Computational Complexity in the Social Sciences (???????????)

1
Computational Complexity in the Social Sciences
(???????????)

• Will Tracy
• CSSS-China 2005

2
What is Complexity?

• A hard question to answer
• Different things to different people
• Big Tent
• Tent Poles
• Interdisciplinary
• Models capturing non-linear interactions/effects
• Multiple and new prospective

3
Value of Multiple Perspectives Video
Example??????? ?????

• Watch Video(???)
• Count each time a person in a (????a?????)
• black t-shirt passes a ball to a person in a
  black t-shirt (??T?????????????T???) AND
• white t-shirt passes a ball to a person in a
  white-shirt (??T?????????????T???)
• Many individuals will get the wrong number, but
  the rooms average should be correct.
  (??????,????????????????????)
• No Talking(????)

4
Play Video
5
Is the lesson real?

• Are social sciences misdirected?
• Economics seems to be.
• Economic Transition Late 20th Century Challenge
• Former Soviet Union follewed HMG/WBs advice
• China did not
• Chinas recent growth a singular event in econ
  history
• 78 95 over 200 million people raised above
  poverty line
• Tragedy in Eastern Europe
• Russia poverty from 1.3 to 40 of pop. (late
  80s 93)
• Need new views/perspectives/paradigms(??)

6
Whats Past is Prolog

• Intro Social Sciences Need New Paradigms
• The Agent-based Approach
• The Spectrum of Computational Modeling
• Introduction to Evolutionary(???) Computation
• Foundations of a New Social Science

7
Agenda

• Intro Social Sciences Need New Paradigms
• The Agent-based Approach
• The Spectrum of Computational Modeling
• Introduction to Evolutionary Computation
• Foundations of a New Social Science

8
Agent-based Modeling

• Agent-based Modeling is a conceptual approach
• Agents typically possess a data structure and an
  instruction list.
• Agent-based models are interesting when
  -interesting macro-level phenomena emerge
  (?????????) from the interaction of agents
  following simple rules produces
• Related to the idea of Emergence(??)

9
Emergence Example Slime Mold

• Dictyostelium (Slime Mold) eats as individual
  cells
• Moves as on unified organism
• No leader or brain cells
• Coordinated movement emerges from simple rules.

10
Consider a Simple ABM of City Traffic

• City Layout
• Agent Rules
• Start Points, Destinations, and Timing
• Road Knowledge / Decision Rules
• Driving Rules
• Many Uses
• Light timing / driving rules / new intersections

11
Agenda

• Intro Social Sciences Need New Paradigms
• The Agent-based Approach
• The Spectrum of Computational Modeling
• Introduction to Evolutionary Computation
• Foundations of a New Social Science

12
The Spectrum of Computational Modeling
Theory Driven
Data Driven
13
The Spectrum of Computational Modeling
Theory Driven
Data Driven
?
14
The Spectrum of Computational Modeling
Theory Driven
Data Driven
?
15
The Spectrum of Computational Modeling
Theory Driven
Data Driven
?
16
The Spectrum of Computational Modeling
Theory Driven
Data Driven
?
17
Agenda

• Intro Social Sciences Need New Paradigms
• The Agent-Based Approach
• The Spectrum of Computational Modeling
• Introduction to Evolutionary Computation
• Foundations of a New Social Science

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What is an Algorithm(??)?

• Evolutionary Computation mostly deals with
  Evolutionary Algorithms
• Genetic Algorithms are the most common type of
  Evolutionary Algorithm
• Before discussing a Genetic Algorithm we should
  define an algorithm
• Definition An algorithm is a list of
  well-defined instructions for completing a task
• Example Call Centers

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What is a Genetic Algorithm?

• A population(?) of algorithms
• The efficacy of each algorithm can be quantified
  in a fitness score
• A stochastic(???) selection of the fittest
  mechanism identifies winners in each generation
  (?)
• Winners get to have children, who will live in
  the populations next generation
• Crossover(??) and mutation(??) add variety(???)

20
Genetic Algorithm Flow Chart
Population of Random Algorithms
(Generation1) ?????(???)
Each Algorithm obtains a Fitness
Score ?????????????
Fitness-based Selection - (??????????)
Stochastic Variation - (????)
New Generation (????)
Create New CS Agents - (??????????)
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The Human Face Example

• A drawing of a human face can be the result of an
  algorithm
• The first instruction IDs what type of eyebrows
• The second instruction IDs what type of eyes
• The third instruction IDs what type of nose
• The fourth instruction IDs what type of mouth
• This type of algorithm can easily be represented
  as a string of numbers (called Chromosomes (???))

