opinion dynamics in online social networksmmds-data.org/presentations/2014/gollapudi_mmds14.pdf ·...
TRANSCRIPT
Opinion Dynamics in Online Social Networks
Sreenivas Gollapudi
MSR Silicon Valley
Joint work with Abhimanyu Das, Rina Panigrahy, Mahyar Salek, Renato Paes Leme, Emre Kiciman, Kamesh Munagala
Opinions and Social Networks • Opinions of individuals increasingly shaped/influenced by their social network
• Has an effect on what people express and how they express
• Dynamics of opinion formaKon in an online social network • How does online social interacKons affect opinion evoluKon? • Consensus, PolarizaKon effects? • Important for viral markeKng, informaKon disseminaKon, influencers
• Three key components in the dynamics • User • Network • Message
I’ll present three studies highlighKng the role of each of the components in opinion formaKon and its applicaKons
Overview • Role of user
• Focus on the aUributes of the user such as stubbornness or propensity to conform on the dynamics of opinion formaKon.
• Receiver centric • Role of network
• Highlight the effect of the network on well-‐studied phenomenon like wisdom-‐of-‐the-‐crowd to compute the average opinion of a ‘social‘ crowd.
• The ‘social’ aspect of the crowd assumes an underlying dynamics of opinion formaKon • More of an applicaKon of opinion dynamics
• Role of message • Show that considering contents of a message admits fundamentally different problems from the well-‐studied influence maximizaKon.
• Sender centric
Role of the User
Modeling Opinion Dynamics
• NormaKve Influence: Users influenced by opinion of neighbors due to social norms, conformity, group acceptance, etc
• InformaKonal Influence : Users lacking necessary informaKon use opinion of neighbors to update their beliefs
• We consider informaKonal influence while modeling opinion dynamics
How do users update their opinions when faced with opinions of their neighbors?
• Averaging Models: • DeGroot [‘74]: Expressed Opinion shaped by current opinion and weighted average of neighborhood opinions
• Friedkin & Johnsen[‘90]: Expressed Opinion shaped by innate opinion Yi(0), stubbornness parameter α, and average of neighboring opinions
• Voter Models [‘73]: At each step, user randomly adopts one of current neighboring opinions
• Asch’s Conformity Experiments[‘55]: Measure how user response to self-‐evident quesKons changes upon presented with misleading answers from stooges.
(Informational) Opinion Dynamics Models
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Online User Studies • Can we explain user behavior based on exisKng models (Degroot/Stubborn/Voter)?
• User surveys: • esKmate number of dots in images • EsKmate annual sales of various brands.
• For each survey: • Users asked to provide iniKal answers on all quesKons in the survey • Then, each user shown varying number of neighboring answers (syntheKc): generated using Gaussian/Power-‐law/trimodal distribuKons
• Users given opportunity to update their answers
Online User Studies
•
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Neighboring answers: ?
hUp://research.microsoi.com/searchlabs/opinionformaKon
Online User Studies
DistribuKon over stubborn, deGroot and voter
• Voter, deGroot and Friedkin Johnsen models alone cannot capture observed user behavior.
• New model needed that can explain three types of user behavior: • Stubborn: User opinions do not change much -‐ regardless of neighboring opinions • Compromising Behavior (deGroot): Users choose opinions in between their iniKal opinion and neighboring opinions • (Biased) Conforming Behavior (Voter): Users move to opinions chosen at random from neighborhood
Effect of number of neighboring opinions
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Dots Cars/Soda
Stubborn deGroot VoterModel
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Biased Voter Model • User i parameterized by two quanKKes:
• Bias Parameter (pi) and Stubbornness Parameter (αi) • Ni(t) : Set of neighboring opinions at Kme t: [Yn1(t), Yn2(t), .., Ynd(t)]
• Sorted by increasing distance from Yi(t)
• User updates its opinion Yi(t+1) as: • With prob pi set Yi(t+1) = Yn1(t), else with prob pi set Yi(t+1)= Yn2(t), else repeat… • If above step did not set Yi(t+1):
• With prob αi set Yi(t+1) = Yi(t), and with prob (1 -‐ αi ) set Yi(t+1) uniformly at random from [Yi(t) , Yn1(t) ]
Theorem: 1) At equilibrium, distribuKon of different opinions converges (though individual opinions might not converge) 2) If αi, pi < 1, only stable equilibrium corresponds to consensus (might take exponenKal Kme)
Yi(t) Yn1(t) Yn2(t) Ynd(t)
p 1-‐α
p p
Experimental Support for Model
• For conforming users, adopKon of neighboring opinions not uniform random (unlike Voter Model)
• Users give higher weights to “close by” opinions
• For majority of stubborn users, s-‐ values across mulKple quesKons are similar
• Users’ stubbornness behavior relaKvely independent of specific quesKon, number of neighbors
Simulations/Twitter Experiments • Characterize effect of stubborn and bias parameters on Biased Voter opinion dynamics :
• TwiUer Experiments:
• SenKment analysis to extract user senKments from 6-‐months of tweets on four topics • StaKsKcally significant correlaKons between opinions of user and her neighbors on TwiUer
Convergence behavior with different fracKons (5% and 20%) of stubborn nodes with extreme opinions.
