Algorithms to Live By: The Computer Science of Human Decisions

by Brian Christian

Viewed this way, the secretary problem’s most fundamental yet most unbelievable assumption—its strict seriality, its inexorable one-way march—is revealed to be the nature of time itself. As such, the explicit premise of the optimal stopping problem is the implicit premise of what it is to be alive. It’s this that forces us to decide based on possibilities we’ve not yet seen, this that forces us to embrace high rates of failure even when acting optimally. No choice recurs. We may get similar choices again, but never that exact one. Hesitation—inaction—is just as irrevocable as action.

A record of 0–0—an arm that’s a complete unknown—has an expected value of 0.5000 but a Gittins index of 0.7029.

The untested rookie is worth more (early in the season, anyway) than the veteran of seemingly equal ability, precisely because we know less about him. Exploration in itself has value, since trying new things increases our chances of finding the best. So taking the future into account, rather than focusing just on the present, drives us toward novelty.

Regret is the result of comparing what we actually did with what would have been best in hindsight.

It offers a simple prescription for time management: each time a new piece of work comes in, divide its importance by the amount of time it will take to complete. If that figure is higher than for the task you’re currently doing, switch to the new one; otherwise stick with the current task.

Beware: when you go to the gym to work off the extra weight from all that sugar, you can also risk overfitting fitness. Certain visible signs of fitness—low body fat and high muscle mass, for example—are easy to measure, and they are related to, say, minimizing the risk of heart disease and other ailments. But they, too, are an imperfect proxy measure. Overfitting the signals—adopting an extreme diet to lower body fat and taking steroids to build muscle, perhaps—can make you the picture of good health, but only the picture.

So what do these complexity penalties look like? One algorithm, discovered in 1996 by biostatistician Robert Tibshirani, is called the Lasso and uses as its penalty the total weight of the different factors in the model.* By

Living organisms get a certain push toward simplicity almost automatically, thanks to the constraints of time, memory, energy, and attention. The burden of metabolism, for instance, acts as a brake on the complexity of organisms, introducing a caloric penalty for overly elaborate machinery. The fact that the human brain burns about a fifth of humans’ total daily caloric intake is a testament to the evolutionary advantages that our intellectual abilities provide us with: the brain’s contributions must somehow more than pay for that sizable fuel bill. On the other hand, we can also infer that a substantially more complex brain probably didn’t provide sufficient dividends, evolutionarily speaking. We’re as brainy as we have needed to be, but not extravagantly more so.

Giving yourself more time to decide about something does not necessarily mean that you’ll make a better decision. But it does guarantee that you’ll end up considering more factors, more hypotheticals, more pros and cons, and thus risk overfitting.

The satirical “Peter Principle,” articulated in the 1960s by education professor Laurence J. Peter, states that “every employee tends to rise to his level of incompetence.” The idea is that in a hierarchical organization, anyone doing a job proficiently will be rewarded with a promotion into a new job that may involve more complex and/or different challenges. When the employee finally reaches a role in which they don’t perform well, their march up the ranks will stall, and they will remain in that role for the rest of their career. Thus it stands to reason, goes the ominous logic of the Peter Principle, that eventually every spot in an organization will come to be filled by someone doing that job badly.