Diversity

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Diversity

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Diversity
From Chalk to Talk
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Scott E Page De-Center for the Study of
Complex Systems Center for Policy Studies -
ISR Departments of Political Science
Economics The University of Michigan-Ann
Arbor External Faculty Economics Santa Fe
Institute
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Outline

• Background

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Outline

• Background
• Diversity 496

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Outline

• Background
• Diversity 496
• Cultural Diversity
• Toolboxes and Thermometers
• Climate Control and Affirmative Action
• The Ecology of Chain Stores

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Outline

• Background
• Diversity 496
• Cultural Diversity
• Toolboxes and Thermometers
• Climate Control and Affirmative Action
• The Ecology of Chain Stores
• Theory Specific and Deep
• The rule of six
• BARN Theory

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How I got here
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Complex Adaptive Systems

• Agents
• Space social, virtual, geographic
• Adaptation
• Dynamics
• Diversity

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Why?
- War/Terrorism - Markets - Inequality -
Crime - Drugs - Sustainability - Growth -
Culture - Electric Power - Fun
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The Warm Soft Facts

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The Warm Soft Facts

• U.S. becoming more diverse

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The Warm Soft Facts

• U.S. becoming more diverse
• World becoming more connected

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The Adaptive Response

• 2/3 of colleges have diversity requirement

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The Adaptive Response

• 2/3 of colleges have diversity requirement
• Businesses awash in diversity training, coping,
  advocating, etc..

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The Opportunity

• Diversity training not diverse
• Literature
• Anthropology
• Psychology

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The Opportunity

• Diversity training not diverse
• Literature
• Anthropology
• Psychology
• Formal theory has lots to say
• Physics entropy
• Economics portfolio theory, comparative
  advantage
• Political Science Arrows theorem

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Diversity of Diversities

• wealth/energy
• ability
• information/sight
• preferences
• risk attitude
• ideology
• signal/tag
• species

• representation of world
• tool kits
• charisma
• location
• gender
• culture
• identities (multiple)

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Diversity 496
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Cultural Diversity
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Cultural Diversity
Why your partners relatives are so freaking
strange
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Binary Coordination World
Slurp Soup? Y,N
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Binary Coordination World
Slurp Soup? Y,N Shoes in House? Y,N
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Binary Coordination World
Slurp Soup? Y,N Shoes in
House? Y,N Ketchup in Fridge? Y,N
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Binary Coordination World
Slurp Soup? Y,N Shoes in
House? Y,N Ketchup in Fridge? Y,N Mi
familia NYN Mi esposas YNY
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Simple Math
Suppose each family/firm/country coordinates on
only thirty dimensions.
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Simple Math
Suppose each family/firm/country coordinates on
only thirty dimensions. There are then over a
billion possible cultures and two will typically
match on about fifteen of them.
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Games Theory Model
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Games Theory Model
Agents play multiple games simultaneously and
evolve strategies that share cognitive
subroutines.
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Games Theory Model
Agents play multiple games simultaneously and
evolve strategies that share cognitive
subroutines. Company 1 Prisoners Dilemma and
Selfish Game Company 2 Prisoners Dilemma and
Battle of Sexes
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Games Theory Results
Consistent behavioral patterns evolve
in communities of agents (culture
emerges). Company 1 (PD and SI game) Agents
evolve a grim trigger strategy in the
PD. Company 2 (PD and BOS) Agents evolve do
undo others/tit for tat in both games
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Institutional Path Dependence
If as a society becomes more complex it adds new
games in the form of political, religious, and
economic institutions, it will choose game forms
that perform well given existing behavioral
routines (set dependence).
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Institutional Path Dependence
If as a society becomes more complex it adds new
games in the form of political, religious, and
economic institutions, it will choose game forms
that perform well given existing behavioral
routines (set dependence). Behavioral stickiness
creates path dependence. web jenna bednar
university of michigan
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Toolboxes and Thermometers
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Toolboxes and Thermometers
If you know so much about women what are you
doing at the Gas n Sip on a Saturday
night? - From Say Anything
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The Idea
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A,b,x
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x,M
Thermometer Toolbox SAT,IQ
skill sets, mental models,
perspectives
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Unpacking IQ
Given a test a collection of toolbox agents
will create a set of thermometer scores.
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Unpacking IQ
Given a test a collection of toolbox agents
will create a set of thermometer scores. These
scores will tend to correlated if some agents
have more tools than others, hence Spearmans G.
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A Simple Model

• Suppose that there 50 possible tools
• Abu 20 tools
• Craig 12 tools

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Is Abu Smarter?

• Odds that Abu knows all of Craigs 12 tools?

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Is Abu Smarter?

