[epistemic status: thinking out loud]
Hey everyone, I'd like to receive some feedback on a line of thought that came up in a recent discussion.
In Oxford's introductory fellowship, this question came up as part of the exercise for the week on longtermism:
Imagine you could save 100 people today by burying toxic waste that will, in 200 years, leak out and kill thousands (for the purposes of the question, assume you know with an unrealistic level of certainty that thousands will die). Would you choose to save the 100 now and kill the thousands later? Does it make a difference whether the toxic waste leaks out 200 years from now or 2000?
My take is that the question is meant to tease out the answer that it seems better to save more people rather than less, even though those lives are yet to come. In other words the question seems intended to make a case for longtermism and there are many other thought experiments like it.
Here we could make all the usual arguments for longtermism and against having time preferences.
In my group all the fellows at first answered that they would save the thousands in the future, i.e. the expected answer.
Then one of the fellows came up with the following argument, which this post is about:
If we save the 100 people today, we can assume that they are going to have children. With reasonable presumptions about birth rates, we might expect that after 2000 years the combined number of the 100 original people and their descendants far exceeds a few thousand. Thus, it is better to save the 100 people now, as the total value of happiness from their lineage is bigger in expectation than that of the thousands we will save 2000 years from now.
One might call this the “compound interest” argument for saving lives.
My guess is that this argument seems less important right now, because globally birth rates are slowing down and many countries even have negative population growth. It could become more important should we be able to traverse “the precipice” and populate other planets. Then we could plausibly arrive at a rate of population growth that looks exponential, similar to how it looked in the 60s.
It seems likely that smart people have already thought about the argument but that I'm just not familiar enough with the literature on longtermism.
I invite you to point out why the argument is false or irrelevant.
- Does the argument have any practical implications?
- Wouldn't this line of thinking seem implausible for similar reasons to why we dismiss discount rates? Could taking into account the happiness of all descendants of a person imply that people who lived a long time ago were much more important because they have had many descendants? (2)
- If you save a life, to what extent are you responsible for the happiness (or suffering) of all descendants of the person saved?
- Does the argument work the other way around? Should we consider murder even worse because it might prevent a person from having many happy descendants?
The line of argument could also be portrayed by some math, here is a simple growth rate calculation:
If a = initial amount of people saved
r = growth rate
n = number of years
If we take 100 people originally saved, a very small growth rate of 0.2% per year would, after 2000 years, lead to a population of more than a few thousand.
f(2000) = 100*1.002^2000 = ~5438
Of course this is extremely simplified and calculating population growth depends on many more factors and is much harder. A small group of 100 people, for example, will not have the same average growth rate as the population at large. This calculation also doesn’t account for people who are born and die in the meantime; it just gives the population size after 2000 years. If we were to value the number of (happy) lives lived during the whole time in aggregate, we would arrive at a much larger number.
The calculation is just meant to show that it's plausible to arrive at a number higher than a couple thousand, as it was framed in the thought experiment.
Thanks to Adam, Akash, Aaron and everyone else who discussed this with me!