# Measuring Polarization in Online Debates
## 5 Empirical Evaluation  
In this section, we present an empirical evaluation to detect if our optimization algorithm can find distinctive polarization in debates obtained from six representative subreddits with different topics: Halloween, travel, movies, Bitcoin, politics, and worldnews. Intuitively, we expect to have debates with low polarization in the Halloween and travel topics, those with higher polarization in the movies and Bitcoin topics, and those with the highest polarization in the politics and worldnews topics. From each subreddit, we downloaded debates from the last month, excluding the most recent debates that probably are still active, with comments per debate ranging from 50 to 500, and with a limit of 100 debates per subreddit. Table 1 shows the average results for the polarization value (_BipPol_) obtained with our algorithm for each of the six sets of debates using the algorithm with the two initialization methods, so we have two rows per subreddit. In any case, the maximum number of iterations is fixed to the number of users in the debate graph. To analyze the reasons behind the _BipPol_ values obtained, we also show the corresponding average values for the factors _LC_, _RC_ (that make the _SC_ value), and _SWeight_. The table also shows the total number of debates in each set, and the average values for the number of users and number of edges in their corresponding user debate graphs. The average results for the different subreddits show some differences in the _BipPol_ values \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Subreddit** & **\#Debates** & \(|\mathcal{C}|\) & \(|\mathcal{E}|\) & **Alg.** & _BipPol_ & _LC_ & _RC_ & _SWeight_ \\ \hline Halloween & 74 & 78.16 & 30.09 & g0 & 0.4053 & 0.3681 & 0.5603 & 2.1594 \\  & & & g1 & 0.4087 & 0.3685 & 0.5654 & 2.1643 \\ \hline travel & 49 & 75.10 & 60.57 & g0 & 0.4246 & 0.4835 & 0.4005 & 2.3808 \\  & & & g1 & 0.4245 & 0.4836 & 0.4004 & 2.3808 \\ \hline movies & 100 & 146.51 & 123.23 & g0 & 0.4785 & 0.4826 & 0.4189 & 2.3930 \\  & & & g1 & 0.4783 & 0.4825 & 0.4189 & 2.3926 \\ \hline Bitcoin & 100 & 135.01 & 95.82 & g0 & 0.4879 & 0.5332 & 0.3862 & 2.4360 \\  & & & g1 & 0.4883 & 0.5333 & 0.3863 & 2.4367 \\ \hline politics & 100 & 205.93 & 160.72 & g0 & 0.5104 & 0.5713 & 0.3511 & 2.5742 \\  & & & g1 & 0.5105 & 0.5712 & 0.3511 & 2.5752 \\ \hline worldnews & 100 & 148.40 & 163.36 & g0 & 0.5141 & 0.4950 & 0.4076 & 2.5732 \\  & & & g1 & 0.5142 & 0.4949 & 0.4076 & 2.5732 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results with different initialization algorithms with debates from several subreddits. The numbers shown are average values over the debates of each subreddit. Figure 4: Bipartite graph showing sets \(L\) (red nodes) and \(R\) (blue nodes) after running Algorithm 1 using the UDebG of Figure 3 as input. such that we can divide the six subreddits into three groups: subreddits with the lowest _BipPol_, the middle one, and the highest one. In the first group (Halloween and travel), we observe average _BipPol_ values around 0.4. However, looking into the value of the different factors, we can explain why there is an slightly higher _BipPol_ value for the travel subreddit. For the Halloween subreddit, we observe that the agreement users group is more relevant (_RC_ value around 0.56 in contrast to a _LC_ value around 0.36) and a _SWeight_ value around 2.15 (close to the neutral value for the global sentiment between users in agreement and disagreement). By contrast, for the travel subreddit, the _LC_ value is higher than the _RC_ value, but they are more balanced (0.48 versus 0.40), and the _SWeight_ value is around 2.38. So now, negative interactions between both groups are more significant. These differences make sense if one looks into the nature of the discussions in both these subreddits. In the Halloween case, discussions are mainly friendly, discussing ideas about costumes and Halloween decorations. However, in the travel case, we find some controversies in many discussions about certain touristic destinations.