Studying party identification

People’s right to vote is one of the most essential foundations of a democracy and the most common way for individuals to influence the political landscape. It is the temporal division of power upon democratically legitimized political action relies. In consequence, political parties need votes to shape policies. Lucky are those who have a constant high number of partisans who vote for them. Indeed, party identification has been declining for years in all western democracies, but it is—in conjunction with other variables—still a sound indicator for voting intentions [1]. Moreover it indicates—especially in parliamentary systems with proportional representation, like Germany—stability and change of party systems. Thus, a lot of research has made use of ‘party identification’ to explain different phenomena such as voters’ decisions at the ballot box, volatility of voting outcomes because of dealignment, or trust in political systems within parliamentary system where parties are central political actors. [2, 3].

During the so called behavioral revolution (20th century) different models for explaining party ties on the micro-level emerged: rational choice, micro-sociological and social-psychological approaches [4–6]. Party identification is based on the social-psychological assumption that individuals lean towards those parties that represent an individuals belief system, because party tie itself is part of an individual’s belief system. These belief systems get visible in policy making, when e.g. so called advocacy coalitions are tied by their ‘deep core beliefs’ and ‘policy core beliefs’ to enforce a certain political program [7–10]. Party identification emerges from primary learning and individual conditions. It is by definition long lasting, quite persistent over time and less affected by actual events or candidates. But affiliations can change, in- or decrease, e.g. by (social) learning over time or because of party performance [11, 12].

The rise of political parties is—among others—explained by macro-sociological perspectives like the cleavage theory [13]. This approach argues that political parties are the result of cleavages a society faces. Typical cleavages are: state versus church, capital versus labour, centre versus periphery. Nowadays we find more and other conflict lines within a society. New cleavages get visible when established parties do not address (new) concerns and perceived needs and consequently open up room for new parties. It might be that concerns and needs change, it might also be that parties change their profile. Examples for the German case are the success of ‘Bündnis 90/Die Grünen’ (‘Greens’) since the 1980ies and of ‘Alternative für Deutschland’ (‘Alternative for Germany’, AfD) since 2013.

Research outside political sciences regarding party identification often still focuses on an unidimensional spectrum of political ideology, ranging from liberal to conservative on a continuous scale, and uses this scale to correlate it to party tie [14]. With this idea in mind, researchers linked ideology to additional interindividual variables like neurological functioning, personality or religiousness [15, 16]. While these findings extended the knowledge about party affiliation, they might have relied on a limited perspective. [17] claim that the unidimensional model is an oversimplification of people’s ideology. This view is confirmed especially when we take a closer look on the German case with its pluralistic party system, were ‘traditional’ conservative issues are also promoted by liberal parties and vice versa: The Greens for example are pretty successful with their (conservative) profile regarding ‘integrity of creation’ [18, 19], while the right-wing AfD is liberal regarding the market but conservative regarding family, gender and migration. Both of them are wining parties—admittedly, not (only) because of their programs. But: the traditional ‘grand people’s parties’ (in German: Volksparteien)—’Christlich Demokratische Union/Christlich Soziale Union’ (’Christian Democractic Union/Christian Social Union’, CDU/CSU) and ‘Sozialdemokratische Partei Deutschlands’ (‘Social democratic party of Germany’, SPD)—lost enormous support during the last legislative periods.

All of these theories and models have in common that they try to categorize people into different groups. However, they disagree on the number of groups and on how they should be labeled. So it might be helpful to use a method that transcends these dissensions by not presupposing a certain dimensionality, in other words, a bottom-up approach.

Furthermore, comparisons between individuals belief systems or voting behavior and interindividual differences are usually done in retrospect or concurrently (e.g. [20–22]). Political parties usually want to know how many people are generally supporting them. Consequently, a useful approach should not only be independent from limitations to numbers of groups but also be able to inform about party identification, especially in times, when party tie decreases.

Thus, research in this field will benefit from a different approach. We apply a bottom-up process in which we look at people’s interindividual differences to cluster them into robust groups which are later linked to their party identification instead of grouping them a-priori by their party ties or vote choice to explain interindividual differences. More specifically, we analyze longitudinal data from the Socio-Economic Panel Study (SOEP) and use data regarding individuals’ concerns from 2010 to cluster them into groups using a Dirichlet process. Individual concerns are one but central aspect of party identification as they stand for the affective dimension of party tie. Of course, primary learning is crucial for the concept, but as e.g. [11, 12] pointed out, (social) learning—and thus concerns as a criteria to assess political outcomes—are central for ‘party identification’, and they can even change ties. Subsequently, we assess whether stable grouping results in 2010 are linked to party identification in 2017 to test the applicability of the approach. Note this does not necessarily imply that individuals’ concerns cause their party affiliation, as alternative explanations (e.g. certain factors affecting both peoples’ concerns and their party affiliation) are possible.

Dirichlet clustering

For this article, we will use Dirichlet clustering (as described in more detail in the Method section) to identify subgroups of specific concerns.

