The Model Thinker: What You Need to Know to Make Data Work for You (pp. 13-25)

• Authors: Scott E. Page
• Publication, Year: New York: Basic Books, 2018
• Link to Book

Chapter 2: Why Model?

Knowing reality means constructing systems of transformations that correspond, more or less adequately, to reality.

• Jean Piaget

Types of Models

Embodiment Approach

• Aims to capture reality and stresses realism

• Typically focus on he important parts and either strip away unnecessary dimensions or lump them together

• Examples:

  • Ecological glades
  • Legislatures
  • Traffic systems

Analogy Approach

• Aims to abstract from reality

• Tries to capture the essence of a process, system, or phenomenon, without necessarily strictly adhering to reality

  • The "favorite classroom example" is a model which makes an estimate about the amount of leather you might find in a cowhide.

    • To answer this question we assume a "spherical cow" which allows us a reasonable estimate
    • While this is obviously not completely realistic, the general idea is captured and we can make a reasonable guess
    • The model is not perfect but it is still useful to some extent — it also gives us something to build on for improvement

When a physicist assumes way friction but otherwise makes realistic assumptions, she takes the embodiment approach. When an economist represents competing firms a different species and defines produce niches, she makes an analogy. She does so using a model developed to embody a different system.

No bright line differentiates the embodiment approach from the analogy approach.

Alternative Reality Approach

• Purposely does not represent or capture reality

• Functions as analytic and computational playgrounds in which we can explore possibilities

• These models allow researchers to imagine new things and test out-of-the-box hypotheses

• Allows us to ask questions like:

  • "What if energy could be sent safely and efficiently through the air?"
  • "What if we tried to evolve the brain?"

Good Models

• Models should be communicable and tractable

• Communicable means that a models would be describable in some formal language like mathematics or computer code

  • We also need to provide formal definitions of conceptual terms like beliefs or preferences

    • Beliefs can be represented as a probability distribution
    • Preferences can be represented in several ways such as a ranking over a set of alternatives or as a mathematical function

• How tractable something is means how amenable it is to analysis — we should be able to test the model

• Good models should also be described as simply as possible

  • This principal is often referred to as Ockham's Razor

    • Ockham's Razor states, basically, that everything should be made as simple as possible, but not simpler.

The Seven Uses of Models

REDCAPE

Reason

• When constructing a model, we identify the most important actors, entities, and relevant characteristics. We then attempt to describe how they interact and aggregate, which enables us to conclude what should follow from what, and why. This allows us to improve our reasoning about what we are studying. However, to do this we need formal logic.

• Formal logic allows us to:

  • Reveal impossibilities

  • Reveal paradoxes

    • Simpson's paradox — individual subpopulations can contain a larger percentage of women than men but the total population can still contain a larger percentage of men

    • Parrondo's paradox — it is possible for two losing bets, when played alternately, to produce a positive expected return

    • Friendship paradox - most people have fewer friends than their friends have, on average

    • We should not dismiss these examples as mathematical novelties. Each has practical applications: efforts to increase the population of women could backfire, combinations of losing investments could win, and the total length of a network of electric lines, pipelines, ethernet lines, or roads could be reduced by adding more nodes.

  • Uncover mathematical relationships

  • Reveal the conditionality of truths (most important)

    • Logic can show us when our models will break and under what conditions they will thrive

      • This is similar to "tracing the boundaries" of our model's descriptive effectiveness and illuminate realities in the real world

• Critics of models sometimes say that we are simply repackaging what we already know into fancy math

  • What this misses, however, is the conditional form that models offer

    • i.e. — if condition A holds, their result B follows

  • If we try to lead our lives or manage others by unconditional rules, we find ourselves lost in a sea of opposite proverbs. Are two heads better than one? Or, do too many cooks spoil the broth?

(Examples above are taken from the text.)

