# The Opacity Problem in Social Contagion

## TL;DR

This paper identifies the opacity problem in social contagion studies, where critical peer influence levels are uncertain, leading to overestimations, and proposes a method to better estimate these influence thresholds.

## Contribution

It introduces a novel approach to address the opacity problem by combining interval bounding with node-level prediction to improve critical influence estimates.

## Key findings

- Over-estimation of peer influence is common and significant.
- One in five hashtag adoptions has critical value uncertainty.
- Different assumptions about influence intervals change diffusion conclusions.

## Abstract

Fads, product adoption, mobs, rumors, memes, and emergent norms are diverse social contagions that have been modeled as network cascades. Empirical study of these cascades is vulnerable to what we describe as the "opacity problem": the inability to observe the critical level of peer influence required to trigger an individual's behavioral change. Even with maximal information, network cascades reveal intervals that bound critical levels of peer exposure, rather than critical values themselves. Existing practice uses interval maxima, which systematically over-estimates the social influence required for behavioral change. Simulations reveal that the over-estimation is likely common and large in magnitude. This is confirmed by an empirical study of hashtag cascades among 3.2 million Twitter users: one in five hashtag adoptions suffers critical value uncertainty due to the opacity problem. Different assumptions about these intervals lead to qualitatively different conclusions about the role of peer reinforcement in diffusion. We introduce a solution that combines identifying tightly bounded intervals with predicting uncertain critical values using node-level information.