Contemporary collective action, much of which involves social media and other
Internet-based platforms, leaves a digital imprint which may be harvested to
better understand the dynamics of mobilization. Petition signing is an example
of collective action which has gained in popularity with rising use of social
media and provides such data for the whole population of petition signatories
for a given platform. This paper tracks the growth curves of all 20,000
petitions to the UK government over 18 months, analyzing the rate of growth and
outreach mechanism. Previous research has suggested the importance of the first
day to the ultimate success of a petition, but has not examined early growth
within that day, made possible here through hourly resolution in the data. The
analysis shows that the vast majority of petitions do not achieve any measure
of success; over 99 percent fail to get the 10,000 signatures required for an
official response and only 0.1 percent attain the 100,000 required for a
parliamentary debate. We analyze the data through a multiplicative process
model framework to explain the heterogeneous growth of signatures at the
population level. We define and measure an average outreach factor for
petitions and show that it decays very fast (reducing to 0.1% after 10 hours).
After 24 hours, a petition's fate is virtually set. The findings seem to
challenge conventional analyses of collective action from economics and
political science, where the production function has been assumed to follow an
S-shaped curve.Comment: Submitted to EPJ Data Scienc