# Exploring Complex Systems in Social Science

EXPLORING COMPLEX SYSTEMS IN SOCIAL SCIENCE Greg Marfleet Carleton College Department of Political Science ISSUES FOR POLITICAL SCIENCE STUDENTS Concept of Politics: Elite-driven or Institutionally Shaped (top-down causal thinking) Bias toward stability, order, equilibrium (negative feedback) Methods: linear, additive (Econometrics)

Y = b0 + b1x1+ ..+ bnXn + e Models: statistical or qualitative narratives Analysis: Cross-sectional, not dynamic Limited macro-micro linking Orthodoxy in game theory (always with fixed exogenous preferences fixed environment) No common ontology of agents COMPLEXITY CONCEPTS Bottom-up generative Roots in chaos, perpetual novelty Self-organization and Criticality Systems can be dynamic with positive and/or negative feedback

Non-linear processes Models are process oriented: you must grow it to show it Micro to Macro links emergent properties Agents can be adaptive (not fixed) Models require an explicit ontology of agents CLASSIC POLI-SCI VOTING MODEL Median Voter Theorem (Anthony Downs) L A

B R In a two party election (A, B) where voters can be considered as arrayed on a L-R ideological scale, the optimal position for each party is the Median Voter (50%+1). Predicts convergence in policy positions COMPLEX VOTING MODEL Political Insitutions and Sorting in a Tiebout Model (Kollman, Miller and Page)

Issue1 A B Issue2 In an N-issue opinion space, voters are arranged as a landscape with varying density. Parties must dynamically position

themselves to maximize their share of voters by altering their position (P) for each (i). CLASSIC IR MODEL Richardson Arms Race A system of two linear differential equations Arms accumulate because of mutual fear (a, b) There is resistance from society against constantly increasing arms expenditures (m, n) There are factors independent of expenditures that contribute to the buildup of arms (r, s

dx/dt = ay - mx + r dy/dt = bx - ny + s COMPLEX IR MODEL Cederman, Emergent Actors in World Politics States, the main actors in IR, that are often reified in existing theory are themselves the emergent

property of security-seeking sub-units. IR is ultimately connected to individuals security goals TEACHING EXAMPLE #1 Thomas Schelling, Micromotives and Macrobehavior (1978) Segregation Model Simple rule based agents The social structure changes as agents make choices Positive Feedback System Emergent Macro-level outcome Computers not required (just helpful)

Questions: What happens if we change the rules? Could we introduce a negative feedback element? Netlogo Version TEACHING EXAMPLE #2 Miller and Page (2004): The Standing Ovation Problem How does a standing ovation propagate through an audience? (cellular automata) Agents with a simple choice (sit, stand) Agents are socially influenced (neighbors) Spatial arrangements matter (information) Agents may be heterogeneous or homogeneous

Questions: Is there a tipping point? Common binary choices in PS? Netlogo examples SANDPILES, AVALANCHES AND WARS

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