Effect of bias parameter on consensus formaKon (No stubborn nodes)
Role of the Network
Wisdom of Crowd (WoC) Effect
• Average opinion of a diverse group of people oien closer to truth than opinion of any single group member.
• Galton: 1906
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WoC in Online Social Networks • Harness collecKve opinions of online users:
• EsKmate average opinion of group of individuals • Online Surveys, MOOCs, Crowdsourcing Plaworms
• Wisdom-‐of-‐Crowd in the presence of social influences? • Social interacKons undermine wisdom-‐of-‐crowd effect [Lorenz et al ‘11]
Key difference: Social InteracKons among users!
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10 Most Popular answers:
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Opinion Dynamics in Social Networks
• Characterize effect of social interacKons on opinion dynamics of online users.
• FJ Opinion FormaKon Model [Friedkin and Johnsen ‘90]: • Directed Social Graph G = (V,E). For i in V: di: out-‐degree of i, Ni: neighborhood of i • For each user i in V:
• Innate Opinion :Unbiased opinion, formed independent of social influences • Propensity-‐to-‐conform α (in [0,1]): How much is user influenced by social neighborhood • Expressed Opinion (at Kme t) : Shaped by innate opinion, and expressed opinion of neighbors
Factor out social influences when esAmaAng aggregate opinion of crowd
Expressed opinion
Innate Opinion
Expressed opinion of neighborhood
Convergence of Opinion Dynamics
• ProposiKon : If all αi > 0, the above opinion dynamics: • Has a unique equilibrium • Converges to its unique equilibrium
• AssumpKon : αi are known:
• Will present one approach for extracKng αs
• User’s α can be approximated by mining user’s social posts. (e.g :by retweet history, senKment analysis over Kme, etc)
FJ Opinion Dynamics :
Debiasing Social Wisdom • Goal: EsKmate unbiased social wisdom evaluate average innate opinion.
• Challenge : • Cannot query enKre network : Efficient sampling schemes • Can only observe expressed opinions, not innate opinion: De-‐biasing required.
• Problem: Sampling algorithm to poll few nodes in social network and use their expressed opinions to esAmate average innate opinion in the network
Y1(t)
Y3(t) Y8(t)
Y7(t) EsKmate
Related Work
• Social Opinion Dynamics: [Degroot, Friedkin-‐Johnsen, Hegselman-‐Krause] • Models for how users update opinion in presence of opinions of neighboring users.
• ExpectaKon Polling: When polled about expectaKons regarding an outcome, users summarize intent of their social neighborhood [Rothschild et al.]
• Social Sampling: Given graph G={V,E}, f:V{0,1}, find fracKon of users with f=1 by sampling a few nodes.
• Users can summarize opinions of their neighborhood • Performance guarantees using degree-‐based sampling + unbiased esKmator
Sampling Algorithms • Two components:
• SelecKng nodes to sample • (Unbiased) esKmator to compute average innate opinion using sampled expressed opinions
• If innate opinions were available, opKmal strategy is to sample uniformly • Uniform sampling with samples gives us esKmator with absolute error and confidence
• Cannot directly use opinion dynamics equaKon to compute innate opinions from expressed opinions • Expensive: needs access to all the expressed opinions
• Each node inherently performs some aggregaKon of neighboring expressed opinions • FJ Opinion dynamics provides a weaker analog of expectaKon polling
• Use αi and graph structure to guide our sampling strategy.
• IntuiKon: Consider k-‐regular social graphs
• Pick users that have high (stubborn) ? • Expressed opinion close to innate opinion
• Pick users that have low (conforming) but their neighbors have high (stubborn) • Expressed opinion of this user gives informaKon about innate opinion of neighborhood
Influence Sampling
Conformity Sampling: Choose random sample with replacement by sample each node i with probability proporKonal to
Influence Sampling: Choose sample S of size r with replacement by sampling each node i with probability proporKonal to ci = Output: EsKmator =
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Influence Sampling • Performance guarantees:
• Results extend to general graphs:
Theorem (Influence Sampling): 1) is an unbiased esKmator of (i.e. E[ ] = ) 2) Using r= samples, | -‐ | < with prob 1-‐ ( : harmonic mean)
Influence Sampling for general graphs: Choose sample S of size r with replacement by sampling each node i with probability proporKonal to |ci|= | | Output: EsKmator =
Number of samples matches (up to factor) opKmal esKmator when innate opinions can be observed!
