Model Thinker

The Model Thinker by Scott E. Page delves into the world of models, exploring their types, uses, and the significance of adopting a many-model thinking approach. Through numerous real-world examples and formal models, the book demonstrates how models can help us understand complex phenomena, make better decisions, and solve problems across various domains.

1. The Many-Model Thinker

This chapter introduces the concept of many-model thinking, which involves using multiple models to understand complex phenomena. The author argues that in the era of big data, models are more crucial than ever, as they help us make sense of the vast amount of information available. By learning a variety of models, we can overcome the limitations of single models and gain a more comprehensive understanding of the world. For example, in analyzing the 2008 financial crisis, no single model could fully explain the event, but multiple models together provided a more nuanced understanding. The chapter also presents the wisdom hierarchy, which shows how data, information, knowledge, and wisdom are interconnected, with models playing a key role in transforming data into wisdom.

2. Why Model?

Here, Page defines different types of models, including those based on realism, analogy, and alternative reality. He also outlines seven main uses of models: reasoning, explaining, designing, communicating, acting, predicting, and exploring (REDCAPE). For instance, models can be used to design auctions, as seen in the case of the 1993 spectrum auction in the US, where economists used game theory, simulation, and statistical models to create an effective design. This chapter emphasizes that models are powerful tools that can reveal the conditions under which certain results hold, and they enable us to make more informed decisions in various fields.

3. The Science of Many Models

This chapter presents two theorems, the Condorcet jury theorem and the diversity prediction theorem, to illustrate the value of many-model thinking. However, it also acknowledges the challenges of constructing many diverse models, as shown through categorization models. The author discusses the choice between using one big model or many small models, suggesting that it depends on the purpose of the model. For prediction, larger models may be more suitable, while for explanation, smaller models can be more effective. The chapter concludes by introducing the one-to-many approach, which encourages applying a single model to multiple cases, and demonstrates its potential through examples such as using the geometric formula for area and volume to explain various phenomena.

4. Modeling Human Actors

Modeling human behavior is challenging due to the complexity of human characteristics such as diversity, social influence, and agency. This chapter explores different ways to model people, including as rational actors and rule-based actors. The rational-actor model assumes that people make optimal choices, but it has been criticized for its unrealistic assumptions. However, it still has value as a benchmark and for its tractability. Rule-based models, on the other hand, assume specific behaviors and can be more flexible. For example, in the El Farol model, people use adaptive rules to decide whether to go to a nightclub, and the system self-organizes into nearly efficient outcomes. The chapter concludes that there is no one-size-fits-all approach to modeling humans, and multiple models should be used to capture the complexity of human behavior.

5. Normal Distributions: The Bell Curve

Normal distributions, characterized by a bell-shaped curve, are common in many natural and social phenomena. This chapter explains how they arise through the central limit theorem, which states that adding or averaging independent random variables produces a normal distribution. The author discusses the properties of normal distributions, such as the mean and standard deviation, and how they can be used to make predictions and test for significance. For example, in quality control, the Six Sigma method uses the normal distribution to reduce errors by tightening quality control. The chapter also introduces lognormal distributions, which result from multiplying random variables, and shows how they differ from normal distributions.

6. Power-Law Distributions: Long Tails

Power-law distributions, with their long tails, are prevalent in many real-world phenomena, such as city populations, book sales, and earthquake sizes. This chapter focuses on two models that produce power laws: the preferential attachment model and the self-organized criticality model. The preferential attachment model explains how phenomena like the growth of cities and the spread of information can lead to power-law distributions. The self-organized criticality model, on the other hand, shows how systems can reach a critical state and produce large events. The chapter also discusses the implications of long-tailed distributions, such as their impact on equity, catastrophes, and volatility. For example, in the music industry, social influence can lead to a long-tailed distribution of song downloads, resulting in greater inequality.

