  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 petitions website
(http://epetitions.direct.gov.uk) and 1,800 petitions to the US White House
site (https://petitions.whitehouse.gov), 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 (0.7 percent in the US). 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 pervent
after 10 hours in the UK and 30 hours in the US). After a day or two, a
petition's fate is virtually set. The findings challenge conventional analyses
of collective action from economics and political science, where the production
function has been assumed to follow an S-shaped curve.
