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
Behavioral Models
Rule Based Models
When Does Behavior Matter
Categorical and Linear Models
Introduction to Linear Models
Categorical Models
Linear Models
Fitting Lines to Data
Reading Regression Output
From Linear to Nonlinear
The Big Coefficient vs The New Reality
Readings
Why Model?
By: Joshua M. Epstein
- Everyone models, but most models are implicit rather than explicit
- Reasons besides predictions to build modles
- Explain
- Guide data collection
- Illuminate core dynamics
- Suggest dynamical analogies
- Discover new questions
- Promote a scientific habit of mind
- Bound (bracket_ outcomes to plausible ranges
- Illuminate core uncertainties
- Offer crisis options in near-real time
- Demonstrate tradeoffs / suggest efficiencies
- Challenge the robustness of prevailing theory through perturbations
- Expose prevailing wisdom as incompatible with available data
- Train practitioners
- Discipline the policy dialogue
- Educate the general public
- 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.