• Odds that Abu knows all of Craigs 12 tools?
• About one in a million!

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The New Economy
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The New Economy

• Firms solve difficult problems.
• Each firm hires those best (as measured by
  thermometer score) at solving the firms
  problems.
• What can we say about firm and worker
  performance?

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Econ 101
output
number of workers
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A Minor Problem

• Theorem ANY returns to scale in workers is
  possible

output
number of workers
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Why?

• Individual performance
• value of local peakbasin size
• Firm performance
• firm local peaks intersection of individual
  local peaks
• cannot tell local peaks from IQ score

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Collective Performance
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Collective Performance
When you are surrounded by sameness, you get only
variations on the same. -Kevin Sullivan VP
of HR Apple Computers
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A Test of Diversity

• Rank agents by thermometer score
• on a problem

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A Test of Diversity

• Rank agents by thermometer score
• on a problem
• Alpha Group 20 best agents
• Diverse Group 20 random agents

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The Thermometer View
138
139
137
111
121
84
135
132
135
135
75
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Alpha Group Diverse
Group
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A Major Problem

• Most of the time the diverse group does better

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Mathematical Theorem

• Assumptions
• Problem must be difficult
• The set of problem solvers must be
  non-enclosed relative to some partition
• Denumerable set of stopping points
• (implicit assumption that people know calculus)

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Math Intuition

• Best problem solvers lie in small number of
  epsilon balls in space of problem solvers.

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Math Intuition

• heuristic
• perspective

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The Toolbox View
ABD
ABC
ACD
AEG
AHK
FD
BCD
ADE
BCD
BCD
EZ
IL
Alpha Group Diverse
Group
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Conjecture

• Markets lead to inefficient levels of toolbox
  diversity

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Conjecture

• Markets lead to inefficient levels of toolbox
  diversity
• individual incentives may be toward imitation of
  successful tools

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Conjecture

• Markets lead to inefficient levels of toolbox
  diversity
• individual incentives may be toward imitation of
  successful tools
• new tools create positive externalities

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Climate and Diversity
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Climate and Diversity
It is a great shock at the age of five or six to
find that in a world of Gary Coopers you are the
Indian. -James Baldwin
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ADVANCE Project
The University of Michigan just completed a large
study to uncover why the sciences attract so few
women scholars.
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Survey Results
Wages Lab Space Students Research Funds Staff
Support Teaching load
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Survey Results
Wages Same Lab Space Same Students Same Re
search Funds Same Staff Support Same Teachi
ng load Same
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Survey Results
Wages Same Lab Space Same Students Same Re
search Funds Same Staff Support Same Teachi
ng load Same Climate Worse
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A Gender Tipping Model

• Professions 1,2,3, K
• Agents M,F
• Gender M,F
• Tolerance tol in 0,1
• Ability abil(1), abil(2)

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A Gender Tipping Model

• Utility
• Same(pat,j) people of in profession j
• of same gender as agent pat

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A Gender Tipping Model

• Utility
• Same(pat,j) people of in profession j
• of same gender as agent pat
• U(pat,j) tol (1-tol)Same(pat,j) abil(pat,j)

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A Gender Tipping Model

• Utility
• Same(pat,j) people of in profession j
• of same gender as agent pat
• U(pat,j) tol (1-tol)Same(pat,j)
  abil(pat,j)
• if tol 1, U(pat,j) abil(pat,j)

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A Gender Tipping Model

• Utility
• Same(pat,j) people of in profession j
• of same gender as agent pat
• U(pat,j) tol (1-tol)Same(pat,j)
  abil(pat,j)
• if tol 1, U(pat,j) abil(pat,j)
• if tol 0, U(pat,j) Same(pat,j) abil(pat,j)

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Reality
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Model Initial State
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Model End State
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The Tipping Analogy

• We keep hiring women engineers but
• they keep moving to management or
• leaving the firm.

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The Gravity Analogy

• I keep throwing this ball up in the air
• and it keeps coming back to earth.

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The Ecology of Chains
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The Ecology of Chains
We dont want your Albert Camus Happy
Meals! -quote taken from anti
McDonalds posting on www March 2000
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Background

• Market Logic chains efficient

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Background

• Market Logic chains efficient
• Activist Logic
• chains destroy cultural diversity
• chains destroy urban centers
• chains an ecological disaster

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Model

• Firms as ideas
• two hedonic attributes (size and temperature)
• one valence attribute (price or quality)

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Model

• Firms as ideas
• two hedonic attributes (size and temperature)
• one valence attribute (price or quality)
• Cities/Countries as ecologies of firms

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Mexican Food
size
temperature
size of square denotes quality
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Chaining

• Chaining allows ideas in one country to be tested
  in another country

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Pre-Chaining

• Sweden

France
USA
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Welcome to McDonalds!

