Complex Systems Models
in the Social Sciences
(Lecture 8 + 9)
daniel martin katz
illinois institute of technology
chicago ...
Part II of This Class
Starting on Monday,
Part II of this Course
Michael Bommarito Will Lead this Effort
In This Final Lec...
Modeling
Frameworks
What Are Models For?
“a precise and economical statement of a
set of relationships that are sufficient
to produce the pheno...
What Are Models For?
Prediction
Conceptual clarity about assumptions
Insight about why we observe what we do
Evaluating Co...
Modeling
Frameworks
General equilibrium
Differential equations
Decision theoretic
Game theoretic
Social choice
Graph Theor...
Modeling
Frameworks
General equilibrium
Differential equations
Decision theoretic
Game theoretic
Social choice
Graph Theor...
Modeling
Frameworks
General equilibrium
Differential equations
Decision theoretic
Game theoretic
Social choice
Graph Theor...
Game Theory
Currently Dominant
Study of mathematical models of conflict and
cooperation among intelligent, rational
decisio...
The Primacy of
Nash Equilibrium
An “upper” solution concept, in
Myerson’s terms
If not Nash, then not
reasonable to predic...
http://www.youtube.com/watch?v=p3Uos2fzIJ0
Extensions
Axelrod’s computer tournaments
Adaptive party models
M. Laver (NYU Pol Sci) recent work
Formation of nation-sta...
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--comput...
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-...
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
Generating
Complexity
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...
Positive Feedback
positive --> if the resulting action builds upon
the condition that triggers it
These are the more inter...
A positive connection: !
!
For Full Example:
http://serc.carleton.edu/introgeo/models/
loops.html
!
The positive connectio...
a negative connection:!
!
the negative connection in the figure
below for a cooling coffee cup implies a
positive cooling ...
t h e t w o c o n n e c t i o n s
are combined yield a !
negative feedback loop !
!
coffee temperature approaches the stab...
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 Spread
of 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_epi...
“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”
Places to Learn More
http://www.complexityexplorer.org/online-courses
http://complexity.stanford.edu/classes
https://class.coursera.org/nlp/lecture
http://www.r-bloggers.com/?s=machine+learning
ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 and 9 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 and 9 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 and 9 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 and 9 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 and 9 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 and 9 - Professor Daniel Martin Katz
ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 and 9 - Professor Daniel Martin Katz
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ICPSR - Complex Systems Models in the Social Sciences - Lecture 8 and 9 - Professor Daniel Martin Katz

  1. 1. Complex Systems Models in the Social Sciences (Lecture 8 + 9) daniel martin katz illinois institute of technology chicago kent college of law @computationaldanielmartinkatz.com computationallegalstudies.com
  2. 2. Part II of This Class Starting on Monday, Part II of this Course Michael Bommarito 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
  3. 3. Modeling Frameworks
  4. 4. 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
  5. 5. What Are Models For? Prediction Conceptual clarity about assumptions Insight about why we observe what we do Evaluating Counterfactuals
  6. 6. Modeling Frameworks General equilibrium Differential equations Decision theoretic Game theoretic Social choice Graph Theoretic Adaptive Computational Agent-based
  7. 7. Modeling Frameworks General equilibrium Differential equations Decision theoretic Game theoretic Social choice Graph Theoretic Adaptive Computational Agent-based Sometimes You Can Build Ensembles of these Frameworks
  8. 8. Modeling Frameworks General equilibrium Differential equations Decision theoretic Game theoretic Social choice Graph Theoretic Adaptive Computational Agent-based We have Mostly Focused on these ...
  9. 9. 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)
  10. 10. The Primacy of Nash Equilibrium An “upper” solution concept, in Myerson’s terms If not Nash, then not reasonable to predict Problems: Multiple equilibria Importance of out-of-equilibrium beliefs Actually doesn’t predict very well
  11. 11. http://www.youtube.com/watch?v=p3Uos2fzIJ0
  12. 12. Extensions Axelrod’s computer tournaments Adaptive party models M. Laver (NYU Pol Sci) recent work Formation of nation-states, empires Social contagion (S.I.R. Models)
  13. 13. Complexity Models (1) Agents follow simple rules (2) Emergence of macro patterns Flocking Model is a Good Example
  14. 14. 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
  15. 15. Complexity Models (3) Agents’ actions are interdependent Can Be Modeled In Several Ways Networks Are One Important way
  16. 16. 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
  17. 17. Conceptual Building Blocks
  18. 18. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
  19. 19. How Do I Know That I Am On the Highest Peak? Search / Exploration
  20. 20. Search / Exploration
  21. 21. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
  22. 22. phat-dependent path-dependent vs.
  23. 23. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
  24. 24. Simple Rules Generating Complexity
  25. 25. Absence of Top Down Control
  26. 26. Example: The Flocking Model
  27. 27. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
  28. 28. Feedback = the return to the input of a part of the output (can be +, - or 0 )
  29. 29. 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
  30. 30. 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
  31. 31. 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.
  32. 32. 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
  33. 33. t h e t w o c o n n e c t i o n s 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. !
  34. 34. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
  35. 35. Lots of Ways to Potentially Model Diffusion
  36. 36. In General We are Interested in Dynamics Yielding the Spread of Some “Pathogen”
  37. 37. SIR Model is the Classic Compartmental model from epidemiology
  38. 38. S (for susceptible) I (for infectious) R (for removed (i.e. immune or dead)
  39. 39. Lots of Other Variants The SIS model The SEIR model Carrier state http://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology The MSIR model
  40. 40. “Pathogen” could actually be a pathogen OR it could be something else ...
  41. 41. Fads, Customs, Ideology, etc.
  42. 42. Search / Exploration Emergence + Self Organization Path Dependence Feedback Conceptual Building Blocks Diffusion Dependence
  43. 43. We Covered this at great length ...
  44. 44. Networks are “dependency graphs”
  45. 45. Places to Learn More
  46. 46. http://www.complexityexplorer.org/online-courses
  47. 47. http://complexity.stanford.edu/classes
  48. 48. https://class.coursera.org/nlp/lecture
  49. 49. http://www.r-bloggers.com/?s=machine+learning

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