Dynamics of Social Networks of Belief Networks Yong-Yeol (YY) Ahn, - PowerPoint PPT Presentation

Dynamics of Social Networks of Belief Networks Yong-Yeol (YY) Ahn, @yy http://yongyeol.com CNetS, IUNI, School of Informatics and Computing Indiana University Bloomington

Many ways to think about ‘networks of networks’ A network of elements, which themselves are networks. Hierarchical organization: a network of subnetworks (modules) Multiple inter-dependent networks

How to model societal dynamics?

social influence

Asch conformity experiment (1951) https://www.youtube.com/watch?v=NyDDyT1lDhA#t=97

Under the ‘social’ condition

Under the ‘social’ condition Error: Less than 1% → ~37%

Under the ‘social’ condition Error: Less than 1% → ~37% 75% at least one incorrect answer

Smoke Room Experiment

Smoke Room Experiment

Models that emphasize conformity

But if you’ve ever tried to convince another human being…

Conover et al., 2012

Humans strive for “internal consistency” Leon Festinger

“The most fundamental values in a culture will be coherent with the metaphorical structure of the most fundamental concepts in the culture.” Lakoff, George. Metaphors We Live By (p. 22).

“Strict father model” (Lakoff)

“Strict father model” (Lakoff) • The world is a dangerous place.

“Strict father model” (Lakoff) • The world is a dangerous place. • it always will be, because there is evil out there in the world.

“Strict father model” (Lakoff) • The world is a dangerous place. • it always will be, because there is evil out there in the world. • The world is also difficult because it is competitive.

“Strict father model” (Lakoff) • The world is a dangerous place. • it always will be, because there is evil out there in the world. • The world is also difficult because it is competitive. • There will always be winners and losers.

“Strict father model” (Lakoff) • The world is a dangerous place. • it always will be, because there is evil out there in the world. • The world is also difficult because it is competitive. • There will always be winners and losers. • There is an absolute right and an absolute wrong.

“Strict father model” (Lakoff) • The world is a dangerous place. • it always will be, because there is evil out there in the world. • The world is also difficult because it is competitive. • There will always be winners and losers. • There is an absolute right and an absolute wrong. • Children are born bad, in the sense that they just want to do what feels good, not what is right.

“Strict father model” (Lakoff) • The world is a dangerous place. • it always will be, because there is evil out there in the world. • The world is also difficult because it is competitive. • There will always be winners and losers. • There is an absolute right and an absolute wrong. • Children are born bad, in the sense that they just want to do what feels good, not what is right. • Therefore, they have to be made good.

“Nurturant parent model”

“Nurturant parent model” • Both parents are equally responsible for raising the children.

“Nurturant parent model” • Both parents are equally responsible for raising the children. • Children are born good and can be made better.

“Nurturant parent model” • Both parents are equally responsible for raising the children. • Children are born good and can be made better. • The world can be made a better place, and our job is to work on that.

“Nurturant parent model” • Both parents are equally responsible for raising the children. • Children are born good and can be made better. • The world can be made a better place, and our job is to work on that. • The parents’ job is to nurture their children and to raise their children to be nurturers of others.

A belief system: a set of coherent ideas

A belief system: a set of coherent ideas This core set of beliefs can explain a lot of behaviors and positions.

Confirmation bias & Cognitive dissonance

Confirmation bias

Confirmation bias Existing belief biases search for information, interpretation, memory, and so on.

The fox and the grapes

We need to incorporate this.

The wall 1. Let’s focus on how individuals behave. 2. Let’s focus on social structures

The wall 1. Let’s focus on how individuals behave. 2. Let’s focus on social structures

The wall 1. Let’s focus on how individuals behave. 2. Let’s focus on social structures

The wall 1. Let’s focus on how individuals behave. 2. Let’s focus on social structures

s 1 s 2 s 3 s 4 s 5

But how can we implement ‘internal consistency’? s 1 s 2 s 3 s 4 s 5

Common ways to model beliefs But how can we implement ‘internal consistency’? s 1 s 2 s 3 s 4 s 5

Common ways to model beliefs Spins But how can we implement ‘internal consistency’? s 1 s 2 s 3 s 4 s 5

Common ways to model beliefs Spins But how can we implement ‘internal consistency’? s 1 s 2 s 3 s 4 s 5 Vectors

s 1 s 2 s 3 s 4 s 5

s 1 s 2 s 3 s 4 s 5 s 1 s 4 s 2 s 5 s 3

s 1 s 2 s 3 s 4 s 5 Maybe we should s 1 s 4 have a network. s 2 s 5 s 3

A person’s mind Concepts

Social Knowledge Structure (SKS) model Greenwald et al. 2002

social balance theory Joe Bill Jill

social balance theory Joe “The enemy of my enemy is my friend.” Bill Jill

obama obama - + - + good good + + ME ME ‘consistent’

obama obama - - - + good good - + ME ME ‘inconsistent’

Combining peer influence with coherence

Model

Internal consistency m = − 1 X E ( i ) a jk a kl a jl N ∆ j,k,l (social balance)

Social influence 2 X S m · ~ ~ E ( s ) m = − S q , k max N ( N − 1) q ∈ Γ ( m ) Spin model

Total energy m = − 1 2 X E ( i ) X S m · ~ ~ E ( s ) a jk a kl a jl m = − S q , k max N ( N − 1) N ∆ q ∈ Γ ( m ) j,k,l “peer influence” “coherentism” h i X JE ( i ) m + IE ( s ) H = m m ∈ M

Two energies 1 X h E ( i ) i = E ( i ) Individual: m . | M | m ∈ M 1 h E ( s ) i = X E ( s ) society: m , | M | m ∈ M

Phase transition

Even a homogeneous society may spontaneously become unstable

Even a homogeneous society may spontaneously become unstable Homogeneous population + Unstable belief system

Even a homogeneous society may spontaneously become unstable � 10 3 (a) 5 4 min E ( s ) � E ( s ) 3 Homogeneous 2 1 population 0 1 . 0 (b) 0 . 5 h E ( i ) i + 0 . 0 � 0 . 5 � 1 . 0 (c) 1 . 0 Unstable belief 0 . 8 h S g /N i 0 . 6 S o ( E = 1 ) system S f ( E = � 1 ) 0 . 4 0 . 2 0 . 0 0 50 100 150 200 t

Consistency of Zealots

Consistency of beliefs (balance in the belief network)

How well can we convert the cult?

More nuanced, complex ‘truth’ may have hard time convincing a cult with strong coherence and less truth.

(a) (b) It can become almost impossible to convert a cult (a) (b)

Summary • “Network of networks” as a framework to model social changes. • We need to consider internal consistency as a key part of the opinion / social dynamics model. • Such consideration can provide explanations of many social phenomena. Johan Bollen Nathaniel Rodriguez