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Contamination effects in mixed-member electoral systems: a dissemination of measurement techniques

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Abstract

There is widespread agreement that both tiers of a mixed-member electoral system do not operate independently of one another and that instead they interact, producing contamination effects. These tend to raise the number of parties away from what Duverger’s Law or the M + 1 rule suggest. However, the field has not yet determined an undisputed methodological approach to answer the following question: raised by how much, exactly? This paper identifies and differentiates amongst three major measurement techniques, herein titled the Difference Approach, the Likeness Approach, and the Simulation Approach. By doing so, it provides a more concise map of each of their logics, their varied implementations, their drawbacks, as well as possible ways forward.

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Notes

  1. The terms “tiers” and “arenas” are used interchangeably.

  2. For other types of contamination, see Herron et al. (2018).

  3. Where Y stands for the response variable; u stands for units or population; t stands for the units that received treatment; and c stands for the units left under control (i.e. received no treatment).

  4. For the first mention of contamination, see Shugart and Carey (1992).

  5. Where n is the number of parties, and \(p_{i}^{2}\) is the proportion of votes (or seats) of the ith party.

  6. Where N is \(1/\sum\nolimits_{i = 1}^{n} {p_{i}^{2} }\) and \(p_{i}^{2}\) is the proportion of votes of the winning party, squared.

  7. Maeda (2008), for example, proposed using what he referred to as “the treatment-effects model” in the study of contamination effects.

  8. One must consider that mixed-member systems vary considerably in terms of history, tier linkage, electoral threshold, and institutional contexts (Rich 2015). In fact, it is why—depending on their particular objectives—contamination studies tend to control for potential exogenous and endogenous factors that could also influence the rise in number of parties (see Herron and Nishikawa 2001; Kostadinova 2002; Thames and Edwards 2006; Riera 2012; Rich 2015).

  9. The sample was based on Chhibber and Kollman’s (2004) study of federalism and party competition.

  10. Kostadinova (2002) shows that mixed-member systems produce larger party systems than SSD systems. Nishikawa and Herron (2004) show that party systems are largest in PR systems with and without d’Hondt formulas, followed by mixed-member systems with linked tiers, mixed-member systems with unlinked tiers, and pure SSD systems. And Bochsler (2009) shows that “the outcome of mixed systems [varies] substantially from country to country”.

  11. A total of nine pure SSD and twenty-six PR elections.

  12. To my knowledge, this is the only design of the sort in contamination studies, although clearly not electoral studies as a whole (see Cox et al. 2000; Ansolabehere et al. 2000; or Fauvelle-Aymar and Lewis-Beck 2008).

  13. Per the paper, whereas Thistlethwaite and Campbell (1960) were the first to use an RDD, Lee (2008) was the first to use it in electoral studies.

  14. The authors focused on Germany’s two strongest parties: The SDP and the CDU/CSU. The reason was that, even though small parties received a share of the vote, estimating incumbency effects was not possible because “they never win district seats” (Hainmueller and Kern 2008). For further evidence of incumbency and spillover effects see Kang et al. (2018).

  15. Per Hainmueller and Kern (2008), “the complication that makes the interpretation of prior results ambiguous is the possibility that there exists some unobserved Z that we cannot control for. Since Z is likely to be correlated with MV, estimates of β tend to be biased. For the RD design, in contrast, local random assignment ensures that our estimate of β is unconfounded at the threshold, and we do not need to control for any covariates. Just as in randomized experiments, the inclusion of covariates should not appreciably affect our estimates of β (apart from increasing their precision)”.

  16. It is a tool designed by Nagayama (1997) to graph candidate strength in SSDs. Per Taagepera (2004: 301), the left side of the triangle “denotes perfect parity of the top two contestants, while its right side denotes the dominance of the strongest contestant over a single opponent. At the peak, the two contestants have equal strength, and there are no others. The left corner area of the triangle corresponds to the presence of multiple contestants”.

  17. The TF ratio, proposed by Singer (2013), is “the vote share secured by the parties finishing fourth or worse as a proportion of the votes secured by the first runner-up”.

