  Online petitions are an important avenue for direct political action, yet the
dynamics that determine when a petition will be successful are not well
understood. Here we analyze the temporal characteristics of online-petition
signing behavior in order to identify systematic differences between popular
petitions, which receive a high volume of signatures, and unpopular ones. We
find that, in line with other temporal characterizations of human activity, the
signing process is typically non-Poissonian and non-homogeneous in time.
However, this process exhibits anomalously high memory for human activity,
possibly indicating that synchronized external influence or contagion play and
important role. More interestingly, we find clear differences in the
characteristics of the inter-event time distributions depending on the total
number of signatures that petitions receive, independently of the total
duration of the petitions. Specifically, popular petitions that attract a large
volume of signatures exhibit more variance in the distribution of inter-event
times than unpopular petitions with only a few signatures, which could be
considered an indication that the former are more bursty. However, petitions
with large signature volume are less bursty according to measures that consider
the time ordering of inter-event times. Our results, therefore, emphasize the
importance of accounting for time ordering to characterize human activity.