• Sweden

France
USA
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Cool phone!

• Sweden

France
USA
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Niche Landscape

• Sweden

France
USA
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Result Hetero-Homogeneity

• Sweden

France
USA
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Policy Question

• Should countries like France or cities
• like Ann Arbor erect barriers to chains?

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Policy Question

• Should countries like France or cities
• like Ann Arbor erect barriers to chains?
• www.wallmartsucks.com

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Model Specifics

• Countries have unique cultures
• Countries prefer own cultures
• The culture of a new idea is proportional to
  market share

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The French are NOT crazy if..

• Ideas distribution normal

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The French are NOT crazy if..

• Ideas distribution normal
• k countries become like USA

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The French are NOT crazy if..

• Ideas distribution normal
• k countries become like USA
• compare kT th order statistic to T th

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The French are NOT crazy if..

• Ideas distribution normal
• k countries become like USA
• compare kT th order statistic to T th
• Order statistics grow like log(T)
• log(kT) log(k) log(T)

log(T) log(T)
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BUT

• If ideas build upon past ideas, then it
• appears to be the case that the standard
• economic arguments hold.

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Theory Specific and Deep
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The Rule of Six
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The Rule of Six
Its a Markov Process -John Holland
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The Rule of Six
Its a Markov Process -John Holland as told
to me on 7/5/1995, 8/14/1997,9/21/1999,
10/24/2000, 9/14/2001, 10/13/2001
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Markov Theory

• Finite set of states
• healthy, sick
• rich, poor

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Markov Theory

• Finite set of states
• healthy, sick
• rich, poor
• Discrete time periods

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Markov Theory

• Finite set of states
• healthy, sick
• rich, poor
• Discrete time periods
• Fixed Transition Mapping
• P(rich at t to poor at t1) 0.1

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Ergodic Theorem

• A Markov Process has a unique stable equilibrium

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Ergodic Theorem

• A Markov Process has a unique stable equilibrium
• History does not matter

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Ergodic Theorem

• A Markov Process has a unique stable equilibrium
• History does not matter
• Redistribution does not help

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Interactions

• Four types of students
• A,B,C,D

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Interactions

• Four types of students
• A,B,C,D
• Students meet in pairs
• AB, AA, AC, etc.

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Interactions

• Four types of students
• A,B,C,D
• Students meet in pairs
• AB, AA, AC, etc.
• Types change as result of process
• AB - AA, AC - AA
• DB - DD, DC - DD

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No Ergodic Theorem

• Probability that B becomes an A or a D depends on
  the proportion of As and Ds in the population.

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No Ergodic Theorem

• Probability that B becomes and A or a D depends
  on the proportion of As and Ds in the
  population.
• Therefore, the transition probabilities change
  over time

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The Rule of Six

• Theorem An interaction structure can admit
  multiple equilibria if and only if
• NUMBER OF TYPES GROUP SIZE
• is greater than or equal to six

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Implication

• Agent diversity and size of interactions (and
  connectivity) are substitutes in creating
  diversity at the population level.

