Social Contagion Social Contagion Models Principles of Complex - PowerPoint PPT Presentation

Social Contagion Social Contagion Social Contagion Models Principles of Complex Systems Background Granovetter’s model Course 300, Fall, 2008 Network version Groups Chaos References Prof. Peter Dodds Department of Mathematics & Statistics University of Vermont Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License . Frame 1/86

Social Contagion Outline Social Contagion Models Background Granovetter’s model Network version Groups Social Contagion Models Chaos Background References Granovetter’s model Network version Groups Chaos References Frame 2/86

Social Contagion Social Contagion Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Frame 4/86

Social Contagion Social Contagion Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Frame 5/86

Social Contagion Social Contagion Social Contagion Models Examples abound Background Granovetter’s model Network version ◮ fashion Groups ◮ Harry Potter Chaos ◮ striking References ◮ voting ◮ smoking ( ⊞ ) [6] ◮ gossip ◮ residential ◮ Rubik’s cube segregation [15] ◮ religious beliefs ◮ ipods ◮ leaving lectures ◮ obesity ( ⊞ ) [5] SIR and SIRS contagion possible ◮ Classes of behavior versus specific behavior: dieting Frame 6/86

Social Contagion Framingham heart study: Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Evolving network stories: ◮ The spread of quitting smoking ( ⊞ ) [6] ◮ The spread of spreading ( ⊞ ) [5] Frame 7/86

Social Contagion Social Contagion Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Two focuses for us ◮ Widespread media influence ◮ Word-of-mouth influence Frame 8/86

Social Contagion Social Contagion Social Contagion Models Background Granovetter’s model Network version We need to understand influence Groups Chaos ◮ Who influences whom? Very hard to measure... References ◮ What kinds of influence response functions are there? ◮ Are some individuals super influencers? Highly popularized by Gladwell [8] as ‘connectors’ ◮ The infectious idea of opinion leaders (Katz and Lazarsfeld) [12] Frame 9/86

Social Contagion The hypodermic model of influence Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Frame 10/86

The two step model of influence [12] Social Contagion Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Frame 11/86

Social Contagion The general model of influence Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Frame 12/86

Social Contagion Social Contagion Social Contagion Models Background Why do things spread? Granovetter’s model Network version Groups ◮ Because of system level properties? Chaos References ◮ Or properties of special individuals? ◮ Is the match that lights the fire important? ◮ Yes. But only because we are narrative-making machines... ◮ We like to think things happened for reasons... ◮ System/group properties harder to understand ◮ Always good to examine what is said before and after the fact... Frame 13/86

Social Contagion The Mona Lisa Social Contagion Models Background Granovetter’s model Network version Groups Chaos References ◮ “Becoming Mona Lisa: The Making of a Global Icon”—David Sassoon ◮ Not the world’s greatest painting from the start... Frame 14/86 ◮ Escalation through theft, vandalism, parody, ...

Social Contagion The completely unpredicted fall of Eastern Europe Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Timur Kuran: [13, 14] “Now Out of Never: The Element of Frame 15/86 Surprise in the East European Revolution of 1989”

Social Contagion The dismal predictive powers of editors... Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Frame 16/86

Social Contagion Social Contagion Social Contagion Models Background Granovetter’s model Network version Groups Chaos Messing with social connections References ◮ Ads based on message content (e.g., Google and email) ◮ Buzz media ◮ Facebook’s advertising: Beacon ( ⊞ ) Frame 17/86

Social Contagion Getting others to do things for you Social Contagion Models Background A very good book: ‘Influence’ by Robert Cialdini [7] Granovetter’s model Network version Groups Six modes of influence Chaos References 1. Reciprocation: The Old Give and Take... and Take 2. Commitment and Consistency: Hobgoblins of the Mind 3. Social Proof: Truths Are Us 4. Liking: The Friendly Thief 5. Authority: Directed Deference 6. Scarcity: The Rule of the Few Frame 18/86

Social Contagion Examples Social Contagion Models Background Granovetter’s model Network version ◮ Reciprocation: Free samples, Hare Krishnas Groups Chaos ◮ Commitment and Consistency: Hazing References ◮ Social Proof: Catherine Genovese, Jonestown ◮ Liking: Separation into groups is enough to cause problems. ◮ Authority: Milgram’s obedience to authority experiment. ◮ Scarcity: Prohibition. Frame 19/86

