Online movements spread explosively rather than diffusively

I’m very happy that a favourite!! paper of mine is finally published in EPJ Data Science. The paper that is titled “Rapid rise and decay in petition signing” tries to analyse and model the dynamics of popularity of online petitions.

Traditionally, collective action is known to follow a chain-reaction type of dynamics with a critical mass and a tipping point that could be all described with an S-shaped curve (schematically shown in Figure below), however, we spent about 3 years to only fail at finding any type of Sigmoid function that can fit our data!

Screen Shot 2017-10-02 at 19.17.22

The S-curve of success that is not relevant anymore!

Instead, we tried to a fit a multiplicative model with a strong decay modification. That was a much better fit to the data. It grows exponentially at the beginning, but then comes a very rapid decay in the novelty of the movement. Remember, our attention span is very short in the digital age!

Apart from the mathematical details of this fitting exercise, there are important consequences emerging from this observation:

  1. Online collective actions have very different dynamics to what we know from traditional offline movements.
  2. Online movements are explosive and much less predictable.
  3. The typical time-scale of such movements is in the range of hours and few days at longest, not weeks or years!
  4. This fast dynamic is independent of the extent of the success and prevalence of the movement.
  5. Instead of reaching a critical mass in later stages of a movement, one has to try to have a large initial momentum in order to success.

There is more to this obviously and if you’re interested, please have a look at the paper here.

The abstract of the paper reads:

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 ( and 1,800 petitions to the US White House site (, 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% 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.




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