mat.” International Journal of Electronic Governance 5: 349–66. https://doi.org/10.1504/ijeg.2012.051314.Search in Google Scholar

Marschall, S. 2011a. “Idee und Wirkung des Wahl-O-Mat.” APuZ 51–52: 41–6.Search in Google Scholar

Marschall, S. 2011b. “Wahlen, Wähler, Wahl-O-Mat.” APuZ. https://www.bpb.de/shop/zeitschriften/apuz/33534/wahlen-waehler-wahl-o-mat/ (accessed September 8, 2023).Search in Google Scholar

Nahm, F. 2016. “Nonparametric Statistical Tests for the Continuous Data: The Basic Concept and the Practical Use.” Korean Journal of Anesthesiology 69: 8. https://doi.org/10.4097/kjae.2016.69.1.8.Search in Google Scholar

Ooms, J. 2014. “The Jsonlite Package: A Practical and Consistent Mapping Between Json Data and R Objects.” arXiv:1403.2805 [stat.CO]. https://arxiv.org/abs/1403.2805.Search in Google Scholar

R Core Team. 2022. “R: A Language and Environment for Statistical Computing.” https://www.R-project.org/.Search in Google Scholar

Rosenthal, R. 1991. Meta-Analytic Procedures for Social Research. Thousand Oaks, California: Sage.10.4135/9781412984997Search in Google Scholar

Schoofs, J. 2017. Der flüchtlings- und integrationspolitische Wettbewerb bei den Landtagswahlen im März 2016, 109–13. Wiesbaden: Springer Fachmedien Wiesbaden.10.1007/978-3-658-15714-2_16Search in Google Scholar

Stecker, C., and T. Däubler. 2016. “Ein Vergleich der programmatischen Schnittmengen möglicher Koalitionen nach den Landtagswahlen in Baden-Württemberg, Rheinland-Pfalz und Sachsen-Anhalt.” http://www.mzes.uni-mannheim.de/publications/papers/koal-o-mat-analyse.pdf.Search in Google Scholar

Stecker, C., and T. Däubler. 2017. “Koal-O-Mat: Inhaltliche Schnittmengen von Jamaika, Groko und Co. vor der Bundestagswahl 2017.” http://www.mzes.uni-mannheim.de/publications/papers/koalomat_\analyse_bund_2017.pdf.Search in Google Scholar

Van Camp, K., J. Lefevere, and S. Walgrave. 2014. The Content and Formulation of Policy Statements in Voting Advice Applications. A Comparative Analysis of 27 VAAs, 11–31. ECPR Press.Search in Google Scholar

Volkens, A., P. Lehmann, N. Merz, S. Regel, Annika Werner, O. P. Lacewell, and H. Schultze. 2013. The Manifesto Data Collection. Berlin: Wissenschaftszentrum Berlin für Sozialforschung (WZB).Search in Google Scholar

Wagschal, U., and P. König. 2014. “Alle gleich? Analyse der programmatischen Parteienunterschiede bei Bundestagswahlen auf der Basis des Wahl-O-Mats.” Zeitschrift für Parlamentsfragen 45 (4): 865–84, https://doi.org/10.5771/0340-1758-2014-4-865.Search in Google Scholar

Wagschal, U., and P. König 2015. Die Links-Rechts-Positionierung der Parteien bei den Bundestagswahlen 2005 bis 2013: Eine empirische Analyse anhand des Wahl-O-Mat, 185–210.10.1007/978-3-658-02915-9_9Search in Google Scholar

Wagschal, U., and T. Waldvogel. 2022. “Die Parteipositionen bei der Bundestagswahl 2021: Unterschiede und Überschneidungen in den Parteienprofilen?” In Die Bundestagswahl 2021: Analysen der Wahl-, Parteien-, Kommunikations-und Regierungsforschung, 1–22. Springer.10.1007/978-3-658-35758-0_14-1Search in Google Scholar

Walgrave, S., M. Nuytemans, and K. Pepermans. 2009. “Voting Aid Applications and the Effect of Statement Selection.” West European Politics 32 (6): 1161–80. https://doi.org/10.1080/01402380903230637.Search in Google Scholar

Wickham, H. 2016. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. https://ggplot2.tidyverse.org.10.1007/978-3-319-24277-4_9Search in Google Scholar

Wickham, H. 2022. stringr: Simple, Consistent Wrappers for Common String Operations. https://stringr.tidyverse.org, https://github.com/tidyverse/stringr.Search in Google Scholar

Wimmel, A. 2019. “Europa-Lager im deutschen Parteiensystem auf Basis des Wahl-O-Mat.” Zeitschrift für Parteienwissenschaften 2: 185–94.Search in Google Scholar

Wurthmann, L. C., S. Marschall, and M. Billen. 2019. “Regierungsoptionen zwischen Bürgerwille und Issue-Nähe – eine Analyse von Koalitionspräferenzen vor der Bundestagswahl 2017.” https://doi.org/10.1007/978-3-658-25050-8_13.Search in Google Scholar

Received: 2024-03-05

Accepted: 2024-08-08

Published Online: 2024-08-28

Published in Print: 2024-11-26

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/spp-2024-0009

Keywords for this article

voting advice applications; Wahl-O-Mat; party proximities; proximity measures