7. Linear Models

Linear models are the simplest and most widely used type of model. This chapter reviews linear functions and how regression is used to fit data to a linear function, revealing the sign, magnitude, and significance of effects. However, it also notes that data may not fall exactly on the regression line due to errors, noise, and heterogeneity. The chapter expands to multivariable linear models, using Mauboussin’s skill-luck equation as an example to show how multiple variables can be included in a regression. It also discusses the limitations of relying solely on linear regression, such as the potential for big-coefficient thinking to stifle innovation, and suggests considering more speculative models to identify innovative options.

8. Concavity and Convexity

This chapter explores nonlinear models, specifically those based on convexity and concavity. Convex functions, like the exponential growth model, show an increasing slope, while concave functions exhibit diminishing returns. For example, in economic production models, profits per unit sold may be a convex function of a firm’s size, while utility from consumption is often concave. The chapter constructs economic growth models using the Cobb-Douglas production function, which shows how investment in capital and labor can drive growth. It also discusses the role of innovation in sustaining growth and how different growth models can explain the success and failure of nations. For instance, the Solow* growth model reveals that innovation has a multiplier effect on output.

9. Models of Value and Power

In this chapter, Page defines two measures of value and power in cooperative game models: last-on-the-bus value and Shapley value. The last-on-the-bus value represents an actor’s marginal contribution when joining a group, while the Shapley value is the average marginal contribution across all possible sequences of adding people to a group. The author uses examples such as a firm with language speakers and a crew team to illustrate how these values are calculated. The Shapley value has an axiomatic basis, satisfying four conditions that make it a reasonable measure of value and power. The chapter also applies the Shapley value to voting games, showing that there can be a disconnect between the percentage of seats a party controls and its actual power.

10. Network Models

Networks are everywhere, and this chapter covers the basics of network models, including their structure, common types, formation, and function. Network structure is characterized by measures such as degree, path length, clustering coefficient, and community structure. Common network types include random networks, hub-and-spoke networks, geographic networks, small-world networks, and power-law networks. The chapter explains how networks form through processes like random connection and preferential attachment. It also discusses the importance of network structure, such as the friendship paradox, the six degrees of separation phenomenon, and the robustness of networks. For example, the friendship paradox states that, on average, people’s friends have more friends than they do, which can be seen in various networks like Facebook.

11. Broadcast, Diffusion, and Contagion

This chapter focuses on models that describe the spread of information, technologies, behaviors, beliefs, and diseases. The broadcast model applies when information spreads from a single source, resulting in an r-shaped adoption curve. The diffusion model, on the other hand, captures the spread through person-to-person contact and produces an S-shaped curve. The Bass model combines both processes, and the SIR model from epidemiology includes a rate of recovery. The SIR model is particularly important as it produces a tipping point, where small changes in the attributes of the disease or product can lead to significant differences in the outcome. For example, a small increase in the probability of spreading a new band’s music could determine whether it becomes a huge success like the Beatles or fades away.

12. Entropy: Modeling Uncertainty

Entropy is a measure of uncertainty, information content, and surprise. This chapter defines information entropy and presents its axiomatic foundations. It shows how entropy can be used to distinguish between different classes of outcomes, such as equilibrium, periodicity, randomness, and complexity. For example, equilibrium outcomes have zero entropy, while random processes have maximal entropy. The chapter also discusses maximal entropy distributions, which depend on the constraints. In the absence of data, assuming a maximal entropy distribution can be a reasonable approach. Finally, the chapter explores the positive and normative implications of entropy, suggesting that the desired level of entropy depends on the situation, whether it’s designing a tax code or a city.

13. Random Walks

This chapter focuses on the Bernoulli urn model and the random walk model. The Bernoulli urn model describes random processes with discrete outcomes, like drawing balls from an urn. We can use it to analyze streaks, such as in sports or investing. The random walk model, which builds on the Bernoulli urn model, tracks cumulative outcomes. For example, in a one - dimensional random walk, the position can move up or down randomly. It can explain phenomena like the life spans of firms and species. The model also helps analyze stock prices, showing that they are nearly random walks, which challenges the efficient market hypothesis.

