Opinion Market Model: Stemming Far-Right Opinion Spread using Positive Interventions

TL;DR

The Opinion Market Model is introduced, a two-tier online opinion ecosystem model that considers both inter-opinion interactions and the role of positive interventions that outperforms the state-of-the-art predictive models on both datasets and captures latent cooperation-competition relations.

Abstract

Online extremism has severe societal consequences, including normalizing hate speech, user radicalization, and increased social divisions. Various mitigation strategies have been explored to address these consequences. One such strategy uses positive interventions: controlled signals that add attention to the opinion ecosystem to boost certain opinions. To evaluate the effectiveness of positive interventions, we introduce the Opinion Market Model (OMM), a two-tier online opinion ecosystem model that considers both inter-opinion interactions and the role of positive interventions. The size of the opinion attention market is modeled in the first tier using the multivariate discrete-time Hawkes process; in the second tier, opinions cooperate and compete for market share, given limited attention using the market share attraction model. We demonstrate the convergence of our proposed estimation scheme on a synthetic dataset. Next, we test OMM on two learning tasks, applying to two real-world datasets to predict attention market shares and uncover latent relationships between online items. The first dataset comprises Facebook and Twitter discussions containing moderate and far-right opinions about bushfires and climate change. The second dataset captures popular VEVO artists' YouTube and Twitter attention volumes. OMM outperforms the state-of-the-art predictive models on both datasets and captures latent cooperation-competition relations. We uncover (1) self- and cross-reinforcement between far-right and moderate opinions on the bushfires and (2) pairwise artist relations that correlate with real-world interactions such as collaborations and long-lasting feuds. Lastly, we use OMM as a testbed for positive interventions and show how media coverage modulates the spread of far-right opinions.

Figures (6)

• Figure 1: We illustrate how the positive intervention $X(t)$ (defined in \ref{['eq:opinionsharemodel_tendency']}) suppresses far-right opinions on a simulated toy opinion ecosystem with two far-right (0+, 1+) and two moderate (0-, 1-) opinions. For instance, 0+ and 1+ can represent the opinions "the Greens policies caused the Australian bushfires" and "mainstream media cannot be trusted," respectively; 0- and 1- can be obtained as their negations. Top row: the exogenous signal $S(t)$ (defined in \ref{['eq:opinionvolumemodel']}) and the intervention $X(t)$. Middle row: total daily opinion market size quantified by our model's first tier, split into far-right (+) and moderate (-) opinion volumes. Bottom row: market shares and the interactions between the four opinions estimated by our model's second tier. Nodes are opinions; their sizes indicate market share; edges represent exciting (red) and inhibiting (blue) relations. $X(t)$ suppresses far-right opinions for $t > 50$. Shown are average market shares before (left) and after (right) $t=50$.
• Figure 2: Parameter recovery results on synthetic data. In (a), we show the convergence of the RMSE of the $\boldsymbol{\alpha}$ and $\boldsymbol{\beta}$ estimates and the negative log-likelihood as we increase the training time $T$. In (b), we show the difference between our estimates for $\{\boldsymbol{\mu}, \boldsymbol{\alpha}, \boldsymbol{\beta}, \boldsymbol{\gamma}\}$ and the true values. Dashed green lines and orange lines are the mean and median values, respectively.
• Figure 3: Fitting and predicting with Omm on the Bushfire Opinions dataset. We train Omm on the first 1800 timesteps and predict on timesteps 1801 to 2160 (shaded area). We show results for Facebook (top row) and Twitter (bottom row). (a) Actual (dashed blue lines) vs. fitted/predicted (orange lines) volumes; (b) Actual (left panels) and fitted during training and predicted during testing (right panels) opinion market shares on Facebook and Twitter. We aggregate the far-right and moderate opinions.
• Figure 4: Predictive evaluation of Omm on (a) Bushfire Opinions and (b) VEVO 2017 Top 10 datasets. Boxplots are sorted left to right by the mean (shown with green triangle). Shaded boxplots correspond to versions of Omm. The top panels show the platform-averaged SMAPE of volumes on $\mathcal{T}_{pred}$. Bottom panels plot the KL divergence of predicted and actual market shares.
• Figure 5: Interpretability of Omm. (a) Endogenous elasticities $e(s^p_i(t), \lambda^q(t|j))$ across opinion pairs $(i,j)$ on respective platforms $(p,q)$ in the bushfire dataset. Elasticities have direction and should be read from column (source) to row (target) for the platform and within each matrix. For example, the bottom-right matrix corresponds to influences from Twitter to Twitter; the cell $\{4-, 4+\}$ ({row, column}) is the influence of opinion $4+$ on $4-$, positive and large meaning that $4+$ has a strong reinforcing effect on $4-$. (b) YouTube elasticities $e(s^{YT}_i(t), \lambda^{YT}(t|j))$ across artist pairs $(i,j)$ in the VEVO 2017 Top 10 dataset.