Transcript Computational Modeling in the Social Sciences

Computational Modeling in the
Social Sciences
Ken Kollman
University of Michigan
Overview
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Modeling in the social sciences
Comparisons and definitions
Types of computational models
Agent-based modeling
Achievements
Promise
Limitations
Models
• Disciplined story-telling
• “a precise and economical statement of a set of
relationships that are sufficient to produce the
phenomena in question” (Schelling).
• Complicated enough to explain something not so
obvious or trivial, but simple enough to be
intuitive once it’s explained (Schelling)
• A difficult tradeoff
Two Levels of Simplicity
• Simple models---Prisoner’s Dilemma,
Edgeworth box, Supply and Demand
• Not so simple, but profound---Arrow’s
theorem, Chaos theorems, Nash theorem
Goals of Models
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Prediction
Insight
Conceptual clarity
Sometimes things “pop out”
Some Want Models to
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Have an equilibrium
Have theorems (closed-form solutions)
Be rigorous
Be deductive
Have rational agents
Have rational individuals
Types of Modeling
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General equilibrium
Differential equations (egs., arms race models)
Decision theoretic
Game theoretic (cooperative, noncooperative)
Social choice
Adaptive
Computational
Agent-based
Game Theory Currently
Dominant
• Theory of interdependent decisions
• Study of mathematical models of conflict and
cooperation among intelligent, rational decisionmakers (Myerson)
• Rational---optimizing Bayesians
• Intelligent--decision-makers know and understand
everything they do and we do (NOT complete
information)
• Example of non-intelligence--price theory (agents
don’t know the model)
Great Strides in Economics and
other Social Sciences
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Rich theory
Cumulative
Widely applicable
Some design successes (eg., auctions)
Three Types of Computational
Models
• Simulations--numerical examples, usually
of an equilibrium outcome
• Computations--numerical approximations
of equilibria that cannot be solved
analytically (Judd)
• Agent-based models--diverse, interacting,
boundedly-rational, adaptive agents, not
necessarily an equilibrium
Agent-based Models
• “Analysis of simulations of complex social
systems” (Axelrod)
• Purpose? “To aid intuition, ” not to analyze the
consequences of assumptions (Axelrod)
• Often, but not always, computational
• Schelling’s segregation model as an example
• Can be reduced form (pick up where modeler left
off) or can be platform for artificial world
(calculates each agent’s behavior and aggregates)
Schelling: Moving Dimes and Nickels
Simple Model by Page of Gender
in Professions
“We keep hiring women scientists but
they keep moving to management or
leaving the firm.”
Page Tipping Model
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Two gender types
Utility=comfort level + interest + ability
Agents can move professions
Feedback
Reality
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Men
Women
Nursing
Sales
Math
Education
Model: Initial State
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Model: End State
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“If you didn’t grow it you didn’t
show it” (Epstein)
Kollman, Miller, Page Models of
Political Competition
• Political parties competing for support
• Each voter has a favorite policy position in
the space of possible policies
• Parties move in the space to win votes
• Receive feedback from opinion polls, and
adapt according to information
• Hill-climb toward higher vote totals
Adaptation on Electoral Landscapes
Computational Models Can
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Equilibrate
Cycle
Lead to perpetual novelty
All three
Computational Models Can
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Complement mathematical models
Predict
Provide insight
Offer conceptual clarity
Have things “pop out”
Complexity Models, Complex
Adaptive Systems Models
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Santa Fe Institute
Emergence
Adaptation
Non-equilibrium
Agent-based
Feedback
From More General to Less
• Models
• Computational models
• Agent-based models
Achievements
• Segregation (Schelling)
• PD games (Axelrod)
• Feedback in markets (Epstein and Axtell,
Tesfatsion, Arthur et al)
• City Formation (Krugman)
• Disease transmission (Simon)
Achievements (cont’d)
• Organizational hierarchies and feedback (March,
Harrington)
• Political competition (Kollman, Miller, and Page)
• Diversity and decision-making (Hong and Page)
• Emergence of complex societies (Padgett and
Ansell)
• Spread of culture or empire (Nowak, Cederman)
• Industrial Organization (Harrington)
Promise
• Answering difficult questions other approaches
cannot---multi-layered institutions, diversity,
learning, feedback, spontaneous emergence, path
dependence
• Simulation and prediction
• Robustness under bounded-rationality
assumptions
Limitations
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Elusive standards
Not always intuitive
Undisciplined modeling
Agents not smart enough
Opposition
• Those opposed to modeling
• Those opposed to bounded-rationality
approaches
• Those opposed to non-equilibrium models
One Funeral at a Time…..