Synergy in Spatial Models of Voting: How Critical Cases Show That Proximity, Direction and Discounting Are Friends, Not Foes

Abstract

The spatial theory of elections is widely used to examine how party policy is linked to voter preferences. Three classic models – proximity, direction and discounting – lay claim to the nature of this link, but their predictions of voting behavior are almost identical. I resolve the problem by decomposing 28 multi-party systems into about 1 million party triplets. This allows me to isolate “critical cases” where model predictions diverge. The combinatorial approach reveals a degree of collinearity between models that may surprise even longtime experts in the field. But while collinearity is a nuisance for scholars, it is a blessing for voters. I find disproportionately strong policy voting when all predictions agree, indicating that there is synergy between the three spatial logics. A selection effect can be excluded using propensity-score matching. These findings suggest that concurrence of proximity, directional and discounting elements in the vote function is inherent to electoral competition.

Acknowledgements

Thanks for helpful comments go to Jørgen Bølstad, Irit Dekel, Elias Dinas, Bob Erikson, Ed Fieldhouse, Mark Franklin, Florent Gougou, Sergi Pardos-Prado, Craig Parsons, Curt Signorino, Carolien van Ham, Bernhard Weßels and anonymous reviewers. Early drafts were presented at the 2007 Graduate Network Conference, the 2007 political economy meeting of the German Political Science Association, the 2012 conference of the European Political Science Association, the 2013 conference of the Midwest Political Science Association and the 2013 comparative politics colloquium at Humboldt University of Berlin.

Disclosure Statement

No potential conflict of interest was reported by the author.

Supplementary Material

Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/17457289.2015.1064437. The data used for this study can be obtained at http://www.piredeu.eu.

Notes

1. Synergy is also different from earlier “unified” models of voting (Iversen 1994; Merrill and Grofman 1999) which posit a mix of direction, proximity and discounting, but no interaction. In a synergetic utility function the three logics affect each other, while in a mixed function they merely coexist.

2. To simplify matters, I will use the term “position” (along with its “extremeness”) for the feature that distinguishes actors in political space. This feature may reflect distance, intensity, or both.

3. Note that this implies an individualized RoA, which is discussed at the end of this section.

4. As A = 0 contradicts the very principle of directional voting, it is excluded in Equations 3 and 4.

5. Practically infinity is not required because a reasonably high value of P has the same effect. Also note that Equation 5 implies that voters at the neutral point do not penalize parties for crossing the RoA. Since these voters by definition do not care about policy, for them there is no mark that parties could overshoot.

6. Indeed, when political space is seen in terms of intensity, any other assumption concerning the location of the neutral point would imply that intensity in one policy direction can be higher than in the other.

7. Given a sufficiently extreme status quo, more moderate voters may prefer centrist parties.

8. The number of triplets per respondent is , where n is the number of parties evaluated. This excludes 12.6% of respondents and 15.3% of party ratings/perceptions due to missing values on core variables (indicating that the conditions of the spatial model are not fulfilled). Moreover, given transitive preferences one triplet per respondent is redundant. These were still kept because selection would not be arbitrary with regard to some of the matching variables of the propensity-score estimator described below. Cluster-robust standard errors are reported to adjust for intra-individual redundancy.

9. Belgium has separate party systems in Flanders and Wallonia.

10. In an analysis of the Irish National Election Study 2002, which contained PTVs, thermometers and likes/dislikes, the PTV yielded the highest item response rate and the closest reflection of preference rankings cast under the Irish single transferable vote system (Van der Eijk and Marsh 2007; for similar results with Dutch data see Kroh 2003, 52). This is not self-evident because PTVs (unlike vote choice) are non-ipsative, that is, their scores are formally independent of each other and not constrained to a certain sum. Empirically, however, the scores turn out to be constrained by a latent dimension on which parties and voters can be located using IRT unfolding models (Van der Eijk and Marsh 2007). This strongly suggests that PTVs reflect a comparison of parties. Moreover, the latent PTV trait correlates highly (.66 and .62, respectively) with equivalent traits extracted from thermometer scores and like/dislike ratings (Van der Eijk and Marsh 2007, 21).

11. Note that the possible rankings shown in Table 1(b) include ties. Rather than resolving ties arbitrarily, I consider them valuable information that theories of party preference need to engage with. To allow for adequate reflection of ties in the various spatial utility functions, predictions were rounded to the first decimal after the operations described in the following two sections.

12. More abstractly, Westholm (1997, 871) extends this argument to rationalization: If voters use the proximity model to express wishful thinking, the phenomenon should be treated as evidence, not as bias.

13. The geometric mean attenuates the sensitivity of the arithmetic mean to extreme values. This is advantageous for my purposes because directional and discounting theory effectively compete for the “critical cases”. A factor value that is unfavorable for its own model may actually benefit the competitor. The geometric mean avoids suppression of one model by the other.

14. But note that “pure” does not imply “true”. As discussed above, the parameter values for the debiased positions merely form one endpoint of the range of possible solutions.

15. It might seem that all success rates are generally poor, but this is innate to the combinatorial approach which requires perfect agreement of preference order and utility function. In a parametric analysis of EES data, left–right proximity alone explains 18% of the variance in PTVs and outperforms all other predictors (Van der Brug, van der Eijk, and Franklin 2007). While spatial utilities thus clearly matter, the aim of the combinatorial approach is not to boost variance explained but to assess relative performance and synergy.

16. The terminology of “treatment and control” was adopted for matching studies by Rosenbaum and Rubin (1983). Unlike in experiments, treatment is not administered randomly but reconstructed statistically.

17. Small-sample problems of LLM are not relevant given the high N.

18. Note that the directional model also loses power for debiased positions. This seemingly counterintuitive effect is due to the extended set of “critical cases”. Accounting for composition with the matching procedure shows that rationalization affects only the proximity model.

19. Note that the joint success rate is disadvantaged vis-à-vis the shared success rate by the lower ceiling of possible improvement over chance. However, no model gets anywhere near 100% (Table 3). Synergy may still be inflated below the ceiling, but the theoretical maximum of this effect is a negligible 0.7%.

20. The cases with two collinear predictions have no clear role in this analysis and are left aside. This further improves the treatment models (as shown in the online Appendix 5).

21. This is perhaps least problematic in the experiment by Lacy and Paolino (2010) who used mock commercials and newspaper articles to make the test environment more realistic. Still, even this careful design differs from a real election with antagonistic campaigns and actual implications.