14. Path Dependence

Path dependence exists in many aspects of life, from individual choices to institutional developments. The chapter uses dynamic urn models, like the Polya process and the balancing process, to explain it. In the Polya process, positive feedbacks lead to extreme path dependence; for instance, in product choices, early decisions can greatly influence later ones. The balancing process, with negative feedbacks, shows how some systems move towards equal allocation. The chapter also distinguishes path dependence from tipping points, using examples like Microsoft’s growth and the assassination of Archduke Franz Ferdinand.

15. Local Interaction Models

Two models of local interactions are studied: the local majority model and the Game of Life. In the local majority model, cells on a checkerboard update based on the majority state of their neighbors. It can represent physical or social systems, like how people in a neighborhood decide whether to maintain a clean yard. The Game of Life, on the other hand, has cells that update according to more complex rules. It can produce various outcomes, from equilibria to complexity, and helps us understand how simple rules can lead to complex phenomena, much like in the human brain.

16. Lyapunov Functions and Equilibria

Lyapunov functions are introduced to determine if a model reaches equilibrium. The chapter shows how to construct these functions for different models, such as the Race to the Bottom Game and the local majority model. For example, in the local majority model, the total disagreement in the population can be used as a Lyapunov function. If a Lyapunov function exists for a model, it must reach an equilibrium. However, not all models have such functions, like the Game of Life in some cases. The chapter also discusses the implications of equilibrium in different systems.

17. Markov Models

Markov models describe systems that transition between states probabilistically. For example, a person’s mood or a country’s political state can be modeled this way. If a Markov model satisfies certain conditions, it reaches a unique statistical equilibrium where the long - run distribution of states doesn’t depend on the initial state. The chapter uses examples like a student’s mood in a biology class and countries’ democratization trends to illustrate this. Markov models have various applications, from ranking webpages to analyzing authorship.

18. Systems Dynamics Models

Systems dynamics models analyze systems with feedbacks and interdependencies. They consist of sources, sinks, stocks, flows, rates, and constants. For example, in a bakery model, the baker’s production rate (flow) depends on the stock of bread. The predator - prey model shows how positive and negative feedbacks interact; an increase in hares leads to more foxes, which then reduces the hare population. These models can be used to explain, predict, and guide action, but they also often produce counterintuitive results, highlighting the limits of human reasoning.

19. Threshold Models with Feedbacks

Threshold - based models are explored, where people’s actions change when an external variable crosses a threshold. Granovetter’s riot model shows how the distribution of people’s thresholds affects the likelihood of a social movement taking off. Schelling’s segregation models demonstrate how tolerant people can still cause segregation. For example, in the party model, random movements can lead to segregation based on people’s tolerance thresholds. The ping - pong model, with negative feedbacks, shows how systems can reach equilibrium or cycle, depending on the diversity of thresholds.

20. Spatial and Hedonic Choice Models

These models represent individual choices over alternatives with spatial and hedonic attributes. In the spatial competition model, like the Hotelling model of ice - cream vendors on a beach, consumers choose the nearer product. This can be applied to political competition, where candidates position themselves based on voters’ ideological preferences. The hedonic competition model helps infer implicit prices for product attributes, such as the value people place on a shorter commute.

Chapter 21: Game Theory Models Times Three

This chapter presents an introduction to game theory models, covering normal-form zero-sum games, sequential games, and continuous action games. In normal-form zero-sum games like Matching Pennies, players’ payoffs sum to zero. Sequential games, such as the Market Entry Game, involve players taking actions in a specific order. The continuous action game, like the Effort Game, shows how players choose effort levels to win a prize. The chapter also discusses the identification problem, where peer effect and sorting models can explain clustered behavior, but it’s hard to distinguish between them with only snapshot data.

