  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.
