Model Thinking Notes

Lectures

Why Model

Why Model?

• Why use models?
  • Lots of fields use models
  • Models produce clearer thinking, make you a better thinker
  • Use and understand data
  • Decide, Strategize and design

Intelligent Citizens of the World

How models make you a better citizen of the world

• "All models are wrong, but some are useful" George EP Box
• Models are the language of business, academia, non-profit, almost all purposes
• Models give us the conditions under which rules are best applied
• Formal models do better than any semi-formal technique
• Models are fertile, a model designed for one system can often be cross applied to other domains
• Models make us humble

Thinking more clearly

How models make us clear thinkers

• Step 1: Name the parts
• Step 2: Identify the relationships (between those parts and how things play out)
• Outcomes: Equilibrium, cycle, random, complex
• Identify logical boundaries (identify conditions under which to apply rules)
• Use models to communicate

Using and understanding data

Models and Data

• Models reveal patterns in data
• Models predict points based on given data
• Produces bounds (ex. in ten years inflation will between 0% and 3%)
• Retrodiction (predicting the past), also good for testing the model
• Prediction other factors (the heliocentric universe model predicted neptune)
• Inform data collection
• Estimate hidden parameters
• Calibration

Usin models to decide, strategize and design

How to use models and data

• Ex. banks, showed interdependence and why some were saved
• Monty Hall problem
• Comparative Statics
• Counterfactuals
• Identify and rank levers
• Experimental design
• Institutional Design - a mechanism the means to achieve an end and the closer the final out come is to the desired is the efficiency of the mechanism
• Real time decision aides
• Help choose among policies and institutions

Segregation and Peer effects

Sorting and peer effects introduction

Sorting and Peer Effect. We hang out with people like us AND we behave like the people we spend time with.

When people think about models they think about equation based models. Agent based models model how individuals with behaviors interact. If the behaviors are optimal, then they are game theory models. The result is outcomes.

Schellings segregation model

Schellings Segregation model. Thomas Schelling. This is an agent based model. Peoples decision is whether or not to move. The models shows that if the threshold to move is that less than 1/3 of neighbors need to be similar the final result will be more than 70% similarity. When the threshold is increased to 50%, the final result is over 90% similarity. At 80%, it can't reach equilibrium. This shows that micromotives and macrobehavior may not align. This can also trigger a tipping point because one person leaving can cause others to leave.

Measuring segregation

Index of dissimilarity

sum of |b/B - y/Y| over all cells

Peer effects

Peer Effects

Developed by Mark Granovetter. Each person has a threshold at which they will join a movement. The threshold is the number of people who need to have already joined. Collective action is more like with lower thresholds, but varied thresholds helps.

Standing ovation model

The Standing Ovation Model

Like the Grenovetter model, there is a threshold to stand. It is also related to the quality of the show. But you can't directly know the quality, you have a signal with is your perception of quality. So if S>T you stand. Higher quality showes have more standing ovations. Lower threshold leads to standing ovation. If the variation in interpretation (diversity or error) is large, it is more likely to be a standing ovation.

Things that lead to standing ovation

• Higher quality
• Lower threshold
• Larger peer effect
• More variation

This model fails to take into account groups of people going together. It also fails to take into account that people in the front (celebrities) can't see anyone and people in the back can see everyone.

The fertility of this model applies to many areas, such as riots, student grades, urban renewal, fitness/health, and online courses.

Identification Problem

Identification. Is grouping because of homophily or peer effects. It's difficult to tell because the outcome looks similar, if not the same. To differntiate, dynamic data is required to see people change or move.

Aggregation

Aggregation

Goes back to Philip Andersons paper "More is different". A water molecule isn't wet, lots of molecules are needed for wettness. Neurons are another example. This is emergence.

Central limit theorem

Binomial distributions and standard deviations. For a given p Mean = pN, SD = (p(1-p)N)^.5. Independent, finite variance sums to normal distribution.

