The probability of your coming into existence was bogglingly small.
The ejaculation that led to your conception contained hundreds of millions of unique spermatozoa. You are the one in half a billion that made it to fertilization. And it was that particular ejaculation that resulted in conception – as opposed to the thousands of ejaculations your father experienced before and after your conception. Your parents met (literally or figuratively, if you’re the product of a sperm donor) and conceived you, instead of conceiving with other potential mates, or not conceiving at all. And this startling history applies to your parents as well – your grandparents – your great-grandparents – and on back to the Australopithecines and beyond – each one the winning sperm of hundreds of millions, the result of a particular ejaculation, a particular union, that could have not happened as easily as your nonexistent brothers and sisters failed to happen.
Are you lucky to be alive?
Most people seem to experience a mixture of terror and delight when contemplating their own unlikeliness in this way – terror at the prospect of never having come into existence, and delight in one’s specialness, one’s victory over the other potential beings. One might even feel pity for those who never got to exist.
The conventional wisdom is that we are all very lucky to be alive – that life is a benefit, a precious gift that has been given to us. This is an important belief. It is a belief that is necessary to justify creating a child – if the child is benefited by being born, then procreation, at least toward him, is morally innocent. Perhaps it is even morally required!
Of course, life isn’t so great for everyone. The world is so bad, in fact, that its badness is the most conclusive argument against the existence of a loving, all-powerful deity. But when antinatalists point out the serious harms that come to all living beings, such as hunger, loneliness, jealousy, pain, illness, fear, and death, we are often told that we are giving an incomplete picture of reality. Reproduction advocates, realizing that the moral innocence of reproduction rests on life having a positive value, advise us to look on the bright side. We are frequently invited to consider the good things about life, the sunsets and puppies and children’s smiles that allegedly blot out the bad and give life its high net positive value. And that’s the folks who are willing to engage the question at all: too often, the question of the value of life is not addressed because it is supposedly just so obvious that life is worth getting. (This is the position taken by Thomas Nagel and Bryan Caplan, among others.)
So is life a precious gift, or is it a costly burden? Are we impossibly lucky to be alive – or impossibly unlucky?
Let’s not argue the point. We can do better: we can measure.
Truncated Utility Functions and the Value of Life
“Utility” is an economic concept similar to happiness, but broader. It is the ultimate emotional evaluation of whether things are good or bad. The concept of utility does not rest on a purely hedonistic model of life; economics recognizes that utility may be gotten from a variety of transactions and experiences, springing from motives self-interested, altruistic, and everything in between.
Broadly speaking, utility is a function of “income” – again, very broadly defined. Income in this sense need not be monetary income in dollars, as from a job or investments, but may include items that are not even available directly on any market, such as affection from other humans and self-respect. I will address below the question of what real human utility functions are actually a function of. (I reserve the right to switch willy-nilly and with no warning between speaking of utility functions that are functions of monetary income and those that are functions of other things, depending upon context to clarify which I mean.)
As Gary Becker and Richard Posner note in the unpublished paper that is one of the primary subjects of this essay (“Suicide: An Economic Approach”), in studying how utility responds to changes in income, economists have primarily focused on middle-class individuals – people who own houses, earn money from investments, and buy fire, health, and automobile insurance. This has led to the conclusions of economics occasionally not being true observations of general human nature, as they often purport to be, but rather observations of middle-class human nature.
One of these suspect observations is that utility functions are concave. This is a typical representation of a concave utility function:
What this means is that a person gets a lot of utility from the first dollar he gets – even the first thousand or ten thousand dollars – but he doesn’t get nearly as much utility from the 40,000th dollar, and even less from the millionth dollar. (Modern American utility functions of income apparently top out at around $75,000 per year.) What this means is that, dollar for dollar, gains are less valuable to the average suburbanite than losses are painful. He would rather pay $1000 a year in car insurance (say) than take a one-in-ten chance at a $10,000 loss during that year in an accident. This phenomenon – that makes the insurance industry viable and makes utility functions concave – is called risk aversion.
Many people behave in ways that are not consistent with risk aversion. They make “bad” bets – bets where the expected payoff (probability of success times magnitude of win) is less than the cost of the bet. They take risks seemingly without regard for possible bad consequences. They appear focused on the present and immediate future, at the expense of the far future (they are “extreme future discounters”). Miserable people and poor people are particularly likely to fit these criteria.
Why are middle-class folks risk averse, but not miserable folks or poor folks?
Bryan Caplan and Scott Beaulier, in their paper “Behavioral Economics and Perverse Effects of the Welfare State,” present a possible solution: irrationality and akrasia. The bad choices made by poor people are a result of their inability to forecast the future effects of their actions, combined with laziness. Welfare and other social programs, rather than making the poor better off, paradoxically make them worse off (say Caplan and Beaulier) because their irrational, akratic minds cannot handle the extra choices. (Note: this is my characterization of Beaulier and Caplan's conclusion; they use euphemistic terms at all times.)
