Lost in Re-Election: A Tale of Two Spanish Online Campaigns

Abstract

In the 2010 decade, Spanish politics have transitioned from bipartidism to multipartidism. This change led to an unstable situation which eventually led to the rare scenario of two general elections within six months. The two elections had a mayor difference: two important left-wing parties formed a coalition in the second election while they had run separately in the first one. In the second election and after merging, the coalition lost around 1M votes, contradicting opinion polls. In this study, we perform community analysis of the retweet networks of the online campaigns to assess whether activity in Twitter reflects the outcome of both elections. The results show that the left-wing parties lost more online supporters than the other parties. Furthermore, we find that Twitter activity of the supporters unveils a decrease in engagement especially marked for the smaller party in the coalition, in line with post-electoral traditional polls.

Appendices

A Methods

1.1 A.1 N-Louvain Method

The Louvian method [4] is widely used as a community detection algorithm because it is efficient and finds the correct clustering in certain types of networks. However, some care needs to be taken when applying this algorithm in our context. In particular, since the algorithm has a random component, different executions may typically produce different partitions for the same network. To obtain robust results and find a reliable cluster assignment, we follow the method introduced in [2], which performs multiple executions of the Louvain algorithm and only considers nodes that fall almost all the times into the same cluster.

To identify each cluster across executions, we improve the previous method by applying the Jaccard index [13] to every pair of clusters $c_i$ and $c_j$ across different executions:

$$\begin{aligned} J(c_i,c_j) = { |c_i \cap c_j| \over |c_i \cup c_j| }. \end{aligned}$$

Thus, clusters across executions are matched if they are the most similar ones. This allows us to assess the proportion of times a node falls within the same cluster. Finally, the method assigns to each cluster all the nodes that appear in that cluster in at least a fraction $(1-\varepsilon )$ of the partitions created, that is to say, $\varepsilon$ represents the sensibility level of the algorithm ($\varepsilon =0.05$ in this study). This procedure allows to validate the results of the community detection algorithm and to guarantee that all the nodes that are assigned to a cluster do actually belong to it with a given confidence. The remaining nodes, that cannot be assigned in a stable way to any of the main clusters, are left out from all the clusters.

1.2 A.2 Cluster Changes Between Networks

To characterize how users change between two consecutive networks, $G_1$ and $G_2$, we consider five possible categories, depending on how a user i that belongs to a cluster in $G_1$ is related to the clustering in $G_2$. Let $c_1(i)$ and $c_2(i)$ denote the cluster to which i belongs in $G_1$ and $G_2$, respectively. There are three main possible scenarios, either the user belongs to the same cluster in both networks,

• 1. $c_1(i)=c_2(i)$ (Same cluster),

• 2. it belongs to different clusters, $c_1(i)\ne c_2(i)$ (Other cluster),

• 3. or i does not fall robustly in any cluster of $G_2$. In this case, we can still assign a cluster to i depending on whether:

  • (a) i retweeted users belonging to the same cluster $c_1(i)$ (we call this category Associated with same cluster), or

  • (b) i retweeted users belonging to another cluster (Associated with other cluster).

  • (c) Finally, if the level of activity of i does not reach the threshold to be included in $G_2$ (we only include interactions that occur at least three times), we assign i to the category None.

B Supporting Information

Table 2. Twitter accounts of the selected political parties and candidates which were used to retrieve the datasets.

Table 3. Retweet network indicators for 2015 and 2016: number of retweets for the whole election (# tweets), number of nodes (N) and edges (E) in the network, clustering coefficient (cl) and average path length ($\ell$).

Table 4. Participation, percentage of obtained votes and parliament seats per party for the 2015 and 2016 elections. Pod+ stands for the sum of Podemos, En Comú Podem, En Marea, and Compromis. In 2016 IU is added to this sum as well.

Table 5. Main clusters per party. In columns: cluster sizes in 2015 and 2016, # of users present in the cluster in 2015 but not in 2016 (lost) and the corresponding percentage, # of users present in the cluster in 2016 but not in 2015 (new), difference (balance) between new and lost users. Last line (UP) is the sum of ECP, Podemos and IU

Fig. 4.

Redistribution of cluster users: amount of users from a 2015 cluster (left) in the 2016 clusters (right). (Color figure online)