Computational Modeling in the Social Sciences

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)

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 • Two gender types • Utility=comfort level + interest + ability • Agents can move professions • Feedback

Reality

Model: Initial State

Model: End State

“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 • 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

One Funeral at a Time…..

Computational Modeling in the Social Sciences

Télécharger la présentation

Plus de contenu associé