Actions are louder than words in social media

We study the relationship between the level of chatter on a social medium (like TWitter) and the level of the observed actions related to the chatter. For example, in a disaster, how does relief-donation chatter on Twitter correlate with the dollar amount received? One hypothesis is that a fraction of those who act will also tweet about it, which implies linear scaling, action ∝ chatter. On the other hand, if there is a contagion effect (those who tweet about donation incite others to donate) and these incited donors tend to be "quiet" and not broadcast their actions, then we expect superlinear scaling action ∝ chatterγ where γ > 1. We show, using a simple model, that the degree sequence of the social media "follower" network plays a key role in determining the scaling exponent γ. For random graphs and power-law graphs, the scaling exponent is at or near 2 (quadratic amplification). We empirically validate the model's predictions using location-paired donation and social media data from U.S. states after Hurricane Sandy. Understanding the scaling behavior that relates social-media chatter to real physical actions is an important step for estimating the extent of a response and for determining social-media strategies to affect the response.