Methodology
• For each survey: • Users asked to provide iniKal answers on all quesKons in the survey • Then, each user assigned 5 other parKcipants as neighbors. Neighbors allowed to see each other’s answers
• Users given opportunity to update their answers • Process repeated for 3 iteraKons
Screenshots for Survey Experiments
Results
• For each quesKon: • original opinion of user (before interacKon) treated as innate opinion • final opinion of user (at end of experiment) treated as expressed opinion • compute user’s conformity parameter (assuming FJ opinion dynamics in social graph)
• Results: • Measure consistency of for a given user.
• How similar are user’s computed values across the 3 survey quesKons How well does FJ opinion dynamics fit the data.
• Run sampling algorithms to esKmate average innate opinion in the graph using only expressed opinions of sampled nodes and their values.
Estimation Error for Sampling Algorithms • Compare mean/variance of error in esKmaKng avg innate opinion using: Influence Sampling, Conformity Sampling, Uniform Sampling
• Also validated performance of our Influence Sampling algorithm on large-‐scale syntheKc data
Estimating conformity parameter α
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Assumptions
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Verifying homophily Topics Total Number
of nodes Average gap between opinions in an edge
Percentage of edges with opinion gap less than 1
Electric Car 1418 0.75 912(64%)
Solar Energy 2717 0.39 2587(95%)
Global Warming 8964 0.52 7738(86%)
Weight Loss 19906 0.79 13781(69%)
Organic Food 483 0.6 404(83%)
Mathematical Program
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Twitter Experiments • Opinions related to three topics –
• Organic Food • Weight Loss • Electric Car
• Opinions extracted using LexalyKcs • Smoothed senKment values into buckets
• Extracted tweets for each topic using relevant keywords • Data from 12/2012 to 5/2013. • Induced Social Graph using TwiUer Follow Graph
Goal: Extract α values from expressed opinions and graph structure.
Role of the Message
The Art of Persuasion • Act of convincing someone to take acKon
• Persuade someone to buy a product, vote for a candidate etc • Techniques vary widely
• Logical argument, emoKonal appeal, threats, bribes…
• Certain persuasion techniques work beUer for some individuals than others.
• The same assumpKons of adopKon don’t apply to all users
• Sender side problem : Can the sender persuade the recipient to adopt the message and propagate it along the network?
• Fundamentally different from informaKon and opinion dynamics that don’t consider the message explicitly. Rather they are based primarily on acKons of others in the network. E.g., Cascade and threshold models [KKT03].
Dimensions of a Message
• Pertains to persuasion that centers around the exchange of messages between the sender and the receiver.
• Taxonomy of persuasion techniques first proposed by Aristotle in Rhetoric – Pathos (emo/onal), Ethos (ethical), and Logos (logical).
• Logos -‐ I like the Surface Pro because I can install most any program that runs on my regular PC and it adds in stylus/touch controls.
• Pathos -‐ I like the book ``The Valley of Amazement'‘ because Oprah loved this novel.
• Ethos – The sender idenKty/credibility becomes central to the persuasion method.
User Studies
• We selected Logical arguments and EmoKonal appeal as the two dimensions.
• The outcome is the polarity of the opinion a recipient has on the subject (+ve or –ve senKment).
• Varied the topics – Automobiles, Soda, and Organic Food.
• Data • Hand selected messages – around 200. • Got them labeled by Turkers into one of four buckets.
Receiver Side Experiment
• IniKally asked the user to present her senKment on the topic.
• Presented messages of the opposite senKment (from a randomly selected bucket)
• SenKment was measured again. 0
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Coke Hyundai Organic Food
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Shii in senKment – dependent on topic and iniKal senKment
Sender Side Experiment
• Ask the sender to create a message that is likely going to be accepted by many.
• The sender was also asked where he would likely post the message
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Choice of message type is topic dependent
Are Users Really Different?
• The last signal to verify is whether users do exhibit different preferences.
• Measure the relaKve standard deviaKon of their senKment shii.
• A large value corresponds to variability in the populaKon
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Different users are persuaded to different extent by the same message
Model of message propagation
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Verifying the Model at Scale • Dataset from Goel et. al., 2014.
• 1 billion events on TwiUer from 6/2011-‐6/2012 • Event: Earliest instance of a tweet containing URL to <videos, news-‐stories, images, peKKons>
• “Earliest”: None of the user’s direct friends have posted the same content previously.
• For every event, construct diffusion tree using Kmestamps, friend-‐graph.
• Structural virality of informaKon diffusions • Average pairwise distance of nodes in the diffusion tree • To formalize disKncKon between “broadcast” and “viral” diffusion
Our persuasion model explains the variance in structural virality observed by Goel et. al., 2014.
Conclusions
• Rich area for developing models based on our learning from analyzing large data.
• Models for opinion formaKon and persuasion • Empirical analysis to moKvate and validate the models
• Small scale online user studies • Large scale analysis of TwiUer data
• Need for large scale social experiments. • Go beyond the prior approaches in sociology and psychology focusing on small-‐scale experiments and conduct large-‐scale online studies
• Challenges include anonymous users as well as faithful reproducKon of the user’s social interacKons in the experiment.
Thank you!