Contagion Dynamics in Online Petitions

The internet and today’s online social media culture provide various possibilities for citizens to express their opinion, political viewpoint and offers new means of participation to individuals. One of these are online petitions. These petitions are initiated and signed online by citizen on petition platforms such as openpetition.de. These platforms provide a low-threshold opportunity to articulate political interests.

From a scientific point of view online petitions are very interesting. Unlike traditional petitions online petitions collected detailed data concerning the spatio-temporal process of signing. Because of the abundance of petitions (thousands) and the signing events (millions) one can analyse petition dynamics to better understand the associated contagion processes. When does a petition become viral? What role is played by mass media in setting off explosive signing events? What topics are particularly likely to go viral? Are petitions in urban areas significantly different in terms of topics and virulence than in rural areas?

For the open petition project we are collaborating with the initiators of the petition platform openpetition.de. We are currently analyzing thousands of spatio-temporally resolved online petitions. The results of this extensive project will be important for the understanding of digital contagion phenomenon in general and thus specifically interesting for designing online campaigns. We are specfically interested in how our results can be leveraged to design online information campaigns that are connected to public health topics, e.g. vaccination.

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Figure 1: Epicurve of four online petitions. Althought the resulting number of votes of petition A, C and D are similar, their epicurves look different.


One of the first obvious findings of our analysis is that the dynamics of online petitions can substantially vary, not only in the eventual number of signatures reached but also in the typical time course of signing events. Figure 1 shows the initial signing dynamics of four sample petitions.

More importantly, signing dynamics differs substantially from regular Poissonian statistics, which however is often assumed as a basic model for petition dynamics. Generically, petition dynamics is not only bursty but exhibits significant memory effects in signing events. Fig. 2 show a phase diagram of an ensemble of petitions in diagram that is spanned by the memory and the burstiness coefficients. For ordinary Poission processes both quantities are zero. We see in this figure that both M and B are significantly positive which means that memory effects and burstiness are strong in petition dynamics. Interestingly petition dynamics is also systematically different from other dynamical processes related to human behavior.
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Figure 2: top: Burstiness B of 1538 petitions with ≥ 1000 votes versus the final number of votes of a petition. bottom: Burstiness B and memory M plane with dot cloud of B and M values of single petitions. The marked area indicates the typical position of the time pattern of human activities (e.g. mail traffic or call center and phone initiation records) according to K.-I. Goh and A.-L. Barabasi Burstiness and memory in complex systems.