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

Using 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.

Behavioral Models

People systematically deviate from optimal solutions. This is often caused by the way we think. Slower thought is closer to rational than quicker decisions.

Prospect theory, people are risk averse for gains and not risk averse for loss. Example you can have A)$400 or B)50/50 shot at $1000, more people choose A. If it you change it to losing money, more people choose B.

Hyperbolic discounting. If you offer someone A) $1000 today or B) $1005 tomorrow they will take A. But if you offer A)$1000 in a year or B)$1000 in a year plus one day they will take B. We discount the near future more than the far future (we value immediate gratification). If you offer someone cake in week they will say "no I'm trying to lose weight", if you offer them cake now, they will take it.

Status Quo Bias. Opt-in vs opt-out. 25% of people will opt-in to organ donation but only 10% of people will opt-out.

Base rate bias. If you get people thinking about one number, they will continue to think of that number in unrelated cases.

WEIRD - Western educated industrialized rich developed countries. Many biases do not hold true across all populations. People learn, if they do something enough or identify the bias they may deviate from it. They can also be computationally difficult and fuzzy.

Rule Based Models

Assume that people follow certain rules. Standing ovation model or shelling model. Rational behavior and biases can both be rules. We have (fixed vs adaptive) X (decision vs game). Fixed rules may be good without being optimal. They are really easy to model. Can often capture main effects. Because people differ, the rules can be ad hoc. Sometimes optimal is simple, but simple rules can often be exploited.

Fixed rules

• Divide evenly
• tit for tat (nice while nice, mean while mean)
• Grim trigger (if you're ever mean, I'll be mean forever)

Adaptive Rules - Decisions

• Gradient rule, keep trying incremental patterns to try and find optimal
• Random, try random things to try and find optimal

Adaptive Rules - Games

• Best response
• Mimicry

When Does Behavior Matter

Context matters.

Categorical and Linear Models

Introduction to Linear Models

• Categorical model - place data into different categories
• Linear models - linear relationships between data
• Non-linear models - Matching data to curves
• Coefficients comparisons (Big Coefficient)

Categorical Models

Categories reduce variation (sum of difference squared).

(Vall - Vcat) / Vall = Variation explained. R-Squared. Higher R^2 means we explained a lot.

Correlation is not causation.

Linear Models

Lines are cool.

Fitting Lines to Data

RMSE. Did not cover how to generate the formula for a line.

Reading Regression Output

Regression models are cool.

From Linear to Nonlinear

Non-linear functions can be approximated by piecewise linear functions.

The Big Coefficient vs The New Reality

Evidence Based _blank_. Models are good for predicting how far a projection remains relevant. Projecting outside observable data leads to New Reality thinking.

Tipping Points

Tipping Points

Highly non-linear, "The straw that broke the camels back". A small change leads to a small effect, NOT exponential growth.

Percolation Models

Checkerboard with random 'on' or 'off' state. Can you make it from the top to the bottom only jumping to touching on squares. If P < .592, it almost certainly does not, at .592 it becomes likely. In the forest fire model at 57%, the fire does not spread far, at 61%, it does. If we think of it as a network rather than a grid, we can create more complex models, such as bank failures or country failures.

Information can also be thought of as the network and new technologies and knowledge fill in gaps allowing new discoveries to made all at once.

Contagion Models 1:Diffusion

Can be used for disease but also information or anything that can spread.

• Wt = people with W at time t
• N = Number of people
• N-Wt = number of people without W
• τ = transmission rate
• Pt = τ(Wt/N)( (N-Wt)/N ) = Probability one person will infect another at a random meeting
• c = contact rate
• Nc = Number or meetings
• Wt+1 = Wt + NcPt

For Pt, when Wt/N is near 50%, the transmission rate is the highest. Early, not enough people are infected to spread it, later, not enough people don't have it. But this is not a tipping point, the curves are smooth, just accelerated.

Contagion Models 2:SIS Models

Now, after someone has been infected, they get better and again become susceptible.

• a = recovery rate
• Wt+1 = Wt + NcPt - aWt
  • Wt+1 = Wt+Wt( cτ * ((N-Wt)/N) - a)

When Wt is small (N-Wt)/N is going to be nearly 1 reducing that segment to (cτ-a). If this value is >0 it will spread, if <0 it will not.

• R0 = cτ/a
  • if R0 > 1, then W spreads, this is the tipping point.

R0 of Real Diseases

• Measles = 15
• Mumps = 5
• Flu = 3

Measles and Mumps are actually SIR model.

If V is the number of people vaccinated

• r0 = R0*(1-V)

This means there is a tipping point for vaccination as well.

So how many people do we need to vaccinate to stop these diseases

• Measles: 14/15
• Mumps: 4/5
• Flu: 2/3

Classifying Tipping Points

Systems can also tip between class (stable, periodic, random, chaotic). Often we fixate on the tipping event but any number of events could have caused the tip.