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The Barn Theory
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The Barn Theory
We ask the leaf are you complete in yourself?
And the leaf answers, No, my life is in the
branches. We ask the branch and the branch
answers, No, my life is in the root. We ask the
root, and it answers No my life is in the trunk
and the branches and the leaves. Keep the
branches stripped of leaves and I shall die. So
it is with the great tree of being. Nothing is
completely and merely individual.
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The Barn
Mutation/Adaptation Network
Big Area Real Novelty Interaction Divers
ity
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The Barn
Mutation
Network Big Area Real
Novelty Interaction Diversity
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Exploration versus Exploitation
To search for solutions to difficult problems or
to evolve strategies in complex environments,
involves a tradeoff between explore and
exploit.
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Exploration versus Exploitation
To search for solutions to difficult problems or
to evolve strategies in complex environments,
involves a tradeoff between explore and
exploit. Genetic Algorithm if the mutation rate
and crossover probabilities are too high, no
structure gets exploited. Alternatively, if
the selection operator is too severe, the
initial best is over exploited.
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Exploration versus Exploitation
value of solution
exploit
explore
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The Evolution of Evolvability
Bedau and Packard and others have shown that you
allow the mutation rate to evolve, then it will
settle into a region in which evolution can be
successful.
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The Evolution of Evolvability
value of solution
mutation rate
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The Barn
Mutation
Network Big Area Real
Novelty Interaction Diversity
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The Edge of Chaos
There are three versions of the edge of chaos
1. Langtons lambda model 2. Kaufmans NK
model 3. The metaphor All require slight
modification
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Langtons Lambda Model
In a Wolfram Style CA 000 0 idea count the
of 1s 001 1 as it passes 3/8 you 010
0 start to see chaos 011 1 100
0 101 1 110 0 111 1
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Langtons Lambda Model
Problem Structured Rules 000 0 111
1 Unstructured Rules 000 1 111 0 CA
rules in these two classes have the same lambda,
all of the chaotic rules are unstructured.
Therefore, the dial metaphor is incorrect.
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Kaufmans NK Model
Binary Strings of length N. Contribution to
string value at bit depends upon bits at K other
sites. 010101000101 Bit 4 0101 .76321 As K
increases, the best string value increases up
until K is large enough that the system appears
chaotic
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The Edge of Chaos
value of solution
K of interactions
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Kaufmans NK Model
The interactions are not evolved in the NK
model. When K is increased, the old interactions
are thrown out and new random interactions
are created.
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Kaufmans NK Model
The interactions are not evolved in the NK
model. When K is increased, the old interactions
are thrown out and new random interactions
are created. (When the radio goes in, the car
goes out!)
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The Metaphor
The edge of chaos metaphor states that if you
have just the right amount of randomness (or
interaction) to support life and or
complexity than if you increase the randomness
(or the interactions) you fall into chaos.
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The Edge of Chaos
value of solution
mutation rate/interactions
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The Long Mesa
value of solution
mutation rate/interactions
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The Edge of Boredom!!
value of solution
mutation rate/interactions
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The Barn
Mutation
Network Big Area Real
Novelty Interaction Diversity
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Topology and Space
Many agent based models fail to work when
either
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Topology and Space
Many agent based models fail to work when
either Too many agents interact with one
another.
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Topology and Space
Many agent based models fail to work when
either Too many agents interact with one
another. Too few agents interact with one
another.
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Rock, Paper, Scissors
Rock All D Toxic E Coli Paper TFT Resistant
E Coli Scissors All C Sensitive E Coli
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Rock, Paper, Scissors
Rock All D Toxic E Coli Paper TFT Resistant
E Coli Scissors All C Sensitive E
Coli Simulations we get stone soup but
diversity on a lattice or a line
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Rock, Paper, Scissors
Rock All D Toxic E Coli Paper TFT Resistant
E Coli Scissors All C Sensitive E Coli Real
Experiments we get one type E Coli in a flask
but diversity on a slide Kerr, Riley, Feldman,
Bohannan (Nature 2002)
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Spacing Out Our Agents
complexity
alone lattice network soup

explore
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Spacing Out Our Agents
complexity
alone lattice network soup

explore
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The Barn
Mutation
Network Big Area Real
Novelty Interaction Diversity
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The Number of Agent Types
In constructing agent based models, we often find
that as we increase the number of distinct agent
types, our models performance increases and then
decreases because the environment leaves the
complex region and becomes a mess.
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Too many agents jumping on the bed
complexity
number of types of agents
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The Barn Theory and Interplay
In agent based models we want just the right
amount of interplay between our agents, and we
have many dials that can adjust interplay.
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Biology
These dials diversity, mutation rate,
interaction, and connections adjust through
evolution.
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The Horse is in the Barn
Robert May showed how a predator prey framework
with multiple species leads to a result that
greater diversity implies more robustness.
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The Horse is in the Barn
Robert May showed how a predator prey framework
with multiple species leads to a result that
greater diversity implies more robustness. But,
Standish and others have since shown that more
diversity implies fewer connections, and fewer
connections means more robustness. (right
Duncan?)
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The Barn
Mutation Network Big Area
Real Novelty Interaction
Diversity
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Human Systems
We adjust our rates of experimentation,
our levels of interactivity, our connections, and
our level of diversity to keep our world
manageable.
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Summary

• Cultures Diverse
• Few connections

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Summary

• Cultures Diverse
• Few connections
• Toolboxes Moderate
• Moderate connections, adaptation, interaction

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Summary

• Cultures Diverse
• Few connections
• Toolboxes Moderate
• Moderate connections, adaptation, interaction
• Genders and Chains Homogeneous
• Lots of connections
• Lots of interdependence

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Final Thought
If we are to achieve a richer culture, rich in
contrasting values, we must recognize the whole
gamut of human potentialities, and so weave a
less arbitrary social fabric, one in which each
diverse human give will find a fitting
place. -Margaret Mead
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To which I add
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To which I add
I yearn for the day when to be different is to be
understood.
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The Difference of Interplay
Whether designed or evolved the amount of
diversity sustained in an agent based model will
be a function of spatial embedding,
interactions, mutation rate, and the ease
of aggregation.