1. Tracking Critical-Mass Outbreaks in Social Contagions (FA9550-15-1-00036 DEF)
PI: Michael Macy (Cornell University; Sociology)
Co-PI: Clay Fink (JHU-APL)
Co-PI: Vladimir Barash (Graphika)
Co-PI: John Kelly (Graphika)
Researchers: Aurora Schmidt (JHU-APL)
Chris Cameron (Cornell)
AFOSR Program Review: Trust & Influence
May 11-15, 2015, USAF Academy, CO.

2. Motivation
Social contagions - ideas or patterns of behavior that spread through social networks - contribute to the spread of social movements and mass mobilization
Is it possible to detect and anticipate the appearance of such movements from observational data?
Mass mobilizations such as the Egyptian revolution and protests in Russia, and Nigeria may not always be predictable, but the science about how people connect and communicate help us understand when such events are likely, or already underway and under-the-radar.

3. Approach
Social media gives us a view into large-scale online social activity; it has also played a role in actual offline events, including social movements
We will evaluate models of social contagions (Barash et al. 2011, Centola & Macy, 2007) using social media data to characterize online content and activity related to social movements with the goal of anticipating the scope of their impact
Under this grant we will test theories of social contagion using Twitter data associated with recent mass mobilization events. Using hashtags and topical tweets as the digital traces of transmitted ideas, we will test if theoretical models of social contagion with this real world data to determine if such phenomena can be detected.

4. Outcomes
Identify social movements from online data; for any identified social movement, anticipate viral outbreaks within the movement’s online component; gain a better understanding of why some movements succeed and persist and others do not
User these same methods to measure the effectiveness of online messaging campaigns by the USG or associated NGOs in regions of interest
This sort of research relates directly to USG needs in the areas of information operations and social/cultural situation awareness. For example, understanding the mechanisms of social contagion online, and their relationship to offline behavior, may allow us to observe social movements as they are developing. It may also allow us to measure the effectiveness of online messaging campaigns.

5. Grant Progress Before Grant: Critical mass model of social contagion
Theoretical results
Collections of online activity (Twitter) from Russia, Turkey, Egypt, and Nigeria
First Six Months (11/15/14 – 5/14/15):
Processed datasets from Twitter for analysis (Nigeria and Russia)
Evaluating theoretical measures for characterizing social contagions on these datasets

6. Social Contagions
Social contagions are social phenomena that can and do spread via social networks
Some social contagions require social reinforcement. When a contagion (social or otherwise) requires social reinforcement, we say the contagion is “complex”
credible information? believable rumor? desirable product?
Even involuntary emotional contagion can be triggered if enough peers adopt

7. Complex Contagions
A person might see how their friends react to an idea or product before forming her own opinion
Higher risk behaviors (expensive purchases, illegal protesting) become more likely with social reinforcement from multiple peers (1 less convincing than 5)
Normative contagions depend on social approval
How are social contagions evaluated?

8. Theoretical Model
Complex contagions model higher-risk behaviors like social movement participation…
… but spread slowly unless and until they reach critical mass
Critical mass is identified by a spike in the contagion growth curve and a drop in the network overlap between current + previous adopters as the contagion spreads from an initial dense core to the wider network

9. Model Results Behavior of PRWa (Small World) inflection
Looked at at tweets collected from Nigeria containing hashtags that were new on or after January 15, 2014 that involved 1000 or more unique users. As the social graph we used the combined retweet and mention/reply graphs for users.

10. Empirical Results
Looked at tweets collected from Nigeria containing hashtags that were new on or after 1/15/14 and 11/15/14
We analyzed these hashtags for signs of complex contagion and critical mass
Two case studies: #mh370 and #bringbackourgirls
We looked at at tweets collected from Nigeria containing hashtags that were new on or after January 15, 2014 that involved 1000 or more unique users. For the social graph we used the combined retweet and mention/reply graphs for users. This graph is an approximation of a user’s friend graph and the tweets they were likely exposed to. In this presentation we contrast two different hashtags: #mh370 which referenced the disappearance of Malaysian Air 370 in March 2014; and the #bringbackourgirls hashtag which referenced the April 2014 kidnapping of 200+ schoolgirls from the north eastern Nigerian city of Chibok by the Boko Haram extremist group. These tags make an interesting contrast: #mh370 was exclusively related to a news story while #bringbackourgirls, while also related to a news event, was associated with a social movement calling for government action and accountability in regard to dealing with the kidnaping, and the Boko Haram crisis at large. We use a number of measures to compare these data streams.