Chapter 22: Models of Cooperation

The chapter explores how cooperation emerges, is maintained, and can be increased. The Prisoners’ Dilemma is used to illustrate the core incentives in many real - world situations. Cooperation can be maintained through repetition, reputation, local clustering, and group selection. For example, in the repeated Prisoners’ Dilemma, the Grim Trigger strategy can sustain cooperation. The cooperative action model shows how clustering can bootstrap cooperation among unsophisticated actors. Group selection, through competition among groups, can also promote cooperation, but its efficacy depends on various factors.

Chapter 23: Collective Action Problems

This chapter focuses on collective action problems, where self - interest doesn’t align with the collective interest. Examples range from Easter Island’s collapse due to overharvesting to modern - day issues like climate change. The chapter analyzes three types of problems: public goods provision, congestion, and renewable resource extraction. In public goods provision, people tend to free - ride. Congestion problems occur when the value of a resource to an individual decreases with the number of users. Renewable resource extraction problems involve the balance between consumption and regeneration. Solutions vary depending on the type of problem.

Chapter 24: Mechanism Design

The chapter introduces the mechanism design framework, which involves aspects like information, incentives, aggregation, and computational costs. It uses the Mount - Reiter diagram to illustrate how mechanisms work. For example, in majority rule voting, it may not always implement a Pareto efficient outcome, while the kingmaker mechanism can. The study of auctions shows that different auction mechanisms, like ascending - bid, first - price, and second - price auctions, can produce the same expected outcome, as proven by the revenue equivalence theorem. The chapter also compares mechanisms for deciding on a public project.

Chapter 25: Signaling Models

This chapter studies signaling models, where people send costly signals to reveal information or their type. In the discrete signaling model, individuals decide whether to send a signal, and the model can have pooling, separating, or partial pooling outcomes. For example, in a scholarship scenario, different levels of rewards can lead to different signaling behaviors among students. The continuous signaling model allows for signals of varying magnitudes. Signaling models can explain various phenomena, from peacock feathers signaling health to college degrees signaling ability.

Chapter 26: Learning Models

The chapter examines individual and social learning models. The reinforcement learning model shows how individuals choose actions based on past rewards. For instance, a parent learning a child’s pancake preference. Replicator dynamics, a social learning model, assumes that the probability of taking an action depends on its reward and popularity. When applied to games like the Guzzler Game and the Generous/Spiteful Game, these models can produce different outcomes. The chapter also discusses more sophisticated learning rules and the application of these models to the culture vs. strategy debate.

27. Multi-Armed Bandit Problems

Multi - armed bandit problems deal with the trade - off between exploration and exploitation when choosing among alternatives with uncertain rewards. In Bernoulli bandit problems, like a chimney cleaning company testing sales pitches, each alternative has an unknown success probability. We compare heuristics such as sample - then - greedy and the adaptive exploration rate heuristic. Bayesian multi - armed bandit problems consider prior beliefs. The Gittins index helps determine the optimal choice, and real - world applications range from drug trials to presidential elections analysis.

28. Rugged-Landscape Models

The rugged - landscape model represents entities as collections of attributes with a value mapping. The fitness landscape model, for example, can be applied to product design like a coal shovel. When multiple attributes interact, it creates a rugged landscape with multiple peaks. The NK model formalizes this, showing how the number of interactions affects the landscape. For instance, in the NK model with different K values, we can see how the number of local optima and the height of the global optimum change, and why a moderate degree of interdependence is often beneficial.

29. Opioids, Inequality, and Humility

This chapter applies many - model thinking to the opioid epidemic and economic inequality. For the opioid epidemic, models like the multi - armed bandit model explain its approval, while Markov and systems dynamics models show how addiction rates can rise. In the case of economic inequality, multiple models are used to analyze its causes. For example, the technology and human capital model explains the impact of technological changes on inequality, and the positive feedback model shows how social influence contributes to it. These analyses reveal the complexity of these issues and the need for a multi - model approach.