Like all clustering algorithms, Dirichlet clustering identifies subgroups in the population so that similarity within subgroups is high while similarity between subgroups is low. Similarity is defined by high likelihood for the answers of each participant to be in a multinomial distribution estimated by the answers of all of her group members. In contrast to other clustering methods, Dirichlet clustering is a Bayesian method, which for this application comes with three major advantages:

1. The result is not a single, fixed ‘best guess’ of the cluster structure, but a posterior distribution over potentially all possible cluster structures, which describe the belief in these structures considering the data. In this distribution, structures in which the members of clusters are closer to each other have a higher probability, while other cluster structures have lower, but not zero, probability. While it is still possible to investigate a single structure that represents the distribution best (i.e., a mean structure) as in classical clustering methods (e.g. k-means), it is also possible to investigate the robustness of each cluster, thus giving a better understanding of the “stability” of clusters. It is even possible to investigate single participants in this posterior distribution.
2. In addition to producing a posterior distribution, Dirichlet clustering can incorporate a prior distribution. In Bayesian statistic, the prior distribution is described by the researcher’s a-priori belief. While in model-based applications of Bayesian statistics, the prior distribution usually describes the prior belief in values of one or more parameter, in Dirichlet process clustering, the prior describes the a-priori belief in different possible assignments of participants to a cluster. So the prior distribution assigns a fixed probability to all possible clustering results. In the current application this prior describes the process of the cluster generation in social groups abstracting from the component which is later described by the data, that is, an idealized social clustering that is driven by the cluster memberships alone. More specifically, the prior in Dirichlet clustering is a rich-gets-richer distribution in which each new person is sorted to the existing clusters with probabilities proportional to the size of the existing cluster. The event to create a new cluster has a fixed weight called α. For example, if cluster with sizes 5, 2, 1 already exist, and α = 2, then the next person joins the first cluster with probability , the second with probability 20%, the third with probability 10%, and forms a new cluster with probability 20%. This prior specifically describes the probabilities of relative cluster sizes, while all permutations of the participants are equally likely in this distribution. It does not incorporate any information from the data, thereby allowing to separate the data-free formation of clusters (the prior) from the data-driven aspects (the likelihood) which together form the final posterior clustering distribution.
   Note that the prior distribution used here, although definitely not a good choice for all clustering problems, is very adequate for social clusters. This is because in social clustering, each person which so far is not decided which group to join will, abstracting from her preferences, be proportionally more likely to join larger existing groups since these clusters are more available in her environment.
3. A helpful side effect of the Bayesian mechanism is that the number of cluster is not fixed as it is in many other clustering algorithms as, e.g., k-means. Instead, in Dirichlet clustering the data will drive the total number of clusters that are most likely. For low participant numbers, the prior (via the parameter α) influences the number of clusters (with higher α giving more a-priori probability for more clusters), while for high numbers of participants the data will asymptotically overwrite the prior, and the optimal number of clusters will be reached.

Dirichlet clustering

The Dirichlet Clustering used in the current study operates on a Dirichlet Process Mixture Model (DPMM) [23, 24] which is shown in Fig 1. This Bayesian model is best imagined as a hierarchical probability distribution over all possible clusterings of a fixed number of objects based on their given features.

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Fig 1. DPMM.

The Dirichlet Process Mixture Model for D concern items, V_d response options in dimension d, concentration parameter α and N persons to be clustered.

https://doi.org/10.1371/journal.pone.0212944.g001

The goal of the method is to sample partitions from this distribution and estimate a sample mean afterwards, which is regarded as the consensus solution of the model. These partitions are generated by a so-called Chinese Restauarant Process (CRP) which implements a Gibbs sampling [25]. The CRP is best imagined as follows: Assume a Chinese restaurant with an infinite number of empty tables. The first guest enters the restaurant and sits down at any table. Another guest entering the restaurant now has the choice between an already occupied table or an empty table. She chooses an occupied table with a probability proportional to the number of guests already at that table, and a new, still empty table with a probability proportional to a fixed value. Each additional arriving guest proceeds according to this principle in order to choose a place to sit. The probability of person N + 1 selecting a table k is therefore (1) So far, people arriving are placed without taking the similarity between these people into account, i.e., the process up to here represents the prior distribution. To add the likelihood to the process the probability of a table being chosen is multiplied by the likelihood that the person to be placed matches the persons at this table. If F represents this likelihood, then (2)

This value is the probability that the item responses of the person to be seated come from an Multivariate Dirichlet-Categorical Distribution (MDCD) associated with the response items. Each cluster is assigned its own MDCD updated each time a guest is seated at a table (cluster) by changing the concentration parameters of the corresponding Dirichlet distributions. These concentration parameters can be thought of as the frequencies of each item response for each concern item by the persons already placed in this cluster. The likelihood function F_k for a person to be placed in an existing cluster via the posterior predictive distribution of the corresponding MDCD and for an empty cluster via its prior predictive distribution is thus calculated as (3) (4) where H is the parameter distribution for the kth cluster. To generate draws (= partitions) from the DPMM, N participants are initially placed probabilistically corresponding to (2) at the tables. Then the additional draws are generated by removing each person sequentially from their current cluster and repositioning it again probabilistically according to Eq 2.

