Bonini’s Paradox: Why Simple Rules Triumph In A Complex World

Bonini’s Paradox states that the more complete a model of a complex system, the less understandable it becomes. This is a useful concept to remember because the world is a complex place, filled with complex institutions and complex people.

Aphorisms aim to cut through such complexity. They are meant to be simple. Take “honesty is the best policy” for example. It’s concise and easy to remember. But it’s also clearly lacking in nuance, and everyone can point to situations where one shouldn’t be honest. The reason it sticks around is because a more nuanced statement like “honesty is the best policy except when the cost of telling the truth is so large that it would be better off if the other side was in the dark” is absolutely useless.

Accuracy matters, but it comes with a cost. You want a map that’s able to tell you something where something is as accurately as possible. A map that uses an extremely high ratio is unable to tell you where a particular building is located on a street. Switch to a map with a 1:1 ratio and you’ll get the most detailed picture, but it would also be entirely unusable.

Bonini’s Paradox isn’t the first formulation of this idea. The British statistician George Box wrote earlier:

“Remember all models are wrong; the practical question is how wrong do they have to be to not be useful.”

This is how we end up with mental models, guidelines, and aphorisms that seem to contradict each other. Consider the following.

Simplicity: Occam’s Razor teaches us that the simplest explanation is the most likely one. John Hickam had an obvious counterargument: “a man can have as many diseases as he damn well pleases”. Between Occam’s Razor and Hickam’s Dictum, you better hope you have a competent and confident doctor.

Taking chances: “You can’t win the lottery if you don’t buy a ticket” sounds good until you realise that you’ll probably lose money over a lifetime playing the lottery. The people buying these tickets are the same people who can’t afford it

Investing: “Nobody ever lost money by taking a profit” is the type of thing a conservative investor would say. But it makes you wonder if he’ll really sleep well at night when he realises that he would’ve made a 129,000% gain on Amazon shares if he bought and held them from IPO to 2020, never selling even as the stock kept hitting a new high.

Gathering feedback: Jeff Bezos makes dozens of Amazon executives and managers spend two days in a customer call centre each year. To him, listening to customers and giving them what they wanted was essential. Henry Ford had another approach: “If I had asked people what they wanted, they would have said faster horses.”

Speech: Popper’s Paradox tells us that there should be a limit to what speech we tolerate, because allowing the intolerant to control discourse would ultimately lead to the disappearance of tolerance. What’s not being said is that those who combat the intolerant are likely to overdo it, thus becoming the very party who truly limits discourse.

Speed: The first mover in business has an advantage because he is able to establish brand loyalty and a strong foundation on which to compete. But the last mover is able to learn from all the mistakes made by first movers without incurring any costs and make improvements from there.

All of the above ideas are true. They also contradict each other. You can’t apply both ideas simultaneously.

You can do two things to resolve this mental conflict.

First, figure out the characteristics of each specific field. “Move fast and break things” is a good idea in the American start-up world. It’s a terrible idea if you’re in a large corporation filled with multiple levels of hierarchy or in a country where both regulation and wrongdoing are prevalent. Risk appetite is the defining factor in this case, and you always want to find out what the defining factor is. There usually is one.

The other thing is to add more mental models to your arsenal. You want to have models that you can tap into in every situation, and you need a lot of them to avoid having to rely on models which aren’t very applicable. Unless you’re Noam Chomsky, you’ll never have the time to seriously explore the nuances of every field.

Rough approximations are enough sometimes. No need to keep fitting square pegs into round holes. Simple rules for a complex world.