Graphs that map movement to velocity will create stable points at y=0 where the slope is negative and unstable points (tipping points) where the slope is positive. If we can move the entire curve, we can make contextual tips by changing the whole environment. For instance a curve with 2 intercepts can be moved so there are no intercepts, stabilizing the whole system or the opposite can happen.

Measuring Tips

Measure 'tippiness' by change in uncertainty.

Diversity Index:

• Given P₀-P_n
• DI = 1 / ΣP_i²
• DI will always be <=N
  • The closer to N, the higher the diversity

Entropy:

• -ΣP_i log₂P_i
• Entropy tells us how much we need to know the outcome

Economic Growth

Introduction to Growth

• Exponential Growth
• Economic Growth
• Solow's Growth Model
• Extension

GDP. Maps closely to life satisfaction in the lower ranges (0-10,000) but not at higher levels (>40,000).

Exponential Growth

• P*(1+R)^t

Rule of 72: 72/R is about how long it takes to double

Continuous Growth: e^rt

Basic Growth Model

Coconut Economy Model

• L_t - Workers at time t
• M_t - Machines at time t
• O_t - Output of coconuts at time t
• E_t - Number consumed at time t
• I_t - Number invested at time t
• s = savings rate
• d = depreciation rate
• O_t = √L_t√M_t
• O_t = E_t + I_t
• I_t = sO_t
• M_t+1 = M_t + I_t - dM_t

Concave - diminishing returns to scale, often a square root function. Each additional widget has a smaller margin.

Lets assume

• L_t = 100
• d = 0.25
• s = 0.3
• M₁ = 4
• O₁ = 10√4 = 20
• M₂ = 4 + 20*0.3 - 0.25*4 = 9
• O₂ = 10√9 = 30
• M₃ = 9 + 30*0.3 - 0.25*9 ~ 16
• O₃ = 10√16 = 40

Suppose we have 400 machines

• O = 10√400 = 200
• M = 400 + 200*0.3 - 0.25*400 = 360

It Shrunk!

Equilibrium is reached when investment = depreciation. In this case it's 144 machines. Because depreciation is linear and output is concave. But innovation allows us to grow by shifting either the return on investment or depreciation.

Solow Growth Model

• L_t Labor
• K_t Capital
• A_t Technology
• O_t Output
• Β Capital intensity, generally about 1/2.
• O_t = A_tK_t^ΒL_t^1-Β

If innovation makes the coconut machines three times as productive (A=3) then long-run GDP goes up by 9.

Endogenous growth: Labor can go to output or technology/idea creation.

Will China Continue to Grow

No.

Why do some Countries not Grow

• Growth requires a strong central government to protect capital and investment, but that government cannot be controlled by a select few
• Growth requires creative destruction (put out of work by robots)

This model has limited fertility, but it can be applied to any similar scenario on any scale - such as personal. Getting better at stuff sustains personal growth.

Diversity and Innovation

Problem Solving and Innovation

The payoff for action a is F(a). Or a is a solution and F(a) is the effectiveness. We will discuss methods of optimizing a for F(a) and discuss why groups are better at optimizing.

Perspectives and Innovation

A good perspective has fewer local optima. The best perspectives have a single optima.

Sum to 15: place cards 1-9 on a table players take turns picking cards. If at any point a player has 3 cards who sum to 15, they win. The trick is that the cards can be arranged as a 3x3 magic square, at which point the game becomes tic-tac-toe.

For any problem there exists an arrangement (perspective) with a single optima. There are also many non-optimal arrangements.

Heuristics

Heuristics are techniques for finding and optimizing solutions.

• Do the opposite
• Big Rocks First

"No Free Lunch" theorm by Wolpert & McCready. All algorithms that search the same number of points with the goal of locating the maximum value of a function defined on a finite set perform exactly the same when averaged over all possible functions. Unless you know something about the problem, you will not know what heuristic to use.

Teams and Problem Solving

Average the local optima for a given perspective.

If person A gets stuck at a local optima in their perspective and passes it to a different person, with a different perspective and that point isn't a local optima, they can improve on it. The only points where a team can get stuck is at the intersection points of all perspectives. Therefor, effective teams are composed of members with different perspectives.

This overlooks complications with communication and errors in judging the value of a solution.

Recombination

Exaptation - using one solution in a new way. Recombination is powerful.

Markov Processes

Markov Models

Markov Models consists of states and transition probabilities. Markov Convergence theorem states that given a few criteria are met, a system will reach equilibrium.

A Simple Markov Model

Markov Transition matrix. Represent transisitons on a Matrix then it can be used in math models. Statistical Equilibrium - model keeps churning, the statistics don't change.

