Base-Rate Blindness

Over the weekend, I had a chance to get to know Apollo Robbins. If you don’t recognize the name, Apollo came to public attention when he pickpocketed members of Jimmy Carter’s Secret Service detail.

The opening paragraphs from the profile that the New Yorker ran suggests what it is like to spend time with Apollo:

A few years ago, at a Las Vegas convention for magicians, Penn Jillette, of the act Penn and Teller, was introduced to a soft-spoken young man named Apollo Robbins, who has a reputation as a pickpocket of almost supernatural ability. Jillette, who ranks pickpockets, he says, “a few notches below hypnotists on the show-biz totem pole,” was holding court at a table of colleagues, and he asked Robbins for a demonstration, ready to be unimpressed. Robbins demurred, claiming that he felt uncomfortable working in front of other magicians. He pointed out that, since Jillette was wearing only shorts and a sports shirt, he wouldn’t have much to work with.

“Come on,” Jillette said. “Steal something from me.”

Again, Robbins begged off, but he offered to do a trick instead. He instructed Jillette to place a ring that he was wearing on a piece of paper and trace its outline with a pen. By now, a small crowd had gathered. Jillette removed his ring, put it down on the paper, unclipped a pen from his shirt, and leaned forward, preparing to draw. After a moment, he froze and looked up. His face was pale.

“Fuck. You,” he said, and slumped into a chair.

Robbins held up a thin, cylindrical object: the cartridge from Jillette’s pen.

https://www.newyorker.com/magazine/2013/01/07/a-pickpockets-tale

It will be useful to have a phrase that captures Jillette’s reaction: a “fuck-you slump.” Time with Apollo makes it possible to experience a whole series of them.

The lasting effect is a heightened awareness that more things are possible than we can contemplate. In interactions with other people, there are always unknown unknowns. If we don’t allow for them, we are blind to them.

Pay Attention to the Base Rate

There are many ways to convey the insight about probabilities known as Bayes' Law. One of the simplest is “rare things happen rarely.” A slightly more helpful one is “pay attention to the base rate,” but only if you know what the “base rate” means.

Suppose I were hiking in the Colorado mountains and happened to see an animal with a striking pattern of black and white stripes. Suppose that the size and shape convinces me that it was an equine, which means that it had to be a zebra, a horse, or an ass. To calculate the base rate for zebra encounters, think about all hikers in the Colorado mountains who encounter an equine. The base rate for zebra encounters is the fraction of equine encounters that involve a zebra. (Pedants will demand that I sprinkle the phrase “conditional on an equine encounter” over these sentences, but I’m not writing for them. They know what the base rate is.) The base rate for zebra encounters in the Rockies is an extremely small number.

Suppose that after my encounter, I conclude that the black and white pattern that I saw is hundreds of times more likely on a zebras than it is on a horse or an ass. What Bayes' law does is protect me from over-reacting to what I see and the calculation the data I see is much more likely if the animal is a zebra. The law is a mathematical expression that says that I should fold in the base rate along with the new data I see to get an accurate estimate of the probability that I saw a zebra. The evidence in this hypothetical case makes it more likely that it was a zebra, but the base rate makes it much more likely that it was a horse or an ass.

If you want to see the math, start with https://en.wikipedia.org/wiki/Bayes'_theorem.

But Get the Base Rate Right

If you have a good estimate of the base rate, it can keep you from overreacting to a noisy bit of data. Zebra encounters are rare. But if your estimate of the base rate is wrong, it can lead you dangerously astray. It is particularly dangerous to assume that a base rate is zero.

This summer, in a part of the Colorado mountains that I’ve explored for my entire life, I had a surprising actual encounter with two large four-legged animals. I wondered at first if they could be mules. The larger one was too big to be an ass, but it did not look like a horse. In sixty years, I’ve never seen a moose in this area, but as I got a clearer view, I concluded that this was a female moose and a calf.

So yes, rare things happen rarely. But it is important to remain open to the possibility that we might encounter something rare, even something so rare that we’ve never seen it before.

If I had set my estimate of the base rate for moose encounters to zero, Bayes' law would have assured me that there was zero chance that the creatures before me were moose. This is base-rate blindness.

Base-rate blindness can be dangerous. A female moose can be very protective of a calf. I kept my distance.

Professors

Professors work in a little reserve, our own little replica of Tanzania, where every equine truly is a zebra. But instead of zebras versus horses, the types we have to recognize are people who strive to maintain a reputation for honesty versus people who are willing to deceive. As we navigate our academic reserve, it is reasonable to assume that the base rate for intentional deception is very low. But this base rate can lead us astray if we apply it to life off the academic reserve.

Lots of people say that they confront scams all the time, and that the bad actors inevitably get the occasional win. But we academics, assure ourselves: “No doubt, the experience for the less sophisticated might be different, but we hardly ever encounter intentional deception. And if we did, it doesn’t put us at any risk because we’d see right through it.”

Lessons Learnt

For someone who is confident about base rates, it is bracing to spend time with Apollo. There is no substitute for the visceral experience of serial fuck-you-slumps. There is something to be said for encounters that leave the lingering thought, “I didn’t even consider the possibility that someone might do that.”

In the abstract, Apollo is transparent about what he does. In my vocabulary, he relies on the fact that the human brain can keep track of only a finite number of random variables. He creates and draws attention to enough of them to exhaust a mark’s mental capacity. The brain sets the base-rate to zero for all the others. At this point, the mark is base-rate-blind to those possibilities.

Closing Thought

What if the hand-wringing about the shrinking demand for human knowledge workers is a distraction? What if the preposterous idea that our AI systems are going to lock us up in the basement and turn us into worker bees that serve them is misdirection? What if pleas for regulation by the leaders of organizations that want to profit from AI are intended to exhaust our ability to consider other possibilities?

Could AI be a con?