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Mistakes in the moral mathematics of existential risk (Part 3: Population dynamics)

“Future people count. There could be a lot of them. We can make their lives go better.” This is Will MacAskill’s elegant and compelling introduction to longtermism … We consider an important other possibility: There might not be a lot of them, after all. The entire population science community predicts the global population to begin shrinking within the lives of children born today. Once this decline begins, it may happen fast … We review population projections and other social scientific facts that show that fertility rates that are normal in much of the world today would cause population decline that is faster and to lower levels than is commonly understood, threatening the long term future.

Spears and Geruso, “With a whimper: Depopulation and longtermism
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1. Introduction

This is Part 3 in my series “Mistakes in the moral mathematics” based on a paper of the same name. In this series, I discuss three mistakes that are often made in calculating the value of existential risk mitigation. I show how these mistakes have led the value of existential risk mitigation efforts to be overestimated, and how they have mislocated debates about the value of existential risk mitigation.

Part 1 introduced the series and discussed the first mistake: focusing on cumulative rather than per-unit risk. When existential risk mitigation is framed as an intervention on risk in our own century, rather than risk across many distant centuries, the value of existential risk mitigation drops dramatically. We saw how a leading paper by Nick Bostrom makes the first mistake.

Part 2 discussed a second mistake: ignoring background risks which are not affected by our intervention. We saw how a leading estimate of the cost-effectiveness of biosecurity interventions by Piers Millett and Andrew Snyder-Beattie falls once background risk is incorporated. We also saw how the second mistake compounds with the first in Millett and Snyder-Beattie’s discussion, leading to a larger overestimate.

Today, I want to focus on a third mistake in the moral mathematics of existential risk: neglecting population dynamics. I split this discussion into two parts. Today’s post focuses on standard demographic models. My next post extends this discussion to nonstandard demographic models.

2. Population size and carrying capacity

Many authors estimate the size of the future human population as follows. First, they carve out a region of space, such as Earth, the solar system, or the Milky Way. Second, they estimate the carrying capacity of this region: the number of humans it could comfortably support. Third, they estimate the duration for which humans might exist in this region. The future human population is then estimated at the duration times the carrying capacity.

We saw in Part 1 that Bostrom gives what he terms a conservative estimate of the future human population in just this way: Earth is assumed able to support a billion people for a billion years, generating a total of 1018 life-years, or about 1016 lives at current life-spans.

Will MacAskill argues similarly in his recent book, What we owe the future. Suppose we assume that Earth can support a population of ten billion humans, and support them for five hundred million years. Then the future holds a total of 1010 * (5*108) life-years, or about 5*1016 lives.

MacAskill dramatizes the point by asking us to imagine ten billion humans as a single stick figure. Then, MacAskill reminds us, history to date holds about 10 to 12 stick figures of humans. However, the future could hold 5 million stick figures of humans, even if humanity never sets out for the stars. Surely those five million stick figures are worth at least as much consideration as the previous ten?

A recently popular defense of longtermism by Will MacAskill and Hilary Greaves argues similarly, following Toby Newberry in deriving estimates of the future human population under the assumptions that humanity stays earthbound, settles the solar system, or colonizes the galaxy. I display these estimates together below:

ScenarioCarrying capacity
Duration (centuries)Future lives
Earthbound (Bostrom)1091071016
Earthbound (MacAskill)10105*1065*1016
Earthbound (Greaves/MacAskill)10101041014
Solar System
Milky Way

That’s a lot of people. Could these estimates be a bit too high?

3. Interlude: Background risk

One theme of this paper is that mistakes in the moral mathematics of existential risk combine together to lead to overestimates. As such, it is always helpful to take notice of previous mistakes that may be repeated by these estimates.

One thing to note about these estimates is that they ignore background levels of existential risk (second mistake). When we redo these estimates with pessimistic (20%) or even optimistic (1% or 0.1%) levels of per-century existential risk, the estimates are reduced, and the penalty is strongest against some of the previously highest estimates.

r = 0.2r = 0.01r = 0.001
Earthbound (Bostrom)10164*10910111012
Earthbound (MacAskill)5*10164*101010121013
Earthbound (Greaves/MacAskill)10144*101010121013
Solar System
Milky Way

This is already quite a haircut. But this isn’t the only place where we go wrong by multiplying duration by carrying capacity. Today, I want to focus on a different place where these estimates take a haircut: standard demographic models.

4. Population dynamics after Malthus

Before the Industrial Revolution, human populations followed a simple pattern. We bred like rabbits until the resources ran out: that is, until there was no more land or food left to support additional children, and the existing population survived near subsistence level. The phrase `breeding like rabbits’ is apt here in more ways than one, since many animal populations follow the same underlying dynamics.

Demographers reserve the term Malthusian dynamics, after Thomas Malthus, for population dynamics in which resources serve as the primary constraint on population size. Malthusian dynamics are as bleak and stark as they sound: they doom us to large, near-subsistence populations seemingly straight out of Parfit’s repugnant conclusion, as Malthus himself reminded us.

After the Industrial Revolution (and in some countries, before that), matters changed. Birth rates began to decline despite rapid increases in the stock of available resources. Increasingly, fertility is shaped less by the question of how many humans we could in principle support, and more by norms and values, which help people decide how many children to actually have. We could, right now, support many more humans than are alive today, but we have chosen not to.

At present, a great number of countries have fertility rates well below the replacement level of two children per woman. For example, fertility is at 1.66 children per woman in the United States, 1.5 in Western Europe, 1.2 in East Asia, and 1.0 in Korea. Here is an illustration of falling fertility rates from Our World in Data:

As these projections reveal, fertility rates are projected to fall below replacement by the end of the century. After that, world population will peak at no more than 10-12 billion people, and then probably begin to fall. Here, again, is Our World in Data:

That’s not so bad. But what happens after 2100? Here comes the bad news.