Gary Becker and Richard Posner have a different solution: miserable and poor people don’t “properly” consider the future, because their lives are so painful that they are effectively suicidal. Poor people look around and rationally weigh the costs and benefits of different courses of action, but choose to gamble on long shots precisely because their current situations are not worth living in. They would just as soon die as remain in their current situations, and so gamble what little they have on the hope of a meaningful life.
Don’t just think gangs and lotteries and crime and crack. Think about people pursuing acting or singing careers, or going to law school or business school, or marrying in haste, or even, perhaps, having children. Such people bet everything – including their futures – on winning a particular gamble, even if it’s not a fair gamble and the likelihood of payoff doesn’t make up for the losses necessarily incurred pursuing the gamble.
The utility function pictured above has a lot of space beneath it and above the x axis, even at the origin. This reflects a judgment that even at zero income, a person takes great value from being alive.
This may or may not fit the facts.
The actual points at which actual human utility functions intersect the x axis may be far to the right of the y axis, as with this utility function for a person who only begins to get positive utility at income Id. For all incomes below Id, the person experiences negative utility – that is, he suffers.
This utility function is a model for the phenomenon that many people (myself included) do not seem to derive much utility at all from incomes (broadly conceived) much greater than zero.
Many people are so miserable that they do not want to enter the future at all. Their whole future projected life is worthless to them. In technical terms, their utility over all future time intervals, appropriately discounted, is less than zero. Also, their current utility (present circumstance) is zero or negative (otherwise they'd stick around a bit longer to pick up extra utility).
Suicide is one option for such people. But there are two other options, according to Becker & Posner (terminology is mine):
- Take what you have and “bet” it on a chance at something that would make life worth living. If it fails, you can always kill yourself. (Gamble)
- Since there is an element of uncertainty to the future, take what you have and use it to make the present livable so you can postpone suicide. Something to make life worth living might be just around the corner. If not, you can always kill yourself. (Palliate & Wait)
The utility function above for inefficient utility producers (like myself), where the utility function dips below the x axis, means that the person modeled must fear losing income below this point, because having income below Id means he will suffer.
But a would-be suicide need not suffer. He has an ace up his sleeve: all suffering is the same as death to him, for he can use death to escape any suffering. His utility function is effectively truncated. It looks like this:
Instead of dipping below the x axis, his utility function continues along the x axis all the way to the y axis (and beyond, if you allow for negative income). Now there is a portion of the utility function that is convex – the signature of risk preference, the opposite of risk aversion described above.
Any income below the critical level Id is worth nothing to the effectively suicidal person. This means that it will not make sense for him to expend any effort in securing income below this level. Like a depressed person who has lost the sense of the value of things, he is not motivated to get up in the morning, to work hard, to be responsible, if all it means is income below Id. It's the same as death to him.
How can we tell who is effectively suicidal? Nonsuicidal people still often rationally accept gambles, even gambles with a risk of death. The main way to tell the difference between effectively suicidal people (with a truncated utility function, as above) and nonsuicidal people is that suicidal people are insensitive to the potential for great losses, and are only motivated by the possibility of a big win; effectively suicidal people accept actuarially unfair gambles which do not properly compensate them for risk of loss (including risk of death). Nonsuicidal people demand to be compensated for risks of loss, including risk of death.
To the extent that people display risk preference and extreme future discounting of losses but not large gains – to the extent that they are willing to accept unfair gambles with a high probability of loss (Gamble) or improve their short-term well-being at potentially great cost to their future selves (Palliate & Wait) – the hypothesis of effective suicidality must be considered. Only by considering and rejecting this hypothesis, based on data and/or reasons, could we meaningfully attribute these features to departures from the rational actor model, as Beaulier and Caplan do prematurely.
Beaulier and Caplan essentially argue against “welfare floors” because by cushioning the bad consequences of a gamble, they make antisocial gambles more attractive. But they ignore that there is a built-in welfare floor in any human society, welfare state or not: suicide.
It is inconsistent to maintain that, on the one hand, a welfare floor is undesirable because negative utilities are necessary as motivators for action, and on the other hand, that utility is rarely negative and hence procreation is morally innocent.
This model does not, however, predict mass suicides at any point, and the fact that suicide remains rare does not mean that many people do not have effectively suicidal, truncated utility functions. All this theory claims is that people act as if they don’t value their lives. Unsuccessful gambles may or may not be followed up with actual suicide; the costs of suicide are often greater than a pre-suicidal person realized when contemplating life paths, and are artificially elevated by the de facto suicide prohibition. Also, cheap palliation is widely available, allowing many would-be suicides (such as myself) to postpone this costly decision.
