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 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 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 100 90 80 70 60 50 40 30 20 10 0 Nursing Sales Math Education Men Women
Model: Initial State 60 50 40 30 20 Men Women 10 0 1 2 3 4
Model: End State 100 90 80 70 60 50 40 30 20 10 0 1 2 3 4 Men Women
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 Complex adaptive systems 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..