News media with online comments sections often receive many toxic and hateful posts, and face the question of how to moderate them. Using a dataset of all comments, published and unpublished, from one of the largest Swiss news media sites, we present a statistical approach for observational analyses of their moderation process.
Our motivation is the tradeoff between the decrease in engagement caused directly by a thorough and heavy-handed moderation system against a fear that unmoderated toxic comments beget further toxic behavior. We operationalize this tradeoff as two classes of effects: (1) the effect of toxicity on downstream behavior and (2) the deadweight-loss of moderation procedure on future engagement. Both of these effects are expressed as controlled direct effects (CDEs), as our analyses must condition on a comment's acceptance in order to measure how downstream comments react to it. Intuitively, our estimand is the causal effect in a counterfactual world without pre-publication moderation.

We exploit a regression discontinuity design to aid causal inference in this setting, although unlike a traditional natural experiment, this does not provide purely design-based causal inferences. Building on recent work on multiply-robust estimators of CDEs, we present a novel doubly robust estimator under the natural experiment. By decomposing an estimator into its design-based component and its fundamentally observational components, we are able to reduce the number of unverifiable assumptions required for causal inference. While this decomposition relies on rich data, including published and rejected comments, our approach holds broad applicability for similar moderation systems.