Social Contagion Getting others to do things for you Social Contagion Models Background Granovetter’s model Network version Groups Chaos References ◮ Cialdini’s modes are heuristics that help up us get through life. ◮ Useful but can be leveraged... Frame 20/86

Social Contagion Social Contagion Social Contagion Models Background Granovetter’s model Network version Groups Chaos References Other acts of influence ◮ Conspicuous Consumption (Veblen, 1912) ◮ Conspicuous Destruction (Potlatch) Frame 21/86

Social Contagion Social Contagion Social Contagion Models Background Granovetter’s model Some important models Network version Groups Chaos ◮ Tipping models—Schelling (1971) [15, 16, 17] References ◮ Simulation on checker boards ◮ Idea of thresholds ◮ Fun with Netlogo and Schelling’s model [20] ... ◮ Threshold models—Granovetter (1978) [9] ◮ Herding models—Bikhchandani, Hirschleifer, Welch (1992) [1, 2] ◮ Social learning theory, Informational cascades,... Frame 22/86

Social Contagion Social contagion models Social Contagion Models Thresholds Background Granovetter’s model Network version ◮ Basic idea: individuals adopt a behavior when a Groups Chaos certain fraction of others have adopted References ◮ ‘Others’ may be everyone in a population, an individual’s close friends, any reference group. ◮ Response can be probabilistic or deterministic. ◮ Individual thresholds can vary ◮ Assumption: order of others’ adoption does not matter... (unrealistic). ◮ Assumption: level of influence per person is uniform (unrealistic). Frame 23/86

Social Contagion Social Contagion Social Contagion Models Some possible origins of thresholds: Background Granovetter’s model Network version ◮ Desire to coordinate, to conform. Groups Chaos ◮ Lack of information: impute the worth of a good or References behavior based on degree of adoption (social proof) ◮ Economics: Network effects or network externalities ◮ Externalities = Effects on others not directly involved in a transaction ◮ Examples: telephones, fax machine, Facebook, operating systems ◮ An individual’s utility increases with the adoption level among peers and the population in general Frame 24/86

Social Contagion Social Contagion Social Contagion Models Background Granovetter’s model Network version Groups Chaos Granovetter’s Threshold model—definitions References ◮ φ ∗ = threshold of an individual. ◮ f ( φ ∗ ) = distribution of thresholds in a population. � φ ∗ ∗ = 0 f ( φ ′ ∗ ) d φ ′ ◮ F ( φ ∗ ) = cumulative distribution = ∗ φ ′ ◮ φ t = fraction of people ‘rioting’ at time step t . Frame 26/86

Social Contagion Threshold models Social Contagion 1 1 Models Background Granovetter’s model 0.8 0.8 Network version Groups 0.6 0.6 Chaos p p References 0.4 0.4 0.2 0.2 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 φ φ ◮ Example threshold influence response functions: deterministic and stochastic ◮ φ = fraction of contacts ‘on’ (e.g., rioting) ◮ Two states: S and I. Frame 27/86

Social Contagion Threshold models Social Contagion Models Background Granovetter’s model Network version Groups Chaos ◮ At time t + 1, fraction rioting = fraction with φ ∗ ≤ φ t . References ◮ � φ t f ( φ ∗ ) d φ ∗ = F ( φ ∗ ) | φ t φ t + 1 = 0 = F ( φ t ) 0 ◮ ⇒ Iterative maps of the unit interval [ 0 , 1 ] . Frame 28/86

Social Contagion Threshold models Social Contagion Models Action based on perceived behavior of others. Background Granovetter’s model 1 2.5 1 Network version A B C Groups 0.8 2 0.8 φ t+1 = F ( φ t ) Pr( a i,t+1 =1) Chaos 0.6 1.5 0.6 f ( φ ∗ ) References 0.4 1 0.4 0.2 0.5 0.2 0 0 0 0 ∗ 1 0 0.5 1 0 0.5 1 φ i φ i,t φ t φ ∗ ◮ Two states: S and I. ◮ φ = fraction of contacts ‘on’ (e.g., rioting) ◮ Discrete time update (strong assumption!) ◮ This is a Critical mass model Frame 29/86