When was the last time you made a decision you regretted? Chances are it wasn’t too long ago. Maybe you ordered fish instead of pasta; maybe you took the wrong job; maybe you invited a friend to dinner who ended up boring you silly. All of these errors in judgement—in fact, every mistake you’ve ever made—could have been avoided, says psychologist Daniel Gilbert, if you’d correctly worked out the answer to a simple formula a Swiss mathematician named Bernoulli proposed hundreds of years ago.
Boiled down to plain English, Gilbert explained in a 2005 talk, Bernoulli’s equation tells us the following: “The expected value of any of our actions—that is, the goodness that we can count on getting—is the product of two simple things: The odds that this action will allow us to gain something, and the value of that gain to us. In a sense, what Bernoulli was saying is that if we can estimate and multiply these two things, we will always know exactly how to behave.”
An easy way to understand this is to think about betting on a coin-toss. If it costs a dollar to bet and the prize for the right guess is a twenty dollar bill, it’s pretty clear that multiplying the odds of winning (50 percent) and the gain from winning (20 dollars) gives you an answer of 10 dollars, far more than what you’re paying to play. Any fool can tell you you should plunk down your dollar.
So why is it so hard to apply Bernoulli’s equation in most of our life?
Reason #1: You’re Terrible At Estimating Odds
When you guess how likely an event is to occur, says Gilbert, you generally rely on personal experience. You know the likelihood of a pirate riding a unicycle down the street is much lower than the likelihood of a guy in jeans riding a bicycle, because you’ve seen the latter a thousand times and never seen the former. But this way of figuring doesn’t work for everything. As Gilbert points out, we see interviews with lottery winners all the time, and never see profiles of lottery losers. But the odds of losing a lottery are obviously far higher than winning one.
Reason #2: You Only See Prices
Estimating gains is even more fraught than estimating odds. One mistake people make is to only consider the price of something when they’re deciding whether to buy it. Pay $5 for a bottle of water while you’re rushing to your seat at the movies? No way, you think—at the convenience store that would only cost a dollar. But parched in the middle of The Hobbit, you realize $5 would totally have been worth the value of slaking your thirst right now.
Reason #3: You Compartmentalize Money
If you lose your 20 dollar theater ticket on your way to the show, says Gilbert, you’re unlikely to buy another to replace it. But if you lose 20 dollars on the way to buy a 20 dollar theater ticket, you’ll almost certainly still make the purchase. What’s the difference? In the first instance, you don’t add the loss to the cost of the new ticket; in the second, you do. (Of course, the net cost and gain to you is the same in both situations.)
Reason #4: The Comparisons You Make Are Always Shifting
Do you want the medium suitcase or the extra-large one? When you look at both in the store, the bigger bag seems obviously better. You’ll be able to fit so much more inside! But having bought it, the medium suitcase won’t be there to make it look good anymore. Odds are whenever you pack for a trip you’ll leave the bag half empty and curse at how heavy and unwieldy it is.
Reason #5: You Get Confused When Rules About Time and Quantity Conflict
Everybody knows, Gilbert points out, that “more is better than less, and now is better than later.” No one (who wasn’t on a diet) would choose two chocolate chip cookies over three, and no one would choose to eat them tomorrow instead of right now. But what if you had to decide between getting two cookies today and the delayed gratification of getting three tomorrow?
That depends. Amazingly enough, it depends less on the length of the delay itself than on how far ahead of time you make the decision. Most people value two cookies today more than three tomorrow, but they value three cookies 366 days from now more than two cookies 365 days from now. The cost of an extra day’s waiting suddenly seems negligible when you’re already going to wait a year. Okay, you might be saying. So what? The kicker, Gilbert explains, is that in 365 days you’re going to change your mind. Damn it, you’ll say. I want those cookies now.
Despite our failure to implement Bernoulli's simple equation, Gilbert is far from a pessimist about human intelligence. To see why, watch him talk about the formula here.
photo by shannen