Agent Based Models in Social Science

1. Agent Based Models in Social Science James Fowler University of California, San Diego

2. The Big Picture: Collective Action • Cooperation • Alternative Models of Participation • Social Networks

3. Cooperation • Evolutionary models • Altruistic Punishment and the Origin of Cooperation PNAS 2005 • Second Order Defection Problem Solved?Nature 2005 • On the Origin of Prospect TheoryJOP, forthcoming • The Evolution of Overconfidence • Experiments • Egalitarian Motive and Altruistic PunishmentNature 2005 • Egalitarian Punishment in HumansNature 2007 • The Role of Egalitarian Motives in Altruistic Punishment • The Neural Basis of Egalitarian Behavior

4. Alternative Models of Political Participation • Computational Models of Adaptive Voters and Legislators • Parties, Mandates, and Voters: How Elections Shape the Future 2007 • Policy-Motivated Parties in Dynamic Political CompetitionJTP 2007 • Habitual Voting and Behavioral TurnoutJOP 2006 • A Tournament of Party Decision Rules • Empirical Models of Legislator Behavior • Dynamic Responsiveness in the U.S. SenateAJPS 2005 • Elections and Markets: The Effect of Partisan Orientation, Policy Risk, and Mandates on the EconomyJOP 2006 • Parties and Agenda-Setting in the Senate, 1973-1998

5. Alternative Models of Political Participation • Experiments • Altruism and TurnoutJOP 2006 • Patience as a Political Virtue: Delayed Gratification and TurnoutPolitical Behavior 2006 • Beyond the Self: Social Identity, Altruism, and Political ParticipationJOP 2007 • Social Preferences and Political Participation • When It's Not All About Me: Altruism, Participation, and Political Context • Partisans and Punishment in Public Goods Games • Genetics • The Genetic Basis of Political Participation • Southern California Twin Register at the University of Southern California: II Twin Research and Human Genetics 2006

6. Political Social Networks • Voters • Dynamic Parties and Social Turnout: an Agent-Based ModelAJS 2005 • Turnout in a Small WorldSocial Logic of Politics 2005 • Legislators • Legislative Cosponsorship Networks in the U.S. House and SenateSocial Networks 2006 • Connecting the Congress: A Study of Cosponsorship NetworksPolitical Analysis 2006 • Community Structure in Congressional Networks • Legislative Success in a Small World: Social Network Analysis and the Dynamics of Congressional Legislation • Co-Sponsorship Networks of Minority-Supported Legislation in the House • The Social Basis of Legislative Organization

7. Political Social Networks • Court Precedents • The Authority of Supreme Court PrecedentSocial Networks, forthcoming • Network Analysis and the Law: Measuring the Legal Importance of Supreme Court PrecedentsPolitical Analysis, forthcoming

8. Other Social Networks • Political Science PhDs • Social Networks in Political Science: Hiring and Placement of PhDs, 1960-2002PS 2007 • Academic Citations • Does Self Citation Pay?Scientometrics 2007 • Health Study Participants • The Spread of Obesity in a Large Social Network Over 32 YearsNew England Journal of Medicine 2007 • Friends and Participation • Genetic Basis of Social Networks

9. What is an Agent Based Model? • Computer simulation of the global consequences of local interactions of members of a population • Types of agents • plants and animals in ecosystems (Boids) • vehicles in traffic • people in crowds • Political actors

10. What is an Agent Based Model? • “Boids” are simulations of bird flocking behavior (Reynolds 1987) • Three rules of individual behavior • Separation • avoid crowding other birds • Alignment • point towards the average heading of other birds • Cohesion • move toward the center of the flock • Result is a very realistic portrayal of group motion in flocks of birds, schools of fish, etc.

11. What is an Agent Based Model? • Comparison with formal models • Same mathematical abstraction of a given problem, • but uses simulation rather than mathematics to “solve” model and derive comparative statics • Comparison with statistical models • Same attempt to analyze data, • but uses simulation data rather than real data

12. Advantages of Agent Based Modeling • Formal • Assumptions laid bare • Flexible • Cognitively: agents can be “rational” or “adaptive” • Tractable • Easier to cope with complexity(nonlinearities, discontinuities, heterogeneity) • Generative • Helps create new hypotheses • Social Science from the Bottom Up • “If you didn’t grow it you didn’t show it.”

13. Disadvantages of Agent Based Modeling • Models too simple • Could be solved in closed-form (Axelrod 1984) • Closed-form solution always preferable • Models too complicated • Not possible to assess causality (Cederman 1997) • What use is an existence proof? • Coding mistakes • Many more lines of code than lines in typical formal proof • Data analysis • What part of the parameter space to search?

