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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.

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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?

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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

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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

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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

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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”

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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

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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

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Model Results

(Sm

all W

orld

)

• Behavior of PRWa

infle

ctio

n

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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

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Empirical Results

• 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

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Empirical Results

• 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

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Empirical Results

• 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

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Empirical Results

• 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

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Empirical Results

• 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

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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

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Project SummaryResearch Objectives:

•Use critical mass model of social

contagion to predict behavior of

social movements from online data

Key Findings:

•Preliminary findings suggest validity

of critical mass model; measures

show important differences between

non-contagions and social

contagions

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

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: 11/15/2014 Project End Date: 11/14/2017

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Publications, Awards, Patents, or Transitions Attributed to the Grant

• N/A

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Additional Slides

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Motivation“Transformative social movements that go viral,

taking experts by surprise”

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Empirical Results

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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

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Theoretical Background• Previous Work: Centola and Macy 2007

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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