Measuring re-election prospects across electoral systems: a general approach applied to Germany

Abstract

This research note presents a general approach for measuring the electoral safety of individual MPs across electoral systems that is based on predicted re-election probabilities estimated from multilevel logistic regression models. In contrast to existing measures, this method yields estimates on an intuitive and readily comparable probability scale, captures the higher sensitivity of re-election prospects to electoral change in the range of close races, and can accommodate regional differences in context conditions such as volatility. The paper implements the approach for two archetypical electoral systems – first-past-the-post (FPTP) systems and closed-list proportional representation (PR) – and estimates re-election prospects for the FPTP and PR tiers of the German mixed electoral system in all Bundestag elections since 1957. While the empirical data presented here is mainly illustrative, the concluding section highlights various questions that future research can address with the new measure.

Keywords:

• Electoral safety
• electoral systems
• electoral competition
• mixed electoral systems
• Germany
• dataset

Acknowledgements

We gratefully acknowledge excellent research assistance by Sven Hillen and Daniel Höhmann as well as very helpful comments and suggestions by the editors and two reviewers of West European Politics.

Notes

1. The full dataset of estimated re-election probabilities is available at https://www.uni-bamberg.de/en/emppol/research/data/.

2. System-level measures of electoral competitiveness (e.g. Kayser and Lindstädt 2015) do not concern us here because they do not differentiate between the safety of different candidates of the same party.

3. For example, a four-point increase in the margin of an MP over her closest competitor considerably increases her electoral safety if the margin grows from one to five points but provides little additional safety if it increases from 21 to 25 points.

4. This problem could be overcome by a logarithmic transformation of the indicator. Such transformations are not used in the existing literature.

5. Due to space restrictions, we cannot discuss additional electoral systems. However, relevant covariates for modelling re-election prospects can be drawn from existing literature (e.g. André et al. 2015). For example, re-election prospects under STV should depend on an MP’s share of first and later preference votes, district magnitude, and the existence of intra-party competitors in the district. In open-list PR systems, an MP’s number of preference votes compared to their co-partisan competitors, the quota of preference votes needed for election, and their list positions should be relevant predictors.

6. We could use any sigmoid (s-shaped) link function. We choose the logit link as it is frequently employed in political science.

7. If available, additional predictors can easily be integrated by adding them to the covariate matrix.

8. Due to the dominance of political parties in European democracies, we model the electoral success of individual candidates solely based on their party affiliation. This also allows us to estimate electoral prospects for new candidates (e.g. if the incumbent retires) based on the success of their predecessors from the same party. Our measurement approach can easily be adapted to include personal characteristics (e.g. demographic characteristics, incumbency, offices held, previous political career, etc.) in the covariate matrix when estimating their re-election prospects.

9. The approach in this paper improves on Stoffel (2014a) by estimating a multilevel model and using an additional predictor (district magnitude) as well as the cross-level interaction.

10. District-level polls are not regularly available or display high levels of uncertainty in most systems and are thus of limited value for cross-national and longitudinal research.

11. Our analysis starts in 1957 because we need at least one prior election under the same electoral rules to estimate re-election probabilities for the FPTP tier. The current rules were introduced in 1953. States that joined the Federal Republic after 1949 are included from their second election onward. Thus, Saarland enters the analysis in 1961 and the five former Eastern German states and Berlin in 1994 (before 1990, MPs from West Berlin were elected indirectly by the state parliament). Our analysis excludes 83 newly created districts that lack previous results. These account for less than 2% of all district observations over our 60-year period.

12. There is a lively but unresolved theoretical and empirical debate on whether the incentives MPs face in mixed electoral systems resemble those of pure systems (in the German case, FPTP and closed-list PR) or are systematically different due to a contamination between the tiers. Proponents of the first perspective advocate the use of mixed electoral systems as quasi-experimental settings for a controlled analysis of electoral system effects (e.g. Moser and Scheiner 2004; Stratmann and Baur 2002). Other scholars emphasise contamination, especially if many MPs, as in Germany, run in both tiers, and thus argue that MPs face different incentives in mixed compared to pure electoral systems (e.g. Crisp 2007; Ferrara et al. 2005; Manow 2015).

13. Estimation was done using RStan (Stan Development Team 2017). The online appendix provides our R code. For each model, we ran four different chains with 10,000 draws each and a thinning factor of five, discarding the initial 5000 rounds to guarantee convergence of all estimated parameters.

14. The following acronyms are used for the different states: BB (Brandenburg), BE (Berlin), BY (Bavaria), BW (Baden-Württemberg), HB (Bremen), HE (Hesse), HH (Hamburg), MV (Mecklenburg-West Pomerania), NI (Lower Saxony), NW (North Rhine-Westphalia), RP (Rhineland-Palatinate), SH (Schleswig-Holstein), SL (Saarland), SN (Saxony), ST (Saxony-Anhalt), and TH (Thuringia).

15. https://www.uni-bamberg.de/en/emppol/research/data/.