My Current Solution to the Repugnant Conclusion

A tricky, tricky puzzle

One of the most interesting, and difficult, puzzles in normative ethics is coming up with a moral theory that avoids what Derek Parfit termed the “Repugnant Conclusion”. Aside from infinite ethics, and a few issues with moral risk and moral uncertainty, this is probably one of the harder problems in contemporary moral philosophy — at least in my view. And, contra what many people seem to think, avoiding the Repugnant Conclusion is everyone’s problem. It is not something that only arises if you are a utilitarian. In this short article, I will give you my take on the issue.

1. The Puzzle

First, we should set up the puzzle. It goes like this. Compare these two hypothetical populations of people:

Population A: There are 100,000 people. They are all living lives that are extremely joyful — they experience all the great and valuable things that make a life go extremely well. They all have happy, tight-knit families. They are all deeply fulfilled. To put things simply, suppose they each are at welfare level 100.

compared with:

Population Z: There are 1,000,000,000,000,000,000,000 people. But they each live a life that is barely worth living. They are barely happy, barely fulfilled, and experience only the slightest, dullest kinds of pleasure. If things were slightly worse, they would no longer find life worth living. To put things simply, suppose they each are at welfare level 1.

Which population is preferable? If you could choose one of these populations to be the case — if you were about to use your telescope to look at a far-away planet, and told that the population on that planet is A or Z — which would you hope were the case? The answer seems blindingly obvious: you should hope A is the case! It is preferable to Z!

The Repugnant Conclusion is the proposition that Z > A — that Z is preferable to A. Hence, the name: such a proposition is repugnant to our understanding of value.

But here’s the puzzle: there seems to be an incredibly strong argument for the Repugnant Conclusion. It goes like this. Imagine a population, B, that is somewhat similar to A. It has quadruple the population — 400,000 people — and they are all almost as happy and well-off as the people in A. They too are very happy, fulfilled, and experience almost-as-intense pleasures. The average welfare in B is, say, 99.9. Which is preferable: A or B? I think it is pretty plausible that the answer is B. It is worth to take a barely-noticeable hit to well-being, if it means four times as many people are going to be experiencing excellent lives. (As a sort of argument by analogy, consider that it is certainly preferable that 100 kids each get $90 for Christmas, than that a single child get $91.)¹

Ok, so B > A. Alright, but now imagine a population, C, that is pretty similar to B. C has quadruple the population — 1,600,000 people — and they are all almost as happy and well-off as the people in B. They too are very happy, fulfilled, and experience almost-as-intense pleasures. The average welfare in C is, say, 99.89. By the same argument, C > B.

Hopefully you see the problem. We can keep going like this: quadrupling the number of people in the population, and ever-so-slightly reducing the welfare of the people involved. We will have A < B < C < D < E < F < …

Eventually, we will get to Z. But hold on! We said that A > Z! This sequence entails (assuming that ‘>’ is transitive) Z > A! Which just is the Repugnant Conclusion.

Basically, the Repugnant Conclusion follows from two really, really plausible principles:

Trade Small-Quality for Big-Quantity: For any population X, and any natural n and real l, such that X has n people each enjoying welfare level l, there is an all-things-considered better population X* of 4n people each enjoying welfare level (0.999999)l.

Transitivity: For any a, b, c, if a is all-things-considered better than b, and b is all-things-considered better than c, then a is all-things-considered better than c.

You have three options: tell some crazy story as to why Trade Small-Quality for Big-Quantity is false, deny Transitivity (insane!), or accept the Repugnant Conclusion (gross!). There is literally no other option.

2. My Favored Solution

Before I tell you about my favored solution, let me start with a motivating case. Consider someone getting a pinprick: they experience a pin ever-so-slightly prick one of their fingers. The pain is extremely slight: just barely noticeable. But it exists. The world is slightly worse because of it. Now, compare this to someone being horrifically tortured: this person has their eyes bludgeoned as they are put in a freezer to slowly die in intense agony and suffocation (in other words, this person is treated exactly how we treat farmed shrimp).

Okay, clearly the single instance of horrific torture is worse than the single instance of the pinprick. But here’s a question: is there some number n such that, if n people experienced a pinprick, that would be worse than the instance of horrific torture? I think not! I think, no matter how many pinpricks there may be, it would be way way way way worse if there were someone in horrific torture. Or, to elevate the stakes: imagine that there were 1 billion people in horrific torture. Is there some number of pinpricks such that that would ever be worse than 1 billion people in horrific torture? I think you have to be crazy to think so! If I were about to look at a far-away planet, and you told me either n people on the planet just experienced a pinprick, or that 1 billion people on the planet experienced horrific torture, you better bet I am praying that it is the former that obtains.

Okay, what is the relevance of this example? Well, I think the lesson of this example is that some burdens — like pinpricks — have a limit to how much disvalue they contribute to a world. A collection of pinpricks, no matter how many, can only make the world so bad. It can be helpful to think of the aggregate disvalue of pinpricks as having a bound or upper limit.

Roughly, I want to tell a similar story about the Repugnant Conclusion and population Z. I think that there is an upper limit to how good a population of lives barely worth living can be. That upper limit is certainly less than how much goodness is in a population like A.

