^A Although Adam Smith is usually cited for the concept of each individual maximizing his or her own utility, it is important to note that he recognized that this was not stable in its simplest form. Smith’s conceptualization was actually quite complex, and he suggested that national economic success depended on what we now recognize as empathy, sympathy, and altruistic punishment. For example, he recognized the importance of governmental assurances of market fairness, as well as the dangers of monopolies, and other complexities beyond the simplicity of maximization of individual profit.³

^B The history of why the Bernoulli brothers came up with subjective utility is interesting, particularly because it gives an insight into the problems that arise from trying to derive microeconomics from first principles.⁴ The brothers were trying to understand how to incorporate probability into utility—How much should you like a 10% chance of getting $50? They assumed, for simplicity, that one should like it 10% as much. Thus, 10% of $50 should be equivalent to $5. The problem with this is that you can create paradoxes from this assumption that are clearly wrong.

The case that the Bernoulli brothers came up with is called “the St. Petersburg paradox” because it was first presented to the Imperial Academy at the court of Peter the Great in St. Petersburg. Imagine a game with the following rules: You pay a fee to get in and then a coin is flipped. The game stops when the coin comes up tails. The game pays out $1 for each coin flip. Thus, if tails appears on the first flip, you get $1, but if you get 99 heads followed by a tails, you get $100. The question is How much would you pay to play this game? Because of the way the game is constructed, the mathematically expected payout is infinite, and a logical (which economists call “rational”) person should be willing to pay anything to play this game.

Of course, people will only pay a small amount to play this. (Compare the St. Petersburg paradox, which feels wrong even though it is logical, to the distortions that were seen by Kahneman and Tversky,⁵ which feel right even though we know they’re illogical, such as the Asian flu example, where describing the problem in terms of people saved or people lost changes the choice [see Chapter 3].)

The Bernoulli brothers proposed that the reason people wouldn’t pay large sums to play this game was because they were actually maximizing “subjective utility” in which higher and higher payouts had less and less value. Thus, $200 was not twice as valuable as $100. Bernoulli specifically suggested a square root function—that is, subjective value is the square root of the actual value offered.

However, it is not difficult to modify the St. Petersburg paradox to wreck any unbounded value function. One possible explanation is that our subjective value functions are not unbounded. Eventually, it doesn’t matter how much money is paid out, it’s just a “big win.” The problem with this hypothesis is that it is very clear (at least for money) that this is not true. Billionaires who have long had every possible desire sated continue to fight for more money. (We will see why later in this chapter.) Current explanations for the St. Petersburg paradox are based on differences in how much we like gains and losses (people hate losses more than they like gains), and the recognition that you can never be offered an infinite amount of money because eventually you’ll break the bank.

My hunch is that part of the answer may be that valuation is done online, and that the valuation system in our brains can’t do the infinite sum needed to make it worth paying into the St. Petersburg paradox. If the person adds up only the first few cases and then says the chance of 10 heads in a row is so unlikely it’s not worth thinking about, then the maximum payout is not infinite. (Of course, people play the lottery, which has a much lower probability of payout.) Even though the Bernoulli brothers’ explanation of the St. Petersburg paradox as a transformation of utility is no longer the accepted story, the concept of an internal modification of subjective utility remains.⁶

^C I bet you never thought cooking for your kids was so fraught with meaning.

^D Sociobiology has gotten a bad rap over the past several decades because the conclusions were taken as prescriptive rather than descriptive, and because they often created broad generalizations from limited observations.¹⁵ We will discuss the issue of differences between prescription and description later (in Chapter 23). Briefly, the goal of science is to understand causality in the world—if the world is in this configuration, then that will happen. For example, the Galilean/Newtonian theory of gravity implies that if I drop a hammer and a feather at the same time in a vacuum, they will hit the ground at the same time. (This was of course tested by Apollo 15 astronauts and found to be completely true.¹⁶) We call this descriptive because it describes the world. On the other hand, what we should do with this knowledge is prescriptive. To say that the double standard of loose sexuality (women lose rank for sexual promiscuity, while men gain it) arises from differences in how much effort women and men have to put into childrearing (it is easier for men to leave than for women to)¹⁷ does not imply that one should encourage that double standard, or that a society that accepts that double standard will be better than one that doesn’t. We will come back to questions of “better” and society in our discussion of morality in Chapter 23. As this issue of sociobiology is not the subject of this book, I’m going to leave it here, with the simple statement that the fact that biology is not destiny does not mean that it isn’t true.

^E This seems silly to us now, but it was due to an inability to quantify the non–food-related attachment component. Remember that psychology moved from the Gestalt theorists (in the late 19th century), who used introspection, to the Behaviorists (early 20th century), who would only examine quantifiable behaviors.

^F The issue of animal rights is a very complex one that is far outside the scope of this book. However, for those who are interested in this issue, I recommend starting from two books by Deborah Blum, The Monkey Wars, which describes the interactions between the animal rights movements and scientists, and Love at Goon Park, which describes the life of Harry Harlow and the influence of his work on the world.

^G Some readers may complain about the sequence that I’ve presented here. In 1900, John Watson is a leading psychologist and argues that children should not be hugged or cuddled, which leads, actually, to high death rates in orphanages and hospitals.²⁹ It takes an interaction between John Bowlby observing what we now identify as separation anxiety in children in hospitals and Harry Harlow doing terrible experiments on monkeys to overturn this view and recommend that children need (as the now-popular saying goes) “eight hugs a day.” It took a half-century for science to correct this mistake. What errors are we facing today? What scientific mistakes are hidden in this book? Should we trust current science at all? This topic is too long and complex to address in this book, but the short answer is that science is a self-correcting system. One could argue that self-correction is the key to science—it may take years or even decades, but science checks itself and corrects itself.³⁰ That’s what has allowed all of the breakthroughs we’ve seen today, from flight to computers. Newton corrected Aristotle, and Einstein corrected Newton. Instead of saying “science is sometimes wrong, we should ignore it,” we need to identify where we think current theories are mistaken and propose experiments that will directly test them—and then trust the answers those experiments give us. (Compare this to alternative description-of-the-world paradigms that claim to have known the answer for hundreds or thousands of years, but have no means of changing hypotheses in response to their relation to facts.³¹)

^H Although, when my wife and I were in college, we had an apartment kept mouse-free by our excellent hunting cat Koshka. When we moved in, there were mice living in the furnace room, but they didn’t last very long.

^I For those who are interested in this, there are a lot of great books on the topic of primate hierarchies and their complexity. See, for example, A Primate’s Memoir (Robert Sapolsky), Sex and Friendship in Baboons (Barbara Smuts), Almost Human (Shirley Strum), Chimpanzee Politics (Frans de Waal), and of course, the entire series of Jane Goodall’s popularizations of her studies of the chimpanzees of Gombe (In the Shadow of Man, Through a Window, and many others).

^J It is remarkable how unpleasant even a small electric shock can be.⁴⁸

^K Several authors have suggested that this is what craving is—the motivation for a thing predicted by cues.⁵⁴ We will return to the question of craving in our discussion of addiction (Chapter 18).

^L Some of the ads were for pizza! Who eats pizza at the movies?

^M Remember that phasic bursts of dopamine signal transitions in value being better than expected, while pauses of dopamine signal transitions in value being worse than expected.⁶⁴ These phasic bursts are like taking a derivative of the expected value signal. Tonic dopamine would then be taking the integral of this value signal, which is the average reward in the environment.⁶⁵