Agent Based Models in Social Science

James FowlerUniversity of California, San Diego

The Big Picture: Collective Action Cooperation

Alternative Models of Participation

Social Networks

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

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 Competition

JTP 2007 Habitual Voting and Behavioral Turnout

JOP 2006 A Tournament of Party Decision Rules

Empirical Models of Legislator Behavior Dynamic Responsiveness in the U.S. Senate

AJPS 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

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

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 Senate

Social Networks 2006 Connecting the Congress: A Study of Cosponsorship Networks

Political 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

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

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

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

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.

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

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.”

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?

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

Tournament Overview A dynamic spatial account of multi-party multi-dimensional

political competition is substantively plausible generates a complex system that is analytically intractable 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

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-entered but 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

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 facto survival threshold (<10%, 2 consecutive elections)

Rule designers’ knowledge of pre-entered rules Diverse and indeterminate rule set to be competed

against

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)

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

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

Results: votes/rule

Results: votes/agent-using-rule

Results: agent longevity

Results: Pairwise performance

KQSTRATSHUFFLEGENETYFISHERPRAGMATISTSTICKY-HUNTERPICK-AND-STICKRAPTORHUNTERHALF-AGGREGATORSTICKERNICHE-HUNTERPATCHWORKNICHE-PREDATORAGGREGATORCENTER-MASSAVERAGEFOOL-PROOFPREDATORFOLLOW-THE-LEADERINSATIABLE-PREDATORMEDIAN-VOTER-SEEKERPARASITEAVOIDERZENOOVER-UNDERMOVE-NEAR-SUCCESSFULJUMPERBIGTENT

B I G T E N T

J U M P E R

M O V E - N E A R - S U C C E S S F U L

O V E R - U N D E R

Z E N O

A V O I D E R

P A R A S I T E

M E D I A N - V O T E R - S E E K E R

I N S A T I A B L E - P R E D A T O R

F O L L O W - T H E - L E A D E R

P R E D A T O R

F O O L - P R O O F

A V E R A G E

C E N T E R - M A S S

A G G R E G A T O R

N I C H E - P R E D A T O R

P A T C H W O R K

N I C H E - H U N T E R

S T I C K E R

H A L F - A G G R E G A T O R

H U N T E R

R A P T O R

P I C K - A N D - S T I C K

S T I C K Y - H U N T E R

P R A G M A T I S T

F I S H E R

G E N E T Y

S H U F F L E

K Q S T R A T

Vote Share By Type

N u m b e r o f P a r t i e s B y T y p e

Results: run-off

Rule Runoff Tournament Mean

vote Median

rank Mean vote

Median rank

KQ-Strat

19.6

1

11.2

1

Pick-and-Stick 15.4 2 6.8 6 Sticky hunter 15.0 3 7.3 5 Genety 14.0 4 8.4 4 Pragmatist 13.6 5 7.4 5 Shuffle 11.6 6 9.7 2 Fisher 10.9 7 7.9 4

Results: No Secret Handshake

B I G T E N T

J U M P E R

M O V E . N E A R . S U C C E S S F U L

O V E R . U N D E R

Z E N O

A V O I D E R

M E D I A N . V O T E R . S E E K E R

P A R A S I T E

F O L L O W . T H E . L E A D E R

I N S A T I A B L E . P R E D A T O R

P R E D A T O R

A V E R A G E

F O O L . P R O O F

C E N T E R . M A S S

A G G R E G A T O R

N I C H E . P R E D A T O R

P A T C H W O R K

N I C H E . H U N T E R

S T I C K E R

H U N T E R

H A L F . A G G R E G A T O R

R A P T O R

P I C K . A N D . S T I C K

S T I C K Y . H U N T E R . M E D I A N . F I N D E R

P R A G M A T I S T

F I S H E R

G E N E T Y

S H U F F L E

K Q S T R A T

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0

T o t a l V o t e s R e c e i v e d P e r S i m u l a t i o n ( T h o u s a n d s )

Results: Evolutionary ReproductionRule Success-updated

fitness = 0.9; = 0.9

Original tournament = 0.0; = 1

KQ-strat

17.0

11.2

Genety 13.9 8.4 Sticky-hunter 11.7 7.3 Shuffle 11.2 9.7 Pick-and-stick 10.4 6.8 Pragmatist 9.6 7.4 Fisher 8.5 7.9 Raptor 4.1 4.9 Hunter 3.7 4.7 Half-aggregator 2.6 4.7 Sticker 1.2 3.9

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

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

Medium Eccentricity is Best

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0

6

8

10

12

14

E c c e n t r i c i t y

( D i s t a n c e F r o m C e n t e r )

Average Vote Share (%)

S T I C K E R

A G G R E G A T O R

H U N T E R

P R E D A T O RA V E R A G E

A V O I D E R

F I S H E R

G E N E T Y

H A L F - A G G R E G A T O R

J U M P E R

K Q S T R A T

M E D I A N - V O T E R - S E E K E R

M O V E - N E A R - S U C C E S S F U L

Z E N O

N I C H E - H U N T E R

P A R A S I T E

Less Motion is Better

0 . 0 0 . 5 1 . 0 1 . 5

6

8

10

12

14

M o t i o n

( A v e r a g e D i s t a n c e M o v e d F r o m P r e v i o u s E l e c t i o n )

Average Vote Share (%)

S T I C K E R

A G G R E G A T O R

H U N T E R

P R E D A T O R

A V O I D E R

G E N E T Y

J U M P E R

K Q S T R A T

M E D I A N - V O T E R - S E E K E R

M O V E - N E A R - S U C C E S S F U L

Z E N O

P A R A S I T E

P A T C H W O R K

P I C K - A N D - S T I C K

R A P T O R

S H U F F L E

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)