icpsr - complex systems models in the social sciences - lecture 9 - professor daniel martin katz
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Complex Systems Models in the Social Sciences
(Lecture 9)
Daniel Martin KatzMichigan State University
College of Law
Part II of This ClassStarting on Monday,Part II of this Course will Focus on Applied Papers
Kyle Joyce from UC-Davis Will Lead this Effort
In This Final Lecture Will:
Highlight the Various Forms of Modeling Frameworks*
Try to Tie Together a Series of Conceptual Building Blocks
*Drawn from Slides by Ken Kollman
Modeling Frameworks
What Are Models For?
“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)
Sometimes it is just Disciplined story-telling - Sometime it can be more
What Are Models For?
Prediction
Conceptual clarity about assumptions
Insight about why we observe what we do
Evaluating Counterfactuals
Modeling Frameworks
General equilibrium
Differential equations
Decision theoretic
Game theoretic
Social choice
Graph Theoretic
Adaptive
Computational
Agent-based
Modeling Frameworks
General equilibrium
Differential equations
Decision theoretic
Game theoretic
Social choice
Graph Theoretic
Adaptive
Computational
Agent-based
SometimesYou Can
Build Ensembles
of theseFrameworks
Modeling Frameworks
General equilibrium
Differential equations
Decision theoretic
Game theoretic
Social choice
Graph Theoretic
Adaptive
Computational
Agent-based
We have Mostly
Focused on these ...
Game Theory Currently Dominant
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)
The Primacy of Nash Equilibrium
An “upper” solution concept, in Myerson’s terms
If not Nash, then not reasonable to predict
Problems:Multiple equilibriaImportance of out-of-equilibrium beliefsActually doesn’t predict very well
http://www.youtube.com/watch?v=p3Uos2fzIJ0
Extensions
Axelrod’s computer tournaments!
Adaptive party modelsM. Laver (NYU Pol Sci) recent work
Formation of nation-states, empires
Social contagion (S.I.R. Models)
Complexity Models
(1) Agents follow simple rules
(2) Emergence of macro patterns
Flocking Model is a Good Example
Justification for Complexity Models
We can’t solve the models we want to study given current analytical techniques--computer is necessary
We believe we are studying agents who adapt, or in some sense are boundedly rational--computer is convenient but in principle not necessary
Computational models are better at modeling our contemporary world
Complexity Models
(3) Agents’ actions are interdependent
Can Be Modeled In Several Ways
Networks Are One Important way
Rule Encoding is Key
Agents Rules are Mixtures of Global rules + Local rules
Simple Birth Rates is Completely Global
Wolf-Sheep is a Mixture
Energy is indexed locally
But Each Agent is still following same rules
Conceptual Building Blocks
Search / Exploration
Emergence + Self Organization
Path Dependence
Feedback
Conceptual Building Blocks
Diffusion
Dependence
How Do I Know That I Am On the Highest Peak?
Search / Exploration
Search / Exploration
Search / Exploration
Emergence + Self Organization
Path Dependence
Feedback
Conceptual Building Blocks
Diffusion
Dependence
phat-dependent
path-dependent
vs.
Search / Exploration
Emergence + Self Organization
Path Dependence
Feedback
Conceptual Building Blocks
Diffusion
Dependence
Simple Rules GeneratingComplexity
Absence of Top Down Control
Example:The Flocking Model
Search / Exploration
Emergence + Self Organization
Path Dependence
Feedback
Conceptual Building Blocks
Diffusion
Dependence
Feedback = the return to the input of a part of the output (can be +, - or 0 )
negative feedback
negative feedback --> negative if the resulting action opposes the condition that triggers it
This class of feedback is often described as auto-regulating in so much as deviations from the equilbriua are dragged back
Positive Feedback
positive --> if the resulting action builds upon the condition that triggers it
These are the more interesting class of effects
Perturbations to the system can generate a novel set of outcomes
A positive connection: !�!
For Full Example: http://serc.carleton.edu/introgeo/models/loops.html
!�The positive connection for a cooling coffee cup implies that the hotter the coffee is the faster it cools. The variables Tc and Tr are coffee and room temperature respectively.
a negative connection: !!�the negative connection in the figure below for a cooling coffee cup implies a positive cooling rate makes the coffee temperature drop.� !
For Full Example: http://serc.carleton.edu/introgeo/models/loops.html
the two connect i ons are combined yield a !negative feedback loop !!
coffee temperature approaches the stable equilibrium of the room temperature.!
going around the loop the positive connection times the negative connection gives a negative loop feedback effect. !
Search / Exploration
Emergence + Self Organization
Path Dependence
Feedback
Conceptual Building Blocks
Diffusion
Dependence
Lots of Ways to Potentially
Model Diffusion
In General We are Interested in Dynamics
Yielding the Spreadof Some “Pathogen”
SIR Model is the Classic Compartmental model
from epidemiology
S (for susceptible)
I (for infectious)
R (for removed(i.e. immune or dead)
Lots of Other Variants
The SIS model
The SEIR model
Carrier state
http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology
The MSIR model
“Pathogen” could actually be a pathogen OR it could
be something else ...
Fads, Customs, Ideology,
etc.
Search / Exploration
Emergence + Self Organization
Path Dependence
Feedback
Conceptual Building Blocks
Diffusion
Dependence
We Covered this at great length ...
Networks are “dependency graphs”
Next Steps ...
ICPSR - Complex Systems Models in the Social Sciences - Lab Session 7 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lab Session 2 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lab Session 4 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lab Session 9 - Professor Daniel Martin Katz