Of course, this all sounds really nice: but it is not yet a solution until I explain what step in the argument I reject. To be clear, the principle I am rejecting is Trade Small-Quality for Big-Quantity. While B may well be better than A, I do think there is a point in the middle where things are no longer improving. Now, I should stress just how weird and unintuitive this position is. What this means is there is some population, say, K, where there are lots of people living pretty-good lives, and if you were to lower the level of well-being in K by even a little bit (like, 0.0000000000000000000000001%) no matter how many more people you added, that would never be better than K.

To put it in terms of pain: if K is a world where 10000000000 people are experiencing a pain of level p, K is worse than a world where 50 TRILLION TIMES as many people are experiencing a pain that is 99.999999999% as intense as p. That’s pretty nuts!! If the level of pain is only slightly less intense, you presumably shouldn’t allow 50 trillion times as many people to experience pain, even if it is a slightly less intense pain. But that’s what my favored solution entails.

Now, I should very clear on what, exactly, my favored solution entails. My favored solution doesn’t exactly entail that there is some pair of worlds <w1, w2> in the sequence where, no matter how small the difference in intensity between w1 and w2, adding more people to w2 could never outweigh w1. What it entails is that, for any real number d, there has to be a pair of worlds <w1, w2> in the sequence where the difference in intensity between w1 and w2 is d, and no matter how many more people are in w2, w2 could never outweigh w1. That’s still really weird though!

How do I accept this? Well, upon reflection, I have come to think the bullet is not that bad of a bullet to bite (or, in another vocabulary, I have successfully coped).

First, let’s note that these sorts of sequences are trading off between two ethical dimensions of populations — the intensity of pain experienced (“quality”) vs the number of people experiencing it (“quantity”). This language is going to be helpful in eliciting some intuitions.

Now, we said that n pinpricks has an upper limit to how bad it can be — one of its dimensions (quality) is too low, such that it puts a hard ceiling on the total disvalue that can obtain in that world. For ease of exposition, lets slap a number on it and say this limit is -1 million. No matter how many pinpricks there are, they can just never be more disvaluable than -1 million. And lets say 1 billion horrific tortures is -1 billion.

Okay, now let’s consider the sequence again, but this time let’s consider it from both sides. First, let’s start at the world with n pinpricks, and compare it to the worlds that are supposed to be better than it —the ones with less people experiencing slightly more intense pain. Since n pinpricks is ~ -1 million, these worlds with shrinking populations, but slightly more intense pains, must have a disvalue of just under -1 million (e.g., -999k). We can call this portion of the sequence “pinprick-dominated” worlds (worlds that can intuitively be dominated by — be better than — a sufficient number of pinpricks).

Similarly, starting at the world with 1 billion tortures, we can compare it to the worlds that are supposed to be worse than it — the ones with more people experiencing slightly less intense pains. Call this portion of the sequence “torture-dominator” worlds (worlds that can intuitively dominate — be worse than — 1 billion tortures).

So, the allegedly weird thing is that, in the complete sequence, we get a torture-dominator right next to a pinprick-dominated world. But is this actually so weird? Think about a sequence of torture dominators, where you are progressively trading off intensity of pain for number of people in pain. As we increase the number of people, and decrease their pain, it becomes less and less clear (at least, to me) that things are worse than the original 1 billion tortures. If our intuition is that a world of n pinpricks scores so low along the dimension of “intensity of pain” that it has a hard cap on how disvaluable it can be, then, as we progress along the sequence of torture-dominators, where intensity of pain is getting lower and lower, increases in quantity have to continually compensate for this loss in intensity. And there is simply a limit to how much compensatory work quantity can do as you keep losing intensity of pain. Indeed, it’ll have decreasing marginal ability to compensate. Eventually, you get to a world where there are so many people in a decent-level of pain that a further loss in intensity of pain is more damaging (to total disvalue) than a gain in quantity.

There may be another, simpler way to help assuage the weirdness of this solution. Those who accept the Repugnant Conclusion will often point to the fact that humans are infamously insensitive to scope, and that we do not really grasp the difference between big numbers (like 10^27 and 10^234). We just nebulously think of them as both really big. There is an interesting, similar kind of bias, I think, that infects our intuition comparing two side-by-side worlds in the sequence trading off quality for quantity. When we get to a world with (say) hundreds of trillions of people in a decent-level pain, and we are comparing it to a world with (say) thousands of trillions of people in slightly less pain, we don’t quite appreciate how vast of a difference it is for that many people to be in slightly more pain. Sure, each individual difference in pain is slight. But it is still more painful, not less. And it is a lot of people in more pain. It should not be so surprising that, when such large quantities of people are involved, even slight increases in pain intensity mean a whole lot more than we might intuitively expect — this is especially so when we pair it with the fact that most of us find it extremely intuitive that quantity cannot continually compensate for losses in pain intensity. If quantity does have a decreasing ability to compensate for losses in pain intensity, we should not be so surprised to find that it gets to a point where even slight differences in pain intensity mean more than large differences in quantity.

Nevertheless, I still find this quite weird. But that is, unfortunately, true of every solution to this puzzle.²

1. Yes, yes, I know that the analogy with kids elicits intuitions about comparing the two scenarios as though there were 100 kids in both cases. But, try to control for this — it still seems to me as though, if I were to look into a telescope at a far-away planet, I should dearly hope that the planet is such that it has 100 kids gleefully screaming about their 90 dollars, than that the planet be such that it has a single kid gleefully screaming about his 91.

2. On this note, I should say that my current belief is that the second most plausible solution to the Spectrum Argument is to simply accept the Repugnant Conclusion.