This CRP implements a Gibbs Sampler which generates samples from the posterior distribution of clusterings. In a final step, a ‘best clustering’, in the sense of an expected grouping, is determined by a median partition paradigm implemented as follows: One first selects an arbitrary candidate as median partition. Afterwards, one optimizes this candidate step by step to obtain a lower mean distance to all partitions in the samples drawn from the CRP. The candidate is optimized by placing each participant sequentially in each existing or a new cluster and monitor the change in the average distance to all other samples. If the mean distance decreases, the change is maintained, and the method proceeds with the next cluster. Otherwise, the change is undone. If there is no improvement after one cycle with all participants, the procedure terminates.

The distance measure used here is the so-called transfer distance, which corresponds to the minimum number of element shifts in two partitions to achieve accordance. For example, the distance between partition P₁ = {{1, 2}, {3, 4}} und P₂ = {{1}{2, 3, 4}} is exactly 1, since only participant 2 has to be moved. This distance can be efficiently calculated, especially for larger and more complicated situations. This is done by reducing the transfer distance problem to a so-called linear sum assignment problem (LSAP), for which fast algorithms exist. We use the reduction of [26], which is based on the idea of [27] and a dynamic version of the implementation of the Hungarian Method of [28] to solve the equivalent LSAP. The whole procedure was introduced by [29].

To generate optimal samples from the DPMM, we first drew 500 samples and discarded them (which is called the Burn-In phase) and then generated 160 × S samples afterwards, from which we kept only each 160th sample. This factor 160 is called the thinning parameter. We chose the total number of obtained samples as S = 2048 in this study. Using a thinning parameter >1 has the disadvantage of reducing the approximation precision, since the highest precision will be obtained when thinning = 1, which means that no samples are discarded after the Burn-In phase. For the calculation of the median partition however, this would result in a non-practical computing time because all of the 160 × 2048 will be taken into account. Consequently, and in accordance with [30], we accepted a small loss in precision to achieve realistic computability.

In addition to the median partition, we also calculated the cluster stabilities. This is achieved by identifying the participants who share a cluster in the median partition and extract the cluster numbers of these participants within each partition of the sample. In this way one gets a sub-partition for each sample partition, in which the participants of interest are assigned to either the same or different clusters. With this one can simply determine the mean similarity or distance of the corresponding sub-partition in the median partition to all the associated sub-partitions in the sample partitions.

As measures of correspondence we used two standardized similarity measures, which are based on the transfer distance and the Mirkin Metric (MM) to calculate a number between 0 (maximum dissimilar) and 1 (identical). The measure based on the transfer distance (TD) is called transfer similarity (TS). It is calculated for two partitions of length N using (5)

The measure based on the MM, referred to as the Mirkin Similarity (MS), is calculated for the same partitions as follows (6) c and d correspond to the number of pairs, which are in the same cluster in P₁ and in different clusters in P₂ (= c) and vice versa (= d) [31].

Data

The data used in this study comes from the Socio-Economic Panel Study [32, 33], an ongoing, representative multi-cohort panel study of households and their members in Germany that began in 1984. The SOEP is a research infrastructure unit of the Leibniz Association and located at the German Institute for Economic Research (DIW Berlin), data are collected by the professional fieldwork organization TNS Infratest Sozialforschung/Kantar public (Munich, [33]). After exclusion of all participants who were not sampled both in 2010 and 2017, the final sample that we analyzed consisted of 8170 individuals (53.08% female) with an average age of 51.08 years (SD = 15.75, in 2010)

Limitations

Due to the use of a clustering algorithm, all results presented in this article are exploratory analyses, driven by the data alone. No hypotheses have been made ahead of the analysis. Results should be interpreted with this in mind.

The limited number of concern items sampled and the fact that only three answer option were available for each item limits the precision to which participants could express their concerns. Future research specific to the concerns of participants might provide more options for the participants, and/or cover a wider range of possible concerns. Analyses of the open concern question might also reveal further insights regarding the links between individuals’ concerns and party identification.

Furthermore, we did not analyze ‘secondary beliefs’ regarding individual fields of concern. Respondents might be concurring regarding their concerns (e.g. general economic development) and thus regarding fundamental values and general policy positions (belief system), but they might differ regarding a specific policy solution, like how resources should be used [7–9]. Thus, we find a certain share of party identification within clusters.

A minor remark, one should avoid to confuse the party identification measured in the SOEP with actual voting behavior. In this study, participants were connected to a party only if they responded that they have a specific party identification. The percentage of participants who stated an identification with specific parties are different from the actual voting outcome in the general election 2017 in Germany [35]. In fact, according to [36] party identification is not necessarily a predictor for voting outcome. (Political) events, protest voting or strategic voting in favor of a specific coalition for example shape voting outcome as well. Unfortunately, we did not have access to the voting behavior of our respondents which is why we encourage future research to test this approach with more extensive data.