Six sigma

Developed by Motorola. Simply setting 6 standard deviations as the bounds. Outside of 6S is 3.4 in a million.

Game of life

Conways Game of life. Covering basic patterns.

Cellular automata

Developed by John Von Neuman. Covering 1D cellular automata.

preference aggregation

Rational (transitive) preferences when aggregated, can produce non-rational collective preferences. This is Condorcet Paradox.

Decision Models

Introduction to decision making

• Normative: using models to make choices
• Positive: Understanding why other make the choices they do.

Two Classes

• Multi-criterion
• Probabilistic

Multi-criterion decision making

Pro-con list - quantitative. Can also do qualitative by adding weights to each row. It's important that the model not tell you what to do, but help you make better decisions.

Spatial choice models

Using cumulative differences in multiple dimensions. Spatial models. Using models to explore others preference space.

Probability: The basics

Classic, frequency, subjective.

Decision trees

Each branch is probability times cost. They can also be used to infer probabilities.

Value of information

By calculating the expected outcome using a decision tree, then figure out the outcomes with the information and taking the difference, you can project the value of information.

Thinking Electrons: Modeling People

Thinking Electrons: Modeling People

People are hard to model, they are Purposeful Actors who are Diverse. We use different models to compensate. Utility = Consumption^.5*Leisure^.5.

• Rational Actor Model - People optimize
• Behavioral - Observe what people do, then model it
• Rule Based - Like Schelling model

Rational Actor Models

Assumes people make optimal choices. Entities have objectives and they make optimal choices to reach it. This should not be confused with selfishness, altruism can be it's own objective.

• Decision - outcome depends only on what I do
• Game - outcome depends partially on what others do

When do we see rationality?

• When the stakes are large
• When repeated (often people aren't rational at first, but become more rational over time)
• Group decisions
• Easy problems

Rational models serve as good benchmark. It is a unique state that tends to be easy to model. Over time, people tend to move towards rational solutions. If there is no bias, mistakes will cancel out and average out to something close to rational.

Readings

Why Model?

By: Joshua M. Epstein

• Everyone models, but most models are implicit rather than explicit
• Reasons besides predictions to build modles
  1. Explain
  2. Guide data collection
  3. Illuminate core dynamics
  4. Suggest dynamical analogies
  5. Discover new questions
  6. Promote a scientific habit of mind
  7. Bound (bracket_ outcomes to plausible ranges
  8. Illuminate core uncertainties
  9. Offer crisis options in near-real time
  10. Demonstrate tradeoffs / suggest efficiencies
  11. Challenge the robustness of prevailing theory through perturbations
  12. Expose prevailing wisdom as incompatible with available data
  13. Train practitioners
  14. Discipline the policy dialogue
  15. Educate the general public
  16. Reveal the apparently simple (complex) to be complex (simple)
• Many models are fertile, they cross apply to many unrelated domains

The Model Thinker: Prologue, Introduction and Chapter 1

Prologue

We have access to a lot of information. Models are the best means to parse it and choose which rules to apply to it.

Introduction

Combining information with models and contrasting it with facts can lead to decisions (Iceland bank example).

Models don't so much have flaws as they have limited scope. Newtonian physics is an 'incorrect' model with broad application. Multiple models help to compensate by extending scope or focusing scope. Many physical systems can be modeled with a single model or at least explain why they are too complex to model. Human systems tend to be more complex.

• Single Model fallacy - the idea we only need a single best model.
• Ration Choices - most models assume humans make rational choices, but we often do not. In high stakes, low complexity people act rational. In high complexity, well, it's complex.

Phil Tetlock found that single model thinkers, what he called hedgehogs, were worse than random at foretelling the future. It is better to use multiple models.

Chapter 1

• Supertanker example - increasing a tankers size increases it's surface area by a square power but it's volume cubically.
• The same model can explain that elephants have a slower metabolism than mice.