11. Empirical Results
In the following slides, #mh370 is on the left and #bringbackourgirls is on the right.
We first looked at how Twitter volume compared to the news cycle. In the case of #mh370, Twitter volume and the news cycle track. We see a different story for BBOG. The girls were kidnapped on April 14, For the first two weeks there was little press attention and some small amount of traffic concerning the event on Twitter. The #bringbackourgirls hashtag was introduced on April 23. It showed an initial spike of activity, but did not really take off until rallies and protests occurred in early May. It was only after this that the issue of the abducted girls became an international news story.
We compared the daily tweet volume of each tag with daily counts of unique news stores about each topic
#mh370 represented a major news story and the tweets track the news cycle
In contrast, tweets related to the Chibok kidnapping lead the news cycle by well over a week

12. Empirical Results
Mass adoptions of a behavior – in our case, the use of hashtags – are not always social contagions. Hashtag adoption may be based on exogenous sources (due to discussions of the tag in the media, for example), or due to a large number of users spontaneous converging on an obvious hashtag formulation (such as #mh370). Since we have only an sample of the actual online activity, we do see a number of adoptions that have a adoption threshold of zero. One would expect that if this were due to having an incomplete sample of the social graph, the proportion of zero adopters would be generally the same from tag to tag. When comparing the two tags here, we see that at its peak of activity, #mh370 has a much higher level of zero adoptions than #bringbackourgirls suggesting exogenous or other sources.
Testing for spread through social network: calculate fraction of innovators (adopting users with no adopter neighbors) over time
#mh370 has a consistently large fraction of innovators
#bringbackourgirls has a consistently small fraction of innovators, even during adoption peak

13. Empirical Results
Complex contagion theory assumes a fixed threshold >= 2 for all nodes in a graph. This is unlikely to hold in the real world. On Twitter, for example, each user may have their own unique threshold and the threshold for them may vary from topic to topic. So we expect a range of threshold values (k) for users adopting a hashtag. We can look, however, at how likely it is for a user to have a threshold >= 2 for a given hashtag. The CDFs show a clear difference in the observed thresholds between the two tags.
Testing for multiple reinforcements (complex contagion) we look at the adoption thresholds (k) for the population of users who adopted the tag
The number of users adopting with two or more adopting neighbors is much greater for #bringbackourgirls than for #mh370

14. Empirical Results
The critical mass model requires an initial dense network for a contagion to break out. We look at the network of adopting users and see if it is denser than expected early on in the hashtag’s lifetime. We test this by looking at the first m users and see if that network is denser than a network formed by a random selection of m adopting users. We see this for #bringbackourgirls and not at all for #mh370.
Testing for dense contagion core: we looked at the first m users that adopted a tag and compared the resulting network to networks associated with m randomly selected adopters as an indicator of the density of the network of originating users
#bringbackourgirls core is much more dense than #mh370

15. Empirical Results
Another measure of local network density is to look at overlap: at the time each user adopts, this is the density of the ties between their friends that have already adopted. We looked at the mean overlap across all adopters on each day and compared it to the cumulative number of adoptions up to and including that day. The critical mass model suggests that a contagion will break out or go viral at the point network density drops due to the increase in long range ties across the network. #bringbackourgirls seems to exhibit this phenomena while #mh370 does not.
Overlap: at the time each user adopts, the density of the ties between their friends that have already adopted
We calculate the mean overlap of all adopters on each day
A drop in the density of ties between adopting users as the number of adoptions is increasing may be evidence of critical mass; this is seen for #bringbackourgirls but not #mh370

16. Next Steps
Extend the measures we have discussed to all Nigerian hashtags to test their effectiveness in identifying complex contagions
Extend work to Russian and Egyptian datasets
For Egypt, we have 700 expert-identified Arab Spring related hashtags to examine; overall we have 1,200 hashtags used more than 500 times and 4,000 hashtags used more than 100 times
Investigate language-related signals associated with social contagions
Begin integration of this work into an a prototype tool for online detection of social contagions

17. Project Start Date: 11/15/2014 Project End Date: 11/14/2017
Project Summary
Research Objectives:
Use critical mass model of social contagion to predict behavior of social movements from online data
Technical Approach:
Use theory-driven measures of social media activity to characterize content related to growing social movements
Base initial work on post hoc analysis collections of Twitter data from multiple regions
Key Findings:
Preliminary findings suggest validity of critical mass model; measures show important differences between non-contagions and social contagions
Benefits to the wider academic or
DoD community:
Identifying/anticipating social movements from online signatures
Measures of effectiveness for online messaging campaigns
Project Start Date: 11/15/ Project End Date: 11/14/2017

18. Publications, Awards, Patents, or Transitions Attributed to the Grant
N/A

19. Additional Slides

20. Motivation
“Transformative social movements that go viral, taking experts by surprise”

21. Empirical Results

22. Theoretical Background
Formal model: networked population of N agents with s << N agents, each agent adopts contagion iff at least a of their neighbors has adopted. No un-adoptions.
When an agent adopts after more than two of their neighbors have adopted, we call this a complex contagion; a simple contagion occurs when an agent adopts after only one neighbor has adopted

23. Theoretical Background
Previous Work: Centola and Macy 2007

24. Theoretical Results Inflection point of PRWa is a critical mass point
Once inflection point is reached, each additional infected node further increases PRWa, creating a positive feedback effect
At this point, a complex contagion starts to behave more like a simple contagion, allowing the infection to spread across the network