DCS/CSCI 2350 Social & Economic Networks How do behavior, - - PDF document
10/28/19 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 1 Diffusion of innovations u Studied in
1
u Studied in sociology since 1940s u One’s choice influences others u Indirect/informational effects – social
u Photo/video going viral
u Direct-benefit effects
u Technology adoption– Xbox/PS4, phone, fax,
email, FB
2
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
3
u Complexity u Observability u Trialability u Compatibility
4
6 7
9
u Modeling diffusion u Connection with the things we know
u Homophily u Clustering u The strength of weak ties
11
12
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
13
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
14
15
u Facilitates diffusion u Granovetter's model: the persons with
u Modeling assumption by Kleinberg & many others
18
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
19
20
u Def. A set of initial adopters causes a
u Always happens?
21
22
u Initial adopters u Network structure u Threshold value q
u Quality of product– payoff parameters a and b
u Example: viral marketing
23
u Weak ties are conveyors of information u But cannot “force” adoption of behavior
Would Align with own community
24
u Does clustering help diffusion?
Every node in these clusters have at most 1/3 fraction
Will they ever adopt the new behavior?
25
u Assuming a threshold of q, cascade will be
u Cluster density: Largest fraction such that no node in
the cluster has lower than that fraction of neighbors within the cluster
density = 2/3 > 1-q for q = 2/5
26
27
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 or seed nodes
Granovetter: seeds must have threshold 0 Kleinberg: seeds can be externally set (their thresholds don't matter) What can go wrong? We: seeds can be externally set as long as their threshold requirements are fulfilled at the end of diffusion
28