  18. Maškarinec (2018) selected Cox’s SF ratio, for example, in order to obtain “insight into the electoral behaviour at the lowest level of aggregation” as well as “the various degrees of strategic defection from less competitive to more competitive districts across SSDs” (see Moser and Scheiner 2009).

  19. Riera (2019) argues that the spike in ENP caused by the reform occurs because those that “[identify] with a minor party are for some elections more likely to: (1) stick to their previous party choice; and (2) participate in elections”.

  20. As well as with findings by Reed (2001).

  21. Where P is the total number of valid votes, Pi is the total number of votes received by party i, PL is the number of votes received by the smallest party still listed as separate from “Other”, and R is the number of votes in the category “Other”.

  22. First, they measure pre-electoral coordination by counting “the candidates participating in an SSD race who are affiliated with a party that ran a list in the PR component”, and second, they “calculate, for each SSD in [the] sample, the average number of parties supporting each candidate by dividing the number of parties running lists in the corresponding PR constituency by the total number of candidates participating in the SSD race” (Ferrara and Herron 2005).

  23. Despite differences in their research objectives, both studies share some similarities in terms of their statistical strategies (in terms of their models and use of explanatory variables and controls). Ferrara (2006) just adds dispersed vote and average coalition size in order to explain the absolute number of candidates and the ENP.

  24. It deals with how voters may interpret a candidate’s ranking on a PR list as a signal of their worth within the party, which could, in turn, affect their voting in the SSD tier.

  25. Five countries used MMM systems, two used partially compensatory MMM systems, and six used non-compensatory MMM systems.

  26. Additionally, Riera (2012) controls for the winner’s performance in the election prior; ethnic fragmentation; the existence of popularly elected heads of state; the de-centralization of political power; federal systems; and second-order elections.

  27. Classifying Mexico amongst mixed-member systems has been the subject of much debate, given its country-specific context and characteristics. Banerjee and Rich considered the debates in Reynolds and Reilly (1997), Massicotte and Blais (1999), and Shugart and Wattenberg (2003).

  28. He ran an OLS model, a RE-GLSE, a Poisson model, and a mixed effects hierarchical model. The objective was to show that “party system fragmentation [would] be higher in systems with SSD-PR linkage mechanisms than in elections conducted under MMM rules” (Rich 2015).

  29. Rich (2015) tests how fused ballots, entry thresholds, and compulsory voting affect party fragmentation and considers the effects of d’Hondt formulas; chamber size; ethnic fractionalization; directly elected presidents; post-communist countries; freedom levels; the number of mixed elections; bicameralism; federalism; and the use of regional or national PR lists.

  30. In this way, “if institutional factors explain Mexico’s perceived divergence, the dummy variable should lack statistical and substantive significance” (and vice versa).

  31. King et al. (1994) refer to Pearson’s (1892) assertion that “the field of science is unlimited; its material is endless; every group of natural phenomena; every phase of social life; every stage of past or present development is material for science. The unity of all science consists alone in its method, not in its material”.

  32. While some countries adopted their mixed-member systems under conditions of democratic normalcy (as did New Zealand), other countries slowly carried their existing mixed-member systems out of autocracy (as did Mexico). The difference in the type of “founding elections” (i.e. a first election after reform and a first election under democracy).

  33. A second part of the study mentioned earlier.

  34. Per Abadie et al. (2015), “the synthetic control method facilitates comparative case studies in instances when no single untreated unit provides a good comparison for the unit affected by the treatment or event of interest”.

  35. From the founding election onwards.

  36. Spain uses a pure PR system, and Canada uses a pure FPTP system.

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Acknowledgements

The author would like to thank Ignacio Lago for his consistent guidance, as well as Aina Gallego, Alba Huidobro, Ruth Dassonneville, and all of the reviewers for their useful comments and critiques throughout.

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Gómez Díaz, A. Contamination effects in mixed-member electoral systems: a dissemination of measurement techniques. Eur Polit Sci 20, 502–520 (2021). https://doi.org/10.1057/s41304-020-00285-8

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