Some researchers call this ability to intuit patterns “Bayesian cognition” or “Bayesian psychology,” because for a computer to make those kinds of predictions, it must use a variation of Bayes’ rule, a mathematical formula that generally requires running thousands of models simultaneously and comparing millions of results.*2 At the core of Bayes’ rule is a principle: Even if we have very little data, we can still forecast the future by making assumptions and then skewing them based on what we observe about the world. For instance, suppose your brother said he’s meeting a friend for dinner. You might forecast there’s a 60 percent chance he’s going to meet a man, since most of your brother’s friends are male. Now, suppose your brother mentioned his dinner companion was a friend from work. You might want to change your forecast, since you know that most of his coworkers are female. Bayes’ rule can calculate the precise odds that your brother’s dinner date is female or male based on just one or two pieces of data and your assumptions. As more information comes in—his companion’s name is Pat, he or she loves adventure movies and fashion magazines—Bayes’ rule will refine the probabilities even more.
Humans can make these kinds of calculations without having to think about them very hard, and we tend to be surprisingly accurate. Most of us have never studied actuarial tables of life spans, but we know, based on experience, that it is relatively uncommon for toddlers to die and more typical for ninety-year-olds to pass away. Most of us don’t pay attention to box office statistics. But we are aware that there are a few movies each year that everyone sees, and a bunch of films that disappear from the theaters within a week or two. So we make assumptions about life spans and box office revenues based on our experiences, and our instincts become increasingly nuanced the more funerals or movies we attend. Humans are astoundingly good Bayesian predictors, even if we’re unaware of it.
Sometimes, however, we make mistakes. For instance, when Tenenbaum and Griffiths asked their students to predict how long an Egyptian pharaoh would reign if he has already ruled for eleven years, a majority of them assumed that pharaohs are similar to other kinds of royalty, such as European kings. Most people know, from reading history books and watching television, that some royalty die early in life. But, in general, if a king or queen survives to middle age, they usually stay on the throne until their hair is gray. So it seemed logical, to Tenenbaum’s participants, that pharaohs would be similar. They offered a range of guesses with an average of about twenty-three additional years in power:
That would be a great guess for a British king. But it’s a bad guess for an Egyptian pharaoh, because four thousand years ago people had much shorter life spans. Most pharaohs were considered elderly if they made it to thirty-five. So the correct answer is that a pharaoh with eleven years on the throne is expected to reign only another twelve years and then die of disease or some other common cause of death in ancient Egypt:
The students got the reasoning right. They intuited correctly that calculating a pharaoh’s reign follows an Erlang distribution. But their assumption—what Bayesians call the “prior” or “base rate”—was off. And because they had a bad assumption about how long ancient Egyptians lived, their subsequent predictions were skewed, as well.
“It’s incredible that we’re so good at making predictions with such little information and then adjusting them as we absorb data from life,” Tenenbaum told me. “But it only works if you start with the right assumptions.”
So how do we get the right assumptions? By making sure we are exposed to a full spectrum of experiences. Our assumptions are based on what we’ve encountered in life, but our experiences often draw on biased samples. In particular, we are much more likely to pay attention to or remember successes and forget about failures. Many of us learn about the business world, for instance, by reading newspapers and magazines. We most frequently go to busy restaurants and see the most popular movies. The problem is that such experiences disproportionately expose us to success. Newspapers and magazines tend to devote more coverage to start-ups that were acquired for $1 billion, and less to the hundreds of similar companies that went bankrupt. We hardly notice the empty restaurants we pass on the way to our favorite, crowded pizza place. We become trained, in other words, to notice success and then, as a result, we predict successful outcomes too often because we’re relying on experiences and assumptions that are biased toward all the successes we’ve seen—rather than the failures we’ve overlooked.
Many successful people, in contrast, spend an enormous amount of time seeking out information on failures. They read inside the newspaper’s business pages for articles on companies that have gone broke. They schedule lunches with colleagues who haven’t gotten promoted, and then ask them what went wrong. They request criticisms alongside praise at annual reviews. They scrutinize their credit card statements to figure out why, precisely, they haven’t saved as much as they hoped. They pick over their daily missteps when they get home, rather than allowing themselves to forget all the small errors. They ask themselves why a particular call didn’t go as well as they had hoped, or if they could have spoken more succinctly at a meeting. We all have a natural proclivity to be optimistic, to ignore our mistakes and forget others’ tiny errors. But making good predictions relies on realistic assumptions, and those are based on our experiences. If we pay attention only to good news, we’re handicapping ourselves.
“The best entrepreneurs are acutely conscious of the risks that come from only talking to people who have succeeded,” said Don Moore, the Berkeley professor who participated in the GJP and who also studies the psychology of entrepreneurship. “They are obsessed with spending time around people who complain about their failures, the kinds of people the rest of us usually try to avoid.”
This, ultimately, is one of the most important secrets to learning how to make better decisions. Making good choices relies on forecasting the future. Accurate forecasting requires exposing ourselves to as many successes and disappointments as possible. We need to sit in crowded and empty theaters to know how movies will perform; we need to spend time around both babies and old people to accurately gauge life spans; and we need to talk to thriving and failing colleagues to develop good business instincts.
This is hard, because success is easier to stare at. People tend to avoid asking friends who were just fired rude questions; we’re hesitant to interrogate divorced colleagues about what precisely went wrong. But calibrating your base rate requires learning from both the accomplished and the humbled.
So the next time a friend misses out on a promotion, ask him why. The next time a deal falls through, call up the other side to find out what you did wrong. The next time you have a bad day or you snap at your spouse, don’t simply tell yourself that things will go better next time. Instead, force yourself to really figure out what happened.
Then use those insights to forecast more potential futures, to dream up more possibilities of what might occur. You’ll never know with 100 percent certainty how things will turn out. But the more you force yourself to envision potential futures, the more you learn about which assumptions are certain or flimsy, the better your odds of making a great decision next time.
Annie knows a lot about Bayesian thinking from graduate school, and she uses it in poker games. “When I play against someone I’ve never met before, the first thing I do is start thinking about base rates,” she told me. “To someone who has never studied Bayes’ rule, the way I play might seem like I’m prejudiced, because if I’m sitting across from, say, a forty-year-old businessman, I’m going to assume all he cares about is telling his friends he played against pros and he doesn’t really care about winning, so he’ll take lots of risks. Or, if I’m sitting across from a twenty-two-year-old in a poker T-shirt, I’m going to assume he learned to play online so he’s got a tight, limited game.