Explain

• Models provide clear logical explanations for empirical phenomena

• Physical phenomena are much more predictable than social phenomena

  • This is because, physical phenomena (like Boyle's Law, which describes how the pressure of a gas tends to increase as the volume of the container decreases) tend to be driven by simple parts, that follow fixed rules, and exist in such large numbers that statistical averaging cancels out any randomness
  • On the other hand, social phenomena are heterogenous, interact within small groups, and do not follow fixed rules

• The most effective models explain both straightforward outcomes and puzzling ones

  • Textbook market models can explain short-term as well as long-term changes in price, while also explaining paradoxes like the high cost of diamonds, which have little practical value, but water, necessary for survival, costs little

As for the claim that models can explain anything: it is true, they can. However, a model-based explanation includes formal assumptions and explicitly causal chains. Those assumptions and causal chains can be taken to data. A model that claims that high levels of criminal behavior can be explained by low probabilities of being caught can be test.

Design

• Models aid in design by providing frameworks within which we can contemplate the implications of choices

• By creating models you can test specific frameworks to understand how different types of designs lead to specific conditional outcomes

  • Thus, if you need to limit specific outcomes from occurring, you can design models that create desirable logical impossibilities

• Page provides the example of the FCC creating a model for auctioning radio licenses

  • Since having radio licenses in neighboring areas are more valuable, and how much someone is willing to pay varies based on what they do or do not own (i.e. do I own a neighboring region), they needed to model many different types of auctions to ensure that people did not blackout of their auction bids, but also ensure that the bidding system could not be taken advantage of strategically by bidders.

Communicate

• By creating a common representation, models improve communication

  • The model $F = MA$ relates force, mass, and acceleration — and does so concisely in equation form
  • This model can be communicated without fear of misinterpretation
  • On the other hand, something like "bigger, faster things generate more power" offers much less precision — how do we define, "bigger," "faster," or "power"?

• Formally defining abstract concepts like political ideology offer this same precision within communication

  • We can also define abstract concepts in different ways, ideology can be defined based on voting records or text analysis of speeches, for example

    • These models allow us to clearly compare entities based on the constructed "scale" — i.e. politician $x$ is more liberal than politician $y$

    • While it is always possible that some of these mathematical constructions are not perfect, this is why we test them against data

      • Even if the model is wrong, it still allows you to clearly observe that fact — perhaps allowing you to understand why it is wrong and then improve it

Act

The great end of life is not knowledge but actions.

— Francis Bacon

• Important decisions made by governments and institutions typically rely on models. Very important decisions rely on very sophisticated models.

• Network models were made of the financial institutions at play during the 2008 bail out to inform which banks to help

• Physical models may be built to inform policymakers decisions as well

  • For example a small model of a dam maybe be built prior to the full scale construction

The general take away here is that models can be helpful for showing if it makes sense to do or not do something specific in the real world. This (to me at least) ties closely to the Design section.

Predict

• Models have long been used to predict
• In the past, explanation and prediction tended to go hand in hand

In perhaps the most famous example of applying an explanatory model to predict, the French mathematician Urban Le Verrier applied the Newtonian laws created to explain planetary movements to evaluate the discrepancies in the orbit of Uranus. He discovered the orbits to be consistent with the presence of a large planet in the out region of the solar system. On September 18, 1846, he sent his prediction to the Berlin Observatory. Five days later, astronomers located the planet Neptune exactly where Le Verrier had predicted it would be.

However, prediction $\ne{}$ explanation!

• Models can predict without explaining and vice versa

  • Deep-learning algorithms can predict product sales, the weather, price trends, etc. but they can't offer much explanation
  • Plate tectonics models explain how earth quakes arise but do not predict when they occur

Explore

• Models are used to explore intuitions and possibilities

• Abandoning constraints of reality can spur creativity

  • What if we make all buses free?

  • What if we let students choose which assignments determine their course grades?

    • By exploring different realities with models, we can interrogate whether making these alternate realities come to life is worth pursing or detrimental to reality

• Exploration sometimes can also simply mean comparing common assumptions across domains

Notes by Matthew R. DeVerna