IMAGINE DISCOVERING ONE FINE DAY THAT YOU ARE IN POSSESSION OF a winning lottery ticket that gives you an instant prize of $100,000. You literally jump for joy.
Now imagine that a week later you buy another lottery ticket, which amazingly turns out to be a winning ticket, giving you yet another $100,000. Another week later, the same thing happens.
Try to rank the levels of joy you would feel each successive time you won the lottery. When would you be happiest? If your answer is that you expect your joy would be strongest the first time, with less additional joy the second and third times, you are no different from most people. Your intuitive expectations in this scenario correspond to one of the most basic assumptions in economic theory, known as “diminishing marginal utility,” which posits that the more wealth you have, the less each additional dollar (or $100,000) adds to your welfare. The marginal utility gives us the extent by which our welfare goes up (or down) as our wealth increases (or decreases).
What happens with negative events is less obvious. Most of the evidence collected by behavioral economists suggests that the suffering endured from, say, losing $2,000 is less than twice the suffering endured from losing only $1,000. It is hard to prove whether the same applies when more serious negative events are involved, i.e., in case of a death of a loved one or an illness, but most economists tend to believe that this is indeed the case. In pseudo-arithmetic terms we can paraphrase this as: one plus one adds up to less than two, but minus one plus minus one adds up to more than minus two.
How does the arithmetic of emotions work? There is very little scientific research on the subject to date. Theoretical economics gives a partial answer to the question with the concept of utility functions. A utility function associates each situation (where “situation” may mean a basket of goods, winning a particular prize in the lottery, or even contracting a disease or suffering personal injury) with a numerical value. This numerical value is meant to represent the subjective emotional reaction of an individual to each such situation.
In 1944, the mathematician John von Neumann and the economist Oskar Morgenstern published one of the most intellectually important books of the twentieth century, The Theory of Games and Economic Behavior.1 In their book, von Neumann and Morgenstern studied utility functions in great detail. One of the more elegant results that they achieved was showing that a person who reacts with decreasing marginal joy to good news will be risk averse.
If offered a choice between a risky lottery or a risk-free sum of money equal to the average payoff of that same lottery, a risk-averse person will always prefer the risk-free option. For example, suppose you offer someone a choice between $1,000 with no risk or a lottery ticket with a 50 percent chance of winning $2,000 and a 50 percent chance of getting nothing. A risk-averse individual will prefer the $1,000 “sure-thing” option, despite the fact that the lottery offers a chance at winning $2,000.
Most people are risk averse. That is why insurance companies earn fortunes in profits. Most of us will choose risky investment instruments, like stocks, only if the expected average payments they offer are higher than those offered by more solid investments. It is true that many of us also like to buy the occasional lottery ticket or sometimes try our luck at the tables at Las Vegas casinos, but this sort of seemingly “risk-seeking” behavior usually involves relatively small amounts of money and can be categorized more as entertainment than true risk taking (unless it gets out of hand and turns into a gambling addiction, which is another matter that we will discuss later in the book).
Our attitudes toward risk are not immediately self-evident from an evolutionary perspective. There are animals that exhibit different risk attitudes from humans. A coauthor of mine, John Kagel, who is a leading researcher in behavioral economics, started off his research career by studying how pigeons relate to risk. Kagel, along with a group of other researchers, conducted experiments in which pigeons were exposed to several different pigeon holes holding differing amounts of food.2 Some of the pigeon holes always had the same amount of food, while others had food amounts that varied over time. The distribution of food in each pigeon hole over time was carefully controlled so that on average they all had the same amount of food.
For example, if one pigeon hole always contained 20 grams of sunflower seeds, another pigeon hole might have 40 grams of sunflower seeds 50 percent of the time and be empty 50 percent of the time.
In contrast to the risk-averse behavior that humans typically exhibit, the pigeons preferred pigeon holes with random amounts of food to those that always contained the same amounts. Kagel suggested that the difference in risk attitude between humans and pigeons might be based on the different environments in which the two species live. Pigeons need a minimal amount of food to survive. A food source that provides less than the minimal amount that a pigeon needs is of no use for surviving. The regular sources of food that pigeons usually encounter in the wild might not provide the minimally necessary amounts, leading pigeons to prefer taking risks in the hopes of obtaining food amounts greater than the minimal threshold they require.
The consumption environment of humans is arguably very different from that of pigeons. Think of how your welfare is affected by different quantities of some commodity that you own. An extra unit from the commodity will raise your welfare substantially if you own little of it, but the rise in welfare will be much less pronounced if you already own a lot of it. In essence, this is what makes us risk averse. Why? Imagine you own five apples and I offer you to trade these apples for a coin toss: if it turns up heads, I give you five more apples; tails, I give you zero apples. If you make this trade, you either lose five apples or gain five apples. If apples are all you have to eat, losing five apples reduces your welfare (because you might starve) more than gaining five apples raises it (because you can try to stretch the five apples longer). Hence, you’d be better off not accepting my offer but rather remaining with your five certain apples. In other words, risk aversion is a rational trait for us humans, and this is why we almost consistently display this trait.
So far we have considered the arithmetic of emotions as it relates to similar events. But what happens when we take into account completely different events? How do winning the lottery and a great night out add up emotionally? How does being informed that you have been awarded an important promotion at work balance against news that a close friend has suddenly died?
Very little research has been conducted to answer these questions, and most of what we know on the subject is indirect. We know that our emotional reactions to events—whether positive or negative—are strongly influenced by the extent to which we focus cognitively on one event or another. If, for example, we experience two positive but different events in quick succession, limits to the amount of attention we can give to both events usually lead us to focus more on one event than another, with more emphasis generally given to the event that we regard as more important. This tends to reduce the cumulative effect of the other event on our emotional state. The emotional reaction will then be close to the maximal reaction we would have to only one or the other event. The emotional arithmetic here is therefore different from the simple addition of two joyous reactions.
The same thing happens with regard to two negative events. Our cognitive attention will be given to the worse of the two, causing the emotional effect of the other negative event to be marginal.
The more interesting scenario is one in which one event is positive and the other event is negative. In this case, again, the relative importance we attach to each event greatly determines which event will have greater effect on our emotional state, but, unfortunately, negative events almost always dominate positive ones. In other words, to cause us to focus on a positive event in juxtaposition with a negative event, the positive event needs to be regarded as much more important than the negative event. If it is only slightly more subjectively important, we will focus more on the negative event and the net emotional effect of both events will be negative.
Clinical depression is frequently accompanied by an obsessive focus on negative thoughts that almost entirely crowd out positive thoughts. Most of us don’t experience extreme focus on negative thought to such an extent that we suffer from clinical depression, but unfortunately when it comes to the addition and subtraction of joy and sadness, even the healthiest among us tend to give more weight to the sadness.