5. What standard demographic models predict

I have continually urged caution in making strong predictions about the long-term future of humanity, and I would be remiss if I did not urge some level of skepticism about extending demographic models beyond the year 2100. Nevertheless, many well-qualified modelers (Basten et al. 2013, Raftery and Sevcikova 2023, Spears et al. 2023) are willing to extend models at least until 2300, and what they show isn’t pretty.

Dean Spears and Mike Geruso of the Population Wellbeing Initiative consider a model with asymptotic fertility of 1.66 children/woman. In this model, annual births have reached a `spike’ from which they will quickly and permanently fall.

How bad could things get? In this model, the entire future of humanity holds no more than 30 billion people, by contrast to the 120 billion people already born. In MacAskill’s parlance, we would expect three `stick figures’ of future humans, rather than five million stick figures.

Importantly, the model conclusions are robust to a wide range of variation in the fertility rate. Spears and Geruso illustrate how the model changes across a range of fertility rates, illustrating each rate with an example region that is already at this fertility rate today.

Across models, it is hard to get more than three stick figures of future humans, and we might well have many fewer humans than that.

If that is right, then longtermists are in trouble, for these numbers fall far below longtermist estimates of the expected number of future human lives. Moreover, these numbers are not obviously sensitive to the capacity of humans to expand beyond the planet Earth. They are, after all, driven primarily by norms and values rather than by resource limitations.

6. Could standard models be wrong?

That is what standard demographic models say. This argument is made by leading demographers, Spears and Geruso, at the Population Wellbeing Initiative, a research institute closely associated with global priorities research and the effective altruism movement. It is echoed by other demographers (Basten et al. 2013, Raftery and Sevcikova 2023), and reflects our best scientific consensus about future demographic trends.

That is not to say that we should invest all of our faith in standard demographic models. But it might be illustrative to explore a few objections to standard demographic models, and the replies which Geruso and Spears offer to them.

First, it might be objected, how can we be so sure that fertility will not rise back above 2.0 (replacement)? While we cannot be sure, the data paints a grim picture. Geruso and Spears write:

Empirically, fertility rates that have fallen and stayed well below replacement levels have so far never rebounded to and stabilized at levels that would avoid depopulation … Fertility in France has been falling since the 1700s. Fertility in England and Wales has been falling since the 1800s … Fertility rates can fall for centuries and then stay low. We know that because they have … Since the 1950 birth cohort, there have been 27 countries with trustworthy statistics where the lifetime average of children per woman has ever fallen below 1.9 … Never, in any one of these 27 countries, has the average ever yet risen above 2 again. Not in Canada (now 1.8), not in Japan (1.4), not in Scotland (1.7), not in Taiwan (1.5). In some of these countries, governments believe they have policies to promote and support parenting. But none of these policies have ever, in fact, achieved a return to fertility levels that would stabilize the population. Zero-for-27, so far.

Second, it might be objected, the fertility rate might equilibrate to replacement level. But why would this happen? The number two is not a magic number, once norms and values enter the mix. People can have any number of children that they would like. As Geruso and Spears note:

Another common response is: won’t fertility rates equilibrate to two, so that population size stabilizes? We reply: But why would that happen? There is no magical force to balance the number of births to the number of deaths … None of the complex personal motivations and economic and cultural forces that drive individual decision-making generate a tendency to hold at 2 … Ask the demographic experts of Japan, where TFR [Total Fertility Rate] has been below replacement for 50 years, whether they’ve encountered evidence of this mysterious equilibrating force.

Finally, it might be objected, perhaps technology will rescue us. Perhaps, and in the next post we will consider what happens if technology does come to the rescue. But people have been claiming for centuries that technology will reverse the fertility decline, and so far the opposite seems to have happened. Here are Spears and Geruso:

Shouldn’t technology solve this? -artificial wombs! robot nannies! AI tutors! longer lifespans and fertility spans! We share the excitement for such a future, but we urge the techno-optimist to reflect that over the past two centuries – as lifespans have lengthened, as work days have shortened, as the world has gotten richer, as fertility has extended to later ages via technologies like ART, as care-work-supporting technology has proliferated (washing machines! disposable diapers! the Snoo!) – fertility has fallen, not risen. Technology expands opportunities, not family sizes, and this brand of fertility-oriented techno-optimism lacks a coherent theory of why people will start choosing children again, among all the wonderful competing goals and options that our new world would offer us.

Again, readers may place some confidence in the optimistic hope that technology will rapidly and permanently expand the human population. In the next post, I will consider what happens under such conditions. But I hope that readers now invest considerable confidence in standard demographic models, on which the human population will be a great deal lower than the longtermist hopes.

7. Conclusion

In this post, we encountered a third mistake in the moral mathematics of existential risk: ignoring population dynamics. We saw that many longtermists make the mistake of estimating the size of the future human population by multiplying the carrying capacity of a region by the expected duration of human civilization in that region. This is a mistake because population dynamics do not answer only to the question of how many humans a given region could support, but increasingly also to the question of how many humans we would like it to support.

We saw that standard demographic models predict a far smaller future population than longtermist estimates do. On one leading model, out of the Population Wellbeing Initiative, MacAskill’s seemingly conservative estimate of five million `stick figures’ of ten billion future humans each is reduced to perhaps 2-3 stick figures.

We also saw that it is not so easy to object to standard demographic models. A number of natural objections fail, which is why demographers and policymakers place substantial confidence in such models.

That isn’t to say that we should not ask what happens if standard demographic models are wrong. In the next post, I show how even on highly optimistic models, incorporating population dynamics tends to dampen the value of existential risk mitigation.


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