The Model Thinker
July 5, 2023

Are you a Many Model Thinker? Here’s how…

By Paul Laughlin

Building on past book recommendations focussed on Statistical Thinking or Critical Thinking skills comes this recommendation of “The Model Thinker”.

I am rarely as impressed and challenged by a book as this one. It is a tour de force of mathematical and statistical models worth understanding and considering. Beyond that, it applies each to real-life problems and brings to life their relevance for the worlds of commerce and public policy decisions. An ethos pervades the entire book; the need to apply many models to enable better thinking about issues.

So, in this post, I will share what I found within “The Model Thinker” by Scott E. Page and why I recommend it as a text to all data & analytics leaders with sufficient maths knowledge. It could be a great aid to continuing to develop, nurture and hone both your knowledge of models and your application. Let’s get started and dig into what you can find in this treasure trove of a book…

Why we need Many Model Thinkers

Let me first give you some background on the author, to establish his credibility as your teacher (via this well-written book). Dr. Scott Page is the Leonid Hurwicz collegiate professor of Complex Systems, Political Science & Economics at the University of Michigan. In addition to that very long job title, he’s also a faculty member of the Santa Fe Institute and teaches at a number of other universities. He has written five books on topics including diversity and complexity theory. But this appears to be his best to date, certainly the most relevant to all mathematically grounded data leaders.

Within the opening three chapters of his book, Scott makes the case for why we need models and many of them. His examples bring to life the twin problems that we need models (not just data) and that any one model is an imperfect representation of the real world (or overfitted). He makes a great case for the benefits of what he calls many model thinking. By this, he means having the knowledge & skills to apply a variety of relevant models to a single problem.

The vast majority of the rest of this book introduces the reader to a broad portfolio of models to consider. In each of the next 24 chapters, Scott introduces a new class of models. He explains the thinking behind that approach, the mathematics of some models in that class and how they could be applied. Here the book excels many others on the market. It combines sufficient mathematical depth to understand and try the model yourself plus guided applications to real-world problems.

Which models are covered in The Model Thinker

Perhaps you’re scratching your head thinking, how can he fill 24 chapters with different classes of models? In your day-to-day work, it might feel like beyond significance testing, regression models, random forest and occasionally clustering – what other models matter? If so, prepare to have your memory jogged (if you studied Maths or Statistics degrees) or your eyes opened. There is a big wide world of mathematical models out there that you may not have considered.

To bring that to life (at just a high level) here are some of the topics covered:

  1. Categorisation Models & Model Error Decomposition Theorem
  2. Rational-Actor Model, Prospect Theory & Rule-Based models of human behaviour
  3. Normal Distribution Models & Central Limit Theorem
  4. Power-Law Distribution Models & Preferential Attachment Model
  5. Linear Models & Multi-Variate Regression Models
  6. Concavity & Convexity, plus related Growth Models
  7. Models of Value & Power (inc. Shapley Value)
  8. Network Models (inc. explaining 6 degrees of separation model)
  9. Broadcast, Diffusion & Contagion Models (inc. SIR Model)
  10. Entropy Models
  11. Random Walk Models (inc. Bernoulli Urn Model)
  12. Path Dependence Models (inc. Polya & Balancing processes)
  13. Local Interaction Models (inc. cooperation in Game Theory)
  14. Lyapunov Models & Equilibria
  15. Markov Models (inc. Markov Decision Models)
  16. Systems Dynamic Models
  17. Threshold Models with feedback (inc. Schelling models)
  18. Spatial & Hedonic Choice Models
  19. Game Theory Models (zero-sum, sequential & continuous)
  20. Models of Cooperation (inc. Clustering Bootstraps Coop)
  21. Collection Action Problems (inc. altruism & congestion)
  22. Mechanism Design (inc. Revenue Equivalence Theorem)
  23. Signalling Models (discrete & continuous)
  24. Learning Models (inc. learning reinforcement)
  25. Multi-Armed Bandit problems (inc. Bernoulli & Bayesian)
  26. Rugged Landscape Models (inc. NK Model)

Phew! I know! I’m tired from just typing the above & refreshing my memory on what I’ve read. No doubt, if you wanted to go slowly & apply all you learnt above this, should count as a degree-level course. However, the magic of this book is with all that detail and example equations, it is still very readable. You can enjoy so much theory because of how each is applied and brought to life.

Application is still what counts with your Models

That last comment highlights the main reason that I recommend this book so highly. It will help mathematically adept data leaders apply their knowledge. Challenging us to not slip back into lazy ways and to consider only one or a few models when approaching familiar problems. Helping us notice the true complexity behind seeking to model human decision-making & behaviour.

Such examples and application advice permeate the whole book. They come to a crescendo in the final chapter. In chapter 29, Scott turns his attention to 3 major challenges in the world today. Opioid addiction, the COVID-19 pandemic & growing inequality. For each of those challenges, he reveals how the use of multiple models can improve both thinking and policymaking. The book is worth reading for this chapter alone, it really helps you to better critically assess past actions & future options.

I hope the above review was useful and inspires you to invest in this book. After an initial read, it could serve you well as a reference. A guide to help you recall other models to consider & how they might apply to what you are seeking to understand. But, even if you don’t buy Scott’s book, do take up the challenge to adopt many model thinking. If you are currently basing your forecast or explanation of human behaviour on just one model, try another. Consider the other dynamics which could be at play. Experiment with using multiple models to give you a multi-dimensional view of that complexity.