14. My Approach to Agent Based Modeling • Write down model • Solve as much as possible in closed-form • Justify simulation with mathematical description of the complexity problem • Use real world to “tune” model • Make predictions • Check predictions against reality • Do comparative statics near real world parameters to assess causality

15. Tournament Overview • A dynamic spatial account of multi-party multi-dimensional political competition • is substantively plausible • generates a complex system that is analyticallyintractable • amenable to systematic and rigorous computational investigation using agent based models (ABMs) • Existing ABMs use a fixed set of predefined strategies, typically in which all agents deploy the same rule. • There as been little investigation of potential rules, or the performance of different rules in competition with each other • The Axelrodian computer tournament is a good methodology for doing this … • … while also offering great theoretical potential to be expanded into a more comprehensive evolutionary system

16. Tournament ABM test-bed • We advertised a computer simulation tournament with a $1000 prize for the action selection rule winning most votes, in competition with all other submitted rules over the very long run. • Tournament test-bed (in R) adapted from Laver (APSR 2005) • The four rules investigated by Laver were declared pre-enteredbut ineligible to win: Sticker, Aggregator, Hunter and Predator • Submitted rules constrained to use only published information about party positions and support levels during each past period and knowledge of own supporters’ mean/median location

17. Departures from Laver (2005) • Distinction between inter-election (19/20) and election (1/20) periods • Forced births (1/election) at random locations, as opposed to endogenous births at fertile locations, à la Laver and Schilperoord • De factosurvival threshold (<10%, 2 consecutive elections) • Rule designers’ knowledge of pre-entered rules • Diverse and indeterminate rule set to be competed against

18. Tournament structure • There were 25 valid submissions – after several R&Rs for rule violations, elimination of a pair of identical submissions and of one in R code that would not run and we could not fix – making 29 distinctive rules in all. • Five runs/rule (in which the rule in question was the first-born) • 200,000 periods (10,000 elections)/run (after 20,000 period burn in) • Thus 145 runs, 29,000,000 periods and 1,450,000 elections in all • Brooks-Gelman tests used to infer convergence, in the sense that results from all chains are statistically indistinguishable. • There was a completely unambiguous winner – not one of the pre-entered rules • However only 9/25 submissions beat pre-announced Sticker (i.e. select random location and never move)

19. Tournament algorithm portfolio • Center-seeking rules: use the vote-weighted centroid or median • Previous work suggests these are unlikely to succeed, a problem exacerbated in a rule set with other species of the same rule • Tweaks of pre-entered rules: eg with “stay-alive” or “secret handshake” mechanisms (see below) • Sticker is the baseline “static” rule for any dynamic rule to beat • Hunter was the previously most successful pre-entered rule • “Parasites” (move near successful agent): have a complex effect • Split successful “host” payoff so unlikely to win – especially in competition with other species of parasite • But do systematically punish successful rules • No submitted rule had any defense against parasites • No submitted parasite anticipated other species of parasite

20. Tournament algorithm portfolio • Satisficing (stay-alive)rules: stay above the survival threshold rather than maximize short-term support • Substantively plausible but raise an important issue about agent time preference – which only becomes evident in a dynamic setting • “Secret handshake” rules: agent signals its presence to other agents using the same rule (e.g. using a very distinctive step size), who recognize it and avoid attacking it • Substantively implausible (?) but, given 29 rules and random rule selection, there was smallish a priori probability that an agent would be in competition with another using the same rule • Inter-electoral explorers: use the 19 inter-election periods to search (costlessly) for a good location on election day • Substantively plausible but raise an important issue about relative costs of inter-electoral moves

21. Results: votes/rule

22. Results: votes/agent-using-rule

23. Results: agent longevity

24. Results: Pairwise performance

25. Results: run-off

26. Results: No Secret Handshake

27. Results: Evolutionary Reproduction

28. Characteristics of successful rules • KQ-strat focused on staying alive, protected itself against cannibalism with a very distinctive step size, and became a parasite when below the survival threshold • Shuffle was a pure staying-alive algorithm, non-parasitic and without explicit cannibalism protection, though unlikely to attack itself since it tends to avoid other agents • Genety had used prior simulations deploying the genetic algorithm to optimize its parameters against a set of pre-submitted and anticipated rules. It was not a parasite, had no protection against cannibalism and did not focus on staying alive. • Fisher distinctively used the 19 inter-electoral periods to find the best position at election time. However, it also satisficed by taking much smaller steps when over the threshold

29. Characteristics of successful rules • Of the three other rules doing significantly better than Hunter: • Sticky-Hunter/Median-Finder conditioned heavily on the survival threshold • Pragmatist simply tweaked Aggregator by dragging it somewhat towards the vote-weighted centroid • Pick-and-Stick simply tweaked Sticker by picking the best of 19 random locations explored in the first 19 post-birth inter-election periods. • Pure center-seeking and parasite rules did badly • Set of successful rules was thus diverse – most systematic pattern being to condition on the survival threshold

30. Medium Eccentricity is Best

31. Less Motion is Better

32. Conclusion • Agent Based Models can help us assess causality in social science • Tournaments can help bring human element into an ABM • However, agent-based modelers must • Keep models simple • Check for closed-form solutions • Ground models in the real world • Work closely with statisticians (EI) and formal modelers (TM)