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Chromosome Scheme
Source John Holland
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Genetic Algorithm Flow Chart
Population of Random Algorithms
(Generation1) ?????(???)
Each Algorithm obtains a Fitness
Score ?????????????
Fitness-based Selection - (??????????)
Stochastic Variation - (????)
New Generation (????)
Create New CS Agents - (??????????)
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A Population of Random Algorithms

• (432653)
• (234652)
• (335421)
• (321456)
• (113245)
• (634522)
• (445615)

25
Genetic Algorithm Flow Chart
Population of Random Algorithms
(Generation1) ?????(???)
Each Algorithm obtains a Fitness
Score ?????????????
Fitness-based Selection - (??????????)
Stochastic Variation - (????)
New Generation (????)
Create New CS Agents - (??????????)
26
www.HotOrNot.com
1.1
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The efficacy of each algorithm can be quantified
(???) as a fitness score

• (432653) - Fit 1.1
• (234652) - Fit 5.4
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1

28
Genetic Algorithm Flow Chart
Population of Random Algorithms
(Generation1) ?????(???)
Each Algorithm obtains a Fitness
Score ?????????????
Fitness-based Selection - (??????????)
Stochastic Variation - (????)
New Generation (????)
Create New CS Agents - (??????????)
29
Selection of the Fittest Mechanism Random draw
three chromosomes

• (432653) - Fit 1.2
• (234652) - Fit 5.4
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1

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Selection of the Fittest Mechanism Random draw
three chromosomes

• (432653) - Fit 1.2
• (234652) - Fit 5.4
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1

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Selection of the Fittest Mechanism Select the
chromosome with the highest fitness

• (432653) - Fit 1.2
• (234652) - Fit 5.4
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1

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Selection of the Fittest Mechanism Copy the
selected chromosome

• (432653) - Fit 1.2
• (234652) - Fit 5.4 (234652)
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1

33
Selection of the Fittest Mechanism Repeat the
process to select second parent

• (432653) - Fit 1.2
• (234652) - Fit 5.4 (234652)
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1

34
Selection of the Fittest Mechanism Repeat the
process to select second parent

• (432653) - Fit 1.2
• (234652) - Fit 5.4 (234652)
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1

35
Selection of the Fittest Mechanism Repeat the
process to select second parent

• (432653) - Fit 1.2
• (234652) - Fit 5.4 (234652)
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1

36
Selection of the Fittest Mechanism Repeat the
process to select second parent

• (432653) - Fit 1.2
• (234652) - Fit 5.4 (234652)
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1 (445615)

37
Selection of the Fittest Mechanism Repeat the
process to select second parent

• (432653) - Fit 1.2
• (234652) - Fit 5.4 (234652)
• (335421) - Fit 4.3
• (321456) - Fit 2.1
• (113245) - Fit 5.6
• (634522) - Fit 3.2
• (445615) - Fit 4.1 (445615)