Markov Model of Democratization

In our model, 20% of dictatorships become democracies and 5% of democracies become dictatorships. The equilibrium point is at 80% democracy. Extending to partially free:

      F    PF    NF
 F | 0.9 | 0.1 | 0.5
PF | .05 | 0.8 | .15
NF | 0.0 | 0.1 | 0.8

Equilibrium

• F: 62.5%
• PF: 25%
• NF: 12.5%

Markov Convergence Theorem

• Must have a finite number of states
• Transition probabilities are fixed
• Can eventually get from any one state to any other
• Not a simple cycle

Given these, there is a unique equilibrium. Therefore

• The initial state doesn't matter
• History doesn't matter
• Intervening to change the state doesn't matter

But

• It can take a long time to reach the equilibrium
• Often, in reality, transition probabilities are not truly fixed

We can conclude that changing state will basically be temporary, but altering the transition probabilities can be permanent.

Exapting the Markov Model

Markov Models can also be used

• To identify writers based on similar transition matricies
• Medical diagnosis

Just using the transition probabilities can be useful.

Lyapunov Function

Lyapunov Function

If we can construct a Lyapunov function for a system, it will go to equilibrium. It's a L Func if

• It has a Maximum value
• There is a k, k>0 such that x_t+1 ≠ x_t → F(x_t+1) > F(x_t) + k

Then at some point x_t+1 = x_t

This goes back to Zeno's paradox.

The Organization of Cities

Model: people have things to do on a weekly rotation. If any one place is too busy, they switch with another place. Eventually, the system reaches equilibrium. It has a minimum value.

Exchange Economies and Externalities

Each person brings stuff to the market. People only trade if it makes them happier. Their happiness must increase by at least a fixed quantum of happiness (k).

But if people can be less happy due to a trade they are not involved in, then the system may not always go up. These are externalities.

Time to Convergence and Optimality

It's easy to find maximum time to convergence (Max/k).

The max is not always optimal.

Lyapunov: Fun and Deep

Offices and Chairs examples - it works for chairs but not for offices.

Lyapunov or Markov

Unlike Markov, Lyapunov does not go to a unique equilibrium. It is dependent on starting points.

Coordination and Culture

Coordination and Culture

• Coordination: Acting similarly
• Culture: Acting differently

We are talking about difference between similarities in groups.

What is Culture and Why Do We Care

Different measures of culture

Pure Coordination Game

People conform if there is a shared advantage. This is different from standing ovation because every one gains, where in SO, it's social pressure.

Emergence of Culture

Axelrod's model - a cellular automata type interaction.

Coordination and Consistency

Turned coordination into a Markov process.

Path Dependence

Path Dependence

Models where history matters.

Urn Models

An urn is a container with a set of colored balls. The balls drawn previously will effect the future.

Bernoulli: balls are returned and outcomes are independent.

Polya: If you draw a red ball, add a red ball. Over time, we will go to one extreme. All distributions are equilibriums and equally likely. Any sequence of events is equally likely.

Balancing: Opposite of Polya, add a ball of the opposite color chosen.

The Sway: Complicated, but the further back an outcome, the larger it's impact (exponentially so).

These demonstrate the difference between period outcomes and equilibrium (ball chosen in a given period vs the long run odds). Path dependence VS phat dependent. Phat depends on the set of outcomes but not their order. Path depends on the order. Phat is computationally MUCH simpler.

Mathematics on Urn Models

For given combination in the Polya model, permutation of that set is equally likely. For B blue balls and R red balls it will be (B!*R!)/((B+R)!)

The probability of any distribution for a given size is equal. So P(50B) == P(50R) == P(49B 1R) == P(25B 25R).

Path Dependence and Chaos

Chaos is extreme sensitivity to initial conditions. But deterministic.

Path Dependence and Increasing Returns

Increasing returns and Polya are very connected, but different processes. Increasing returns may or may be path dependent, and path dependance may or may not be increasing returns.

Exernalities can distinguish an increasing return from a Polya. If a set of options are all equally positive, but the combination of any two has an externality that may not be positive, it will affect future choices. Public projects example. Contingency increases as externalities are negative.

Path Dependent or Tipping Point

In Polya, if we have draw one red ball our diversity index goes from 5 to 3 1/3 so it's not quite a tipping process, but it's similar.

Networks

Networks

Interest in Networks is growing exponentially. Very fertile model. We will explore the structure, logic and function of networks.

The Structure of Networks

A network is nodes and edges. Edges are directed or undirected.

• Degree (node): number of edges attached to a node
• Degree (network): average degree of all nodes. 2*Edges/Nodes
• Neighbors: Nodes connected to a node

The average degree of neighbors of nodes will be at least as large as the average degree of the network. Most peoples friends are more popular than they are.

• Path Length: Minimum number of edges to get from A to B
• Connectedness: Can you get from any one node to any other node

A Markov process is a directed network.

