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Computational Modeling in the Social Sciences. Ken Kollman University of Michigan. Overview. Modeling in the social sciences Comparisons and definitions Types of computational models Agent-based modeling Achievements Promise Limitations. Models. Disciplined story-telling
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Computational Modeling in the Social Sciences Ken Kollman University of Michigan
Overview • 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 • Prediction • Insight • Conceptual clarity • Sometimes things “pop out”
Some Want Models to • Have an equilibrium • Have theorems (closed-form solutions) • Be rigorous • Be deductive • Have rational agents • Have rational individuals
Types of Modeling • 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 decision-makers (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 • 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)
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 • Two gender types • Utility=comfort level + interest + ability • Agents can move professions • Feedback
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
Computational Models Can • Equilibrate • Cycle • Lead to perpetual novelty • All three
Computational Models Can • Complement mathematical models • Predict • Provide insight • Offer conceptual clarity • Have things “pop out”
Complexity Models, Complex Adaptive Systems Models • 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 • 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