DCS/CSCI 2350 Social & Economic Networks How do behavior, - - PDF document
3/5/18 DCS/CSCI 2350 Social & Economic Networks How do behavior, opinion, technology, etc. propagate in a network? Cascading Behavior in Networks Reading: Ch 19 of EK Mohammad T . Irfan Diffusion of innovations u Studied in
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u Studied in sociology since 1940s u One’s choice influences others
u Indirect/informational effects – social learning
u Photo/video going viral
u Direct-benefit effects
u Technology adoption– Xbox/PS4, phone, fax, email,
FB
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u Adoption of hybrid seed corn in Iowa
u Ryan and Gross, 1943
u Adoption of tetracycline by US doctors
u Coleman, Katz, and Menzel, 1966
u Shared ingredients
u Indirect effects u Adoption was high-risk, high-gain u Early adopters had higher socioeconomic status u Social structure was important– visibility of
neighbors’ activity
u Diffusion of Innovations– Everett Rogers (1995)
u Complexity u Observability u Trialability u Compatibility
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u Modeling diffusion u Connection with the things we know
u Homophily u Clustering u The strength of weak ties
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u Mark Granovetter's threshold model of
u Side note: collective behavior vs. collective action
u Model: An individual will adopt action A if at
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u Example
u Emergence of a riot in a crowd of 100 people
(complete graph)
u Thresholds of individuals to get violent
u 0, 1, 2, ..., 99
u What will happen?
u Extensions
u General network u Distribution of thresholds
u Difference with Schelling's model: In Granovetter's
model, slight change of thresholds may lead to completely different global outcome. Extremely important that someone has a threshold
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u Facilitates diffusion u Granovetter's model: the persons with
u Modeling assumption by Kleinberg & many others
u Initially everyone does B u Payoff parameters: b = 2, a = 3 u Threshold for switching from B to A, q = 2/5 u We will set two initial adopters of A and "play
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u Def. A set of initial adopters causes a
u Always happens?
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u Initial adopters u Network structure u Threshold value q
u Quality of product– payoff parameters a and b
u Example: viral marketing
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u Weak ties are conveyors of information u But cannot “force” adoption of behavior
Would Align with own community
u Does clustering help diffusion?
Every node in these clusters have at most 1/3 fraction
Will they ever adopt the new behavior?
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u Thresholds are heterogeneous u Directed, asymmetric network u Relationships can be positive or negative
u Switching back and forth two actions are allowed
u Initial adopters (I.A.)
Granovetter: I.A. must have threshold 0 Kleinberg: I.A. can be externally set (their thresholds don't matter) What can go wrong? We: I.A. can be externally set as long as their threshold requirements are fulfilled at the end of diffusion
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u Model parameters
u Threshold of each node u Influence level from one node to another
u Want to know: What will they do?
DeMint (R, SC) Schumer (D, NY) Paul (R, KY)
Yea/+1 Nay/-1
Johnson (R, WI) Sanders (I, VT)
Yea/+1 Nay/-1
2 4 6
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2 4 6
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Who are the
most influential senators?
110th Congress 2007-09
influential nodes
Who are the
most influential senators?
110th Congress 2007-09
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112th Congress 2011-13 Who are the
most influential senators?
112th Congress 2011-13
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u Main reading: Ch 19 of EK u Granovetter’s threshold model
u http://vserver1.cscs.lsa.umich.edu/~spage/
ONLINECOURSE/R2Granovetter.pdf
u Collective action
u My dissertation
u http://www.bowdoin.edu/~mirfan/papers/
Mohammad_Tanvir_Irfan_Dissertation.pdf
u Section 2.1.1 and Appendix 2A
u External links
u Gladwell’s view:
http://www.youtube.com/watch?v=YFbkVL1X9M8
u Watts’ view:
http://www.fastcompany.com/641124/tipping-point- toast