The Emergence of Cultural Signatures and Persistence of Internal Diversity:

A Model of Conformity and Consistency

Jenna BednarAaron Bramson

Andrea Jones-RooyScott E Page

Outline

• Background– Culture– Institutions and Mechanism Design – Ensembles of Institutions – Broad Forces: Coordination & Consistency

• Coordination Consistency Model– Coordination Model– Our Model– Analytic Results ( and 2)– Computational Results (the rest)

Culture?

Behavior

Beliefs

Semiotics

Preferences

Norms

Survey Approach

Hoftstede:

Power Distance

Individualism

Masculinity

Uncertainty Avoidance

US

Power Distance 32

Individualism 90

Masculinity 60

Uncertainty Avoidance 40

France

Power Distance 61

Individualism 63

Masculinity 32

Uncertainty Avoidance 80

El Salvador vs Korea

El SalKorea

Power Distance 62 56

Individualism 12 11

Masculinity 41 33

Uncertainty Avoid 80 80

Institutions and Behavioral Repertoires

Larger Project

BehavioralRepertoire

Institutions

Bednar and Page (2007) “Can Game(s) Theory Explain Culture? The Emergence of Cultural Behavior Within Multiple Game” Rationality and Society

Larger Project

Behavioral Repertoire

Institutions

Bednar and Page (2007) “Can Game(s) Theory Explain Culture? The Emergence of Cultural Behavior Within Multiple Game” Rationality and Society

Mount-Reiter Diagram

Environment Outcome

Actions (Message Space)

Social Objective

Behavioral Rule

Outcome Function

Equilibrium requires COORDINATED behavior:

- tit for tat

- costly signaling

- alternation

- driving on the left

Multiple Institutions

E O

M

E O

M

E O

M

E O

M

Bednar (2008), Bednar and Page (2007)

Empirical evidence suggests that people avoid cognitive dissonance, that they used cased based decision rules, and that they transfer routines from one setting to another.

We call this consistency.

Coordination Consistency Model

Pure Coordination Game

1,1 0,0

0,0 1,1

A B A B

Player 1

Player 2

Hard and Soft Externalities

An externality is hard (economic) f it’s easily measured

An externality is soft (psychological) if it’s not.

No Bright Line

Some decisions involve both hard and soft coordination externalities. Suppose I’m buying a bike. The more people that buy mountain bikes, the more trails that get created (hard). Buying a mountain bike might also make me hip (soft).

Two empirical regularities explained and two inconvenient truths that lie outside the model.

Coordination

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are needed to see this picture.

Exception Proves Rule

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Dagen H

At 4:45 am on September 3, 1967, all cars on the road in Sweden came to a stop. They switched sides (from the left to the right) and at 5 am, the cars began moving again.

ICT1: Diversity within Cultures

ICT2: Cultural Signatures

Elevator Version

Describe a model in which agents attempt to coordinate with others and to be internally consistent that produces intra cultural heterogeneity, inter cultural heterogeneity, and cultural signatures.

A List of Questions

Ketchup in the fridge?Do people wear shoes inside your house?Do you cross the street when the don’t walk sign is

flashing?Read the newspaper at the breakfast table?Do you hug your friends when you see them?Paper napkins?

YNYYY Nation

Ketchup in the fridge? YesDo people wear shoes inside your house? NoDo you cross the street when the don’t walk sign is

flashing? YesRead the newspaper at the breakfast table? YesDo you hug your friends when you see them? YesPaper Napkins? Yes

How Many Cultures?

Six questions

Two answers each

2 x 2 x 2 x 2 x 2 x 2 = 64

The Set of The Possible

Dead People: bury or burn

Foods you eat?

Dress?

Music you play

Stories you tell

8 x 19 x 40 x 6 x 11 x 23 x 2 x 43 .. = HUGE

Four Assumptions

Coordination: incentive to choose an equilibrium action

Consistency: incentive to be consistent across games

Dynamics: people learn

Errors: people make mistakes

Model

Agent: (H,C,C,H,H,C,C,C)

Coordination rule: match actions of others in common games

Consistency rule: match actions of self on different games

Coordination Rule

Pick two players at random and a game at random. Set the action of the first player equal to the action in the second player.

(H,C,C,H,H,C,C,C) meets (C,H,C,C,H,C,C,H) (C,C,C,H,H,C,C,C)

Coordination Equilibrium

All agents should coordinate in each game but the choices of actions should be arbitrary.

Distinct cultures but no signatures.

(C,C,C,H,H,C,C,C)

Consistency Rule

Pick two games at random. Set the action in the first equal to the action in the second.

(H,C,C,H,H,C,C,C)

(C,C,C,H,H,C,C,C)

Consistency Equilibrium

Each agent should be consistent but no two agents need be consistent in the same way.

Consistent people but no coordination.

(C,C,C,C,C,C,C,C)

(H,H,H,H,H,H,H,H)

Coordination & Consistency

With probability p an agent applies the coordination rule, and with probability (1-p) an agent applies the consistency rule.

Equilibrium

Societies converge to either

(C,C,C,C,C,C,C,C) or (H,H,H,H,H,H,H,H)

Two Considerations

The Second Law

The Trembling Hand

The Second Law

The second law of thermodynamics suggests a unique stable equilibrium--- but it’s not of much predictive value.

Simplest Model

Two agents

Two games

Two actions

States of the World

Coordinated and Consistent

Off by One

Consistent not Coordinated

Coordinated not Consistent

Neither (Total Mess)

Consistency Dynamic

1 2

21

12

Consistency Transition Map

1

1

1/4 1/4

1/2

Coordination Transition Map

1

1/4

1/4 1

1/2

Coordination & Consistency Transition Map

1

1/8

1/4

1/2

1/21/2

1/2

1/8

1/2

Time To Convergence

p = probability of coordination

Limiting Case

With N agents and M dimensions time to equilibrium scales as follows:

T ~ N2M2 for p near 1/2T ~ N2M/p for p near 0T ~ M2N/(1-p) for p near 1

Scott E Page, Leonard M. Sander, and Casey Schneider - Mizell``Conformity and Dissonance in Generalized Voter Models” Journal of

Statistical Physics, 2007.

The Trembling Hand

Agents make mistakes with probability epsilon.

Markov Process

1- 0 0 0

1/4 (1- )/2 . ..

Equilibrium

Tremble of size leads to 2 deviation from consistency and coordination in the single force models but at least 6 deviation in the model with both forces.

Proportion of Population not at Pure Strategy Equilibrium

= amount of tremble (error)

100 Agents, 10 Games, 5 Actions

Heterogeneity and Cultural Signatures

Summary

• Model Produces– Inter cultural differences– Intra cultural differences– Cultural signatures

• Methodological Insights– Models can be too simple– Ensembles of games different from games

Summary

Future Directions– Institutional choices induce behavior– Those behaviors can create spillovers

Other Applications– Party members’ ideal points– Organizational culture