The most important policy implication of the “mathematics of misery” I have outlined here – of the fact that many people appear to attach zero value to their lives – is that procreation becomes much more of a suspect enterprise. If people’s behavior reveals that they do not highly value their lives, then it is not “obvious,” as Bryan Caplan would have us believe, that human beings are benefitted by being brought into existence. A life that produces zero utility in the immediate present, and zero or negative utility for the foreseeable future, is hardly the kind of precious gift that would justify procreation, yet from this model it is likely that a substantial portion of the population of the world lives just this kind of life.
Someone whose utility function is negative for all time intervals would have been better off not having been born. Many people are in this situation through no fault of their own. A second policy implication for recognizing this is a move toward greater compassion in providing “palliative care” to people whose present utility and expected future utility are negative and whose only incentive to remain alive is uncertainty. As a society, we are willing to allow “palliative care” for terminally ill persons, but our middle-class model of risk aversion and the value of life prevents us from recognizing the need for palliative care in “healthy” people as well.
Third, there are implications for harm reduction, regardless of one’s position about the value of life. Viewing utility functions (and hence human motivation) in this light, we can see that a suffering person chooses from available gambles and palliation methods. Outlawing a particular type of gamble or palliation method will likely divert demand to other types of gambles or palliation, and hence will not reduce overall levels of harm unless substitution happens to be toward less harmful activities. Recognition of this “demand for risk” should guide policy decisions regarding dangerous activities.
What Real Human Utility Functions Are Functions Of
The utility function does appear to be a function of income – within a country, wealthier people are less miserable. But it is also a function of one’s past incomes – receiving a higher income increases utility in the short run, but in the long run, it sets a new baseline for utility (this is the hedonic treadmill). Utility is also a function of the incomes of near others (that is, a function of within-group status), which is why more direct income-utility correlation is found within-country than between countries.
However, as I have written previously, more than anything, a human utility function is a function of social belonging. That's the ultimate point not only of income, but of intelligence, beauty, and many other material and non-material goods: they may be traded for social belonging. The ability to provide others with what they want is the opposite of burdensomeness, a pillar factor of suicide risk in Thomas Joiner’s model (the other pillars are social belonging as such, and competence in carrying out the act of suicide). We want income because we want to be able to get the attention of others. We want a safe social place, primarily – and, of course, we want a better social place than the one we currently occupy.
The primary good, for humans, is group belonging. There is only so far up or down you can go in a social group, only so much room for status manipulation – otherwise you have to find a whole new social group. Within a group or class, we’d like to go up, but we’d HATE to go down. Each person sees a huge drop-off in utility when considering the loss of his present group belonging, no matter whether his present group is high or low in status relative to greater society. This has very little to do with absolute material welfare.
This is why the guy choosing television and phones over food is making the right choice. Group belonging really is more important than short-term well-being. He is even displaying risk aversion, as is the poor black parent who gives her child a name that strongly signals group belonging at the expense of belonging in other groups or classes.
It’s extremely difficult to join a whole new social group. Everyone faces a utility drop-off, a chasm, at the prospect of losing social belonging – a process sometimes described as social death. People behave as if losing one’s social group and status is worse than death. This is strong evidence that social death really is worse than death.
Poor Baby or Rich Baby: Which Is Worse?
Data about crime, drug use, and other forms of risk preference and palliation seem to indicate that poor people are more likely than rich people to display the kind of truncated, effectively suicidal utility function I have been discussing. This could support the claim that it is more wrong for a poor person to have a child than for a rich person.
However, when we realize that social belonging trumps everything, we see that what really determines the value of life is the opportunity to be party of a social group. Middle class people have different relevant social groups from poor people, and the very wealthy have different social groups altogether. A child born into one of these groups must establish a place for himself; if few places are available, downward mobility (social death) is indicated. Therefore a person born into a very wealthy social group that has few opportunities for belonging may be in a worse position than a person born into poverty but with many opportunities for belonging.
As Becker & Posner note, the nature of the "Gamble" you can buy depends on your present income; higher present incomes buy better gambles, with a higher probability of success. Therefore, wealthier people may succeed in their suicide gambles more often than poor people, so their gambles are more socially invisible than those of the poor - but they are still making them.
However, the social belonging hypothesis that I have been advancing here (that social belonging is the primary determinant of utility) implies that the income at which life becomes worth living, Id, varies with one's existing social situation, hence with initial income. Wealthy effectively-suicidal people start out with more initial income - they have more to gamble with - but they have a higher mark to reach for their gambles to be successful. It is not clear which effect predominates.