• Clustering Coefficient: Percentage of triples of nodes that have edges between all three nodes.

The Logic of Network Formation

Random Attachment: Each node is connected to a random set of other nodes. For large N, the network almost always becomes connected when P > 1 / (N-1)

Small Worlds Network: Nodes are highly connected to local nodes and have some random connections to non-local nodes.

Preferential Attachment: Nodes arrive and have to decide which other nodes to connect to. New nodes prefer to connect to the most connected nodes. Develops a long-tail N-connection probability distribution.

Network Function

Six degree rule of social networks. N neighbors increase exponentially, so that most important things in life come from 2 or 3 neighbors.

Preferential attachment tends to be robust to random failure but weak against targeted failure.

Randomness and random Walks

Randomness and random Walk Models

We will look at randomness, random walks and randomness vs luck.

Sources of Randomness

Epsilon is the term for error in equations.

Skill and Luck

Outcome = a*Luck + (1-a)*Skill

Paradox of Skill.

Random Walks

Binary random walk (+1, -1 each iteration).

Random Walks and Wall Street

Efficient market hypothesis (weak form).

Finite Memory Random Walks

At any given point in time V_t is equal the sum of X_t for a finite period in the past leading up to t.

Colonel Blotto

Colonel Blotto Game

Derived from the troop placements along fronts, but very fertile model.

Blotto: No Best Strategy

2 players each with T troops. N fronts (with T >> N). Allocate troops across fronts. Players win a front by placing more troops on it. Whoever wins the most fronts wins the game. This is a zero sum game. Any strategy can be defeated.You can win without using all of your troops.

Application of Colonel Blotto

• Electoral College
• Terrorism
• Hiring
• Sports (facets of a sport)

Blotto: Troop advantages

As the number of fronts increases, a larger relative troop advantage is needed to guarantee victory. If you're the weaker player, you want to add fronts.

Multi-player blotto is non-commutative.

Blotto and Competition

Contrasting blotto to other models.

Prisoners' Dilemma and Collective Action

Intro: The Prisoners' Dilemma and Collective Action

Applies in many scenarios. Seven solutions. Collective action involves more than 2 players.

Seven Ways to Cooperation

5 seen in nature, 2 are human solutions.

The ratio of benefit/cost of cooperation is important in all the formulas.

1. Repetition - this is part of why small towns tend to be 'nicer'
2. Reputation (indirect reciprocity)
3. Network reciprocity
4. Groups - groups with more cooperators do better against groups with more defectors
5. Kin selection
6. Laws/prohibitions
7. Incentives

Collective Action and Common Pool Resource Problems

Let x_j be the action of person j Payoff to j = -x_j + Β Σ x_i

These are "free rider" or "common resource" problems. Classic example of "common resource" is fishing.

No Panacea

Context matters. The difference between cows overgrazing and lobster fishing is that you can see the grass, but you can't know how many lobster there are.

Mechanism Design

Mechanism design

How do we design mechanisms in light of hidden actions and hidden data.

Hidden Action and Hidden Information

Designing incentive structures to get the outcomes we want. These are "Moral Hazard" problems.

• C: cost of "good" effort
• P: Probability of desired outcome despite !"good" effort

Incentive to put forth "good" effort: M > c/(1-p). As both C and P go up, M goes up as well.

Auctions

Objective - get as much money as possible.

• Ascending Bids - Keep calling prices until no one pays more
  • Types
    • Rational: Only bid up to your value
    • Psychological: May get carried away or want to win (value of item + value of winning)
    • Rule Following: Pretty much rational
  • Outcome, highest bidder will end up getting it at second price
• Second price auction - Sealed bid but highest bidder gets it at second highest cost
  • Types
    • Rational: Bid your value
    • Rule Following: Close to rational
    • Psychological: Close to rational / random
  • Outcome, people make mostly rational bids. Same outcome as ascending bid auction
• Sealed Bids - Everyone writes down a price, the highest price gets it at cost
  • Types
    • Rational: ?
  • Outcome: Same outcome as ascending bid auction and second price

But...context matters.

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.

Short Primer on Behavioral Economics

http://www.econlib.org/library/Enc/BehavioralEconomics.html

Homo Economicus

Unemotional maximizer used as an agent in economic models

This model has 3 unrealistic traits

• Unbounded rationality
• Unbounded willpower
• Unbounded selfishness

Cabdriver example. Behavioral Finance theory.

The Model Thinker: Chapter 3: Categorical Models

Even the basic step of categorizing is a model and can be effect and is computationally simple.

The Model Thinker: Chapter 4: Linear Models

Nothing presented not in lectures. One sloppy table.

The Model Thinker: Chapter 8:Thresholds and Tipping Points

Reviewed tipping points and the percolation model. Slightly different approach, instead of each square it was each edge. In this scenario the tipping point is .5