All models are wrong. Some are useful!

I work with models a lot. I use them to make real-world effects better comprehensible and thus enable pondering them. When sharing such a model with other people, every once in a while someone cites

All models are wrong, but some are useful. ¹

To be more precise: Usually, only the first part of the quote is cited. I do not want to speculate about the motivations of the persons who cite this quote. They will have their reasons. I mention the quote because from my point of view it is really useful to explain the power and the limitations of models.

All models are wrong

The type of models I usually create and use can be described best as conceptual models or mental models (depending on the respective model). It is not that I try to meet the definitions of those two types of models. I rather work with models most of my life and when I read through the definitions of the different types of models, those two definitions seemed to fit best. Thus, this is more of a retrofit.

A common characteristic of these two model types (and most other model types) is that they abstract away parts of reality. They focus on selected parts of the information, thus creating a selective perception.

Based on that innate characteristic, all models are wrong. Models do not reflect reality as it is. They omit parts of it. But why are we using models if they are “wrong”? Shouldn’t we rather stop using them?

But some are useful

To answer this question, we need to look at the characteristics of reality: Reality tends to be so complex, having so many details, relations and dependencies that it is impossible to reason about it in its wholeness. As humans we can not stay on top of so many ever-changing and mutually influencing details. A human brain simply cannot process this amount of information.

On top of that, we are not capable of understanding non-linear cause-effect relationships – that are the norm in most places of the real world (I will not go into detail of this limitation of the human brain here but come back to that issue and its effects in a later post). Also, the sheer amount of details often keeps us from grasping very essential relationships.

In other words: The more accurate and complete the models are that we try to create, the more precisely they reflect the details and complexity of their real-world counterpart, the less usable they become – especially if they are a model of a complex system. We will not be able to reason based on overly accurate and complete models. We need the simplification, leaving out parts.

This is also known as “Bonini’s paradox”, sometimes also called “Valéry’s paradox”, named after Paul Valéry who was one of the first observers of this paradox.

This means, we have to reduce the amount of information we need to process to be able to usefully reason about it. That is exactly what model building is about: mask out the details you do not need for your task at hand which allows you to focus on the relevant parts. Then you are able to reason about a complicated situation, to analyze it and to decide about future activities. ²

This is the power of models: they help us to focus on the relevant aspects with respect to the task at hand and not getting lost in distracting details.

Finding the right models

So far, so good. But let us be the devil’s advocate for a second:

• We know that models are used all the time for decision making.
• We know that a lot of decisions being made are really bad.

Doesn’t that mean that model building is devoid of value at best? Doesn’t that prove that models do not help us to make better decisions? So again: shouldn’t we better abandon models?

The truth is: Bad models lead to bad decisions. If you focus on the wrong aspects or if you get the facts and relations wrong in your models, they will still help you reasoning but will lead you to the wrong conclusions. Therefore, you need to be really careful while building models.

If I build a model, I usually try to find the common patterns in the literature I read and the observations I make. I try to cross-validate my ideas as good as possible before distilling my findings into a model. While using a model, I still check all the time if and where it breaks. If the model breaks I ponder if there is a better model that does not break based on what I know.

This is a bit inspired by the scientific approach where you create a model on the basis what you currently know. Yet, that model is considered valid only until it is proven wrong ³.

But while always trying to validate and improve my models, I cannot guarantee that they are always correct which brings me to the last aspect.

The limits of models

Even the most carefully designed model can be wrong for any reason. Thus, blindly relying on a model usually is not a good choice. You always need to verify your findings against reality.

Also, reality is always a lot more detailed than your models. It always has many more shades of gray than your model. This also means that at a given point every model breaks because it cannot reflect the intricate details of your reality.

Hence, you always need to adapt your findings to reality. A decision that appears totally clear in your model often is not so clear in reality anymore. Thus, do not blindly apply the findings you made in your model, but match them with reality first and make the required adaptions.

Summary

Models help to reason about complex issues by abstracting away aspects of the real world that are not essential for the reasoning. They also help not to get distracted by irrelevant details. This is the great power of models. They can help to sort out complicated situations a lot better and as a result to make better decisions and to navigate better in a complex environment.

On the other hand, models bear two difficulties:

• If you abstract away the wrong details or relations, models will set you on the wrong track. Thus, it is important to continuously question your models and to drop or evolve them if you learn that they are wrong.
• By definition reality is a lot more complex than any model. As a result, every model will eventually break. Therefore, you always need to adapt the findings from the plain model world to the complex real world.

If you have these two limitations of models in mind, they are really powerful tools for reasoning and can help you a lot in your decision making.

[Update] August 2, 2020: Explained paradox of model completeness vs. usability in more detail. Added reference to Bonini’s paradox.