# On Simulating the Propagation and Countermeasures of Hate Speech in Social Networks
## 6 Simulation Results
### Countermeasures Simulation Results
#### 6.2.1 Educational Bias  
As previously described in Section 5.1, simulations of the usage of education as a countermeasure are based on our definition of hateful user in Section 3. Specifically, we set a user to be hateful when its hate score is larger than a given threshold. As hate score is assigned considering a Gamma distribution, we then induce stronger positive bias in the users' hate score by decreasing the \(\alpha\) parameter in the distribution (see Figure 5).  
Our simulations show that the effect of this countermeasure is two-fold. On the one hand, considering the fraction of hateful persons, we can observe, from the top of Figure 8, that if we take as reference the hate scores set when \(\alpha=10\) in the Gamma distribution, then, all subsequent (lower) \(\alpha\) values imply a substantial decrease in the amount of hateful persons, even if they are not completely removed from the society. Indeed, even with the strongest educational bias, which sets \(\alpha=2\) and reduces the fraction of hateful persons below 0.02 for all the considered network sizes, the amount of haters does not fall below of 1%. Similarly, as shown in the middle of Figure 8, the amount of hateful posts decreases down to below 0.27 for all network sizes when \(\alpha=2\). Additional tests show that the risk of swaps to a hateful society drops from 25% below 5% for the values of \(\alpha=6,4,2\) for all network sizes. These tests also show that the mean hate score have similar values for all network sizes and steadily decrease from ca. 0.4 for the original Gamma distribution (i.e., with \(\alpha=10\)), down to a ca. 0.1 for \(\alpha=2\). This can be explained by the structure of the network that results from using preferential attachment, where some nodes have unproportionally higher influence. Hence, applying a skewed distribution upon it can skew the final distribution even more after opinion diffusion.  
\begin{table}
\begin{tabular}{l c c c c c} \hline
**Metric** & \multicolumn{4}{c}{**Opinion Diffusion Starts after \(t\) Ticks**} \\ \hline  & **0** & **500** & **1000** & **2000** & **5000** \\ \hline Fraction of H users & 0.024 & 0.027 & 0.039 & 0.048 & 0.062 \\ Fraction of posts by H & 0.210 & 0.256 & 0.320 & 0.361 & 0.429 \\ \hline Ratio network density H/N & 79.130 & 79.605 & 58.116 & 63.550 & 26.061 \\ Reciprocity between N & 0.888 & 0.886 & 0.888 & 0.887 & 0.889 \\ Reciprocity between H & 0.725 & 0.751 & 0.736 & 0.758 & 0.761 \\ \hline Mean followers of N & 1.783 & 1.774 & 1.772 & 1.770 & 1.765 \\ Mean followers of H & 2.312 & 2.626 & 2.382 & 2.450 & 2.263 \\ Mean followees of N & 1.788 & 1.784 & 1.784 & 1.784 & 1.780 \\ Mean followees of H & 2.311 & 2.383 & 2.15 On the other hand, the density among hateful users increases as depicted on the bottom of Figure 8. The same happens for the reciprocity and mean follower-followee ratio. This increase is due to the fact that education impedes the emergence of hate strains, so that hateful persons stay among like-minded within highly densely connected hate cores. Additionally, the mean path length of hateful posts increases linearly. This is a consequence of the fact that, although hate posts have much less room to unfold by reposting within hate strains (see Figure 3), hateful posts can still make very long paths by circulating posts between persons within a hate core (see Figure 1). Overall, and despite this increase of the density, the effect of the education countermeasure can be summarised as being very successful.