38
Genetic Algorithm Flow Chart
Population of Random Algorithms
(Generation1) ?????(???)
Each Algorithm obtains a Fitness
Score ?????????????
Fitness-based Selection - (??????????)
Stochastic Variation - (????)
New Generation (????)
Create New CS Agents - (??????????)
39
Example of Stochastic Variation
Parent 1 (234652)
Parent 2 (445615)
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Step One Randomly Select Genes for Mutation
Parent 1 (234652)
Parent 2 (445615)
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Step One Randomly Select Genes for Mutation
Parent 1 (234652)
Parent 2 (445615)
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Step Two Randomly Select a Crossover Point
Parent 1 (234652)
Parent 2 (445615)
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Step Two Randomly Select a Crossover Point
Parent 1 (234652)
Parent 2 (445615)
44
Genetic Algorithm Flow Chart
Population of Random Algorithms
(Generation1) ?????(???)
Each Algorithm obtains a Fitness
Score ?????????????
Fitness-based Selection - (??????????)
Stochastic Variation - (????)
New Generation (????)
Create New CS Agents - (??????????)
45
Create Child Agents
Parent 1 (234652)
Parent 2 (445615)
Child 1 ( )
Child 2 ( )
46
Create Child Agents
Parent 1 (234652)
Parent 2 (445615)
Child 1 (2 )
Child 2 (4 )
47
Create Child Agents
Parent 1 (234652)
Parent 2 (445615)
Child 1 (23 )
Child 2 (44 )
48
Create Child Agents
Parent 1 (234652)
Parent 2 (445615)
Child 1 (231 )
Child 2 (445 )
49
Create Child Agents
Parent 1 (234652)
Parent 2 (445615)
Child 1 (2316 )
Child 2 (4456 )
50
Create Child Agents
Parent 1 (234652)
Parent 2 (445615)
Child 1 (23161 )
Child 2 (44565 )
51
Create Child Agents
Parent 1 (234652)
Parent 2 (445615)
Child 1 (231615)
Child 2 (445653)
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A note on the Population and Generations
Parents are drawn from this bucket
(234652)
(445615)
Generation 2
Generation 1
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A note on the Population and Generations
Their Children will live in this bucket
(231615)
(445653)
Generation 2
Generation 1
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A note on the Population and Generations
Their Children will live in this bucket
(231615)
(445653)
Generation 2
Generation 1

• Sampling with replacement!
• Keep repeating process population size in
• Generation 2 equals that of Generation 1

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Genetic Algorithm Flow Chart
Population of Random Algorithms
(Generation1) ?????(???)
Each Algorithm obtains a Fitness
Score ?????????????
Fitness-based Selection - (??????????)
Stochastic Variation - (????)
New Generation (????)
Create New CS Agents - (??????????)
56
A note on the Population and Generations
Generation 9004
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www.HotOrNot.com
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Original GA Uses

• Evolving me an imaginary girlfriend is of limited
  scientific benefit unfortunately
• GAs often excel at finding near optimal solutions
  to NP Complete (???????????) problems
• Ex The traveling salesmen problem
• No Free Lunch in optimization(???) techniques.

59
Agenda

• Intro Social Sciences Need New Paradigms
• The Agent-Based Approach
• The Spectrum of Computational Modeling
• Introduction to Evolutionary Computation
• Foundations of a New Social Science

60
The Curtain (??) View in 20th Century
Economics

• The system is at equilibrium(??)
• The system is shocked(????)
• Pull a curtain over the system
• Calculate the new equilibrium
• Pull the curtain back, to reveal the system at
  its new equilibrium
• Dont worry about the dynamic, disequilibrium
  behavior that takes place behind the curtain.

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Why the Curtain View? And Whats Wrong with
It?

• Limited pre-WWII computational abilities
• Analytical abilities underlying the Curtain View
  since Newton and Leibniz

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Why the Curtain View? And Whats Wrong with
It?

• Limited pre-WWII computational abilities
• Analytical abilities underlying the Curtain View
  since Newton and Leibniz
• Homogenous(???), Hyper-rationality(???)
• Equilibrium

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No Disequilibrium? - So What?

• Error of Shock Therapy driven by deep level
  belief in the Curtain View
• Deng Xiaoping rejection of the Shock Therapy
  was based on his belief in the importance of
  disequilibrium behavior
• Crossing the River by Feeling for Stones
• ??????
• Evolutionary Computation allows us to model and
  analyze dynamic disequilibrium behavior

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An Evolutionary Computational Approach

• The agent (i.e. firm, investor, government,
  voter, consumer) isnt brilliant.
• The agent tries something.
• If what the agent tries works well, relative to
  the agents peers, the agent keeps it up.
• If what the agent tries works poorly, the agent
  copies (a) more successful peer(s)
• Here the chromosome details the strategy.

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Example Game Theory Chromosome (I)

• The ? are either C or D
• The agents query their History of their
  opponents last 3 moves and then do what their
  chromosome tells them to do

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Example Game Theory Chromosome (II)
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An Evolutionary Computational Approach

• Increased Process Validity
• Outcomes
• Typically converge on economic answer (Game
  Theory Dawid 1999)
• Some research suggests GA offer better
  predictions of human behavior (Ünver 2001, Tracy
  2008, Andreoni Miller 1995 ),
• Observable Dynamic, Disequilibrium Behavior

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Where is this going?
Theory Driven
Data Driven
?
69
Thank you

• And thanks to Lu Liping for help with the
  translations!