One attempt at an objective theory of ethics is utilitarianism, where good is defined as leading to greater happiness for all people considered equally. I'm sympathetic to the idea of objective ethics, and see no other way to make sense of progressive moral intuitions. Some complain that ethics must always be subjective, others quibble with the concepts of happiness or wellbeing. The Repugnant Conclusion paradox critiques the idea that we can collectivize the happiness metric at all. What do we mean when we try to add up happiness over a large number of people?
The paradox proceeds in two steps. Start with a population A, where everybody is very happy. Step 1 is to compare them to population B which has the same number of very happy people, plus the same number again of barely happy people. The argument states that B is "no worse" than A because B starts the same as A and adds more people, and despite being barely happy those people are happier alive than non-existent. Step 2 is to compare B to population C which has the same number of people as B but all of them pretty happy. "Pretty happy" is less happy than "very happy" but much happier than "barely happy". Now we conclude that C is better than B because people are on average and in total more happy in C than they are in B. By transitivity we are forced to agree that C is better than A -- that a population where everyone is very happy is worse than one where they are merely pretty happy, only because the latter has more people.
Hopefully it's easy to see that the conclusion is wrong. If it's not obvious yet the argument can be applied again on population C, resulting in a population E that 's more populous and less happy than C, that we also conclude is better. Taken to the limit we have population Omega consisting of nearly infinite population living at the minimum possible happiness, and conclude this is the best possible outcome. That would be horrible -- i.e. the Repugnant Conclusion.
It's fortunately also easy to see where the argument breaks down. Step 2 is quite plausible. A change in society that makes some people less happy but greatly increases the happiness of others is arguably an ethical change. Some will be displeased but overall the society will be better. Step 1 is where the problem lies. Population B is supposedly "no worse" than population A, but no -- it's definitely worse. We can see that it's worse by looking at how people really judge the quality of a population.
Imagine that you needed to emigrate to one of two countries. You know nothing about them except that the population of country A is 1 million, and every one of them is very happy. You also know that the population of B is 2 million, and half of them are very happy and half of them are barely happy. Which country would you pick? Of course you want to pick the country where everyone is happy. It seems likely that if you went there you'd be very happy too, while if you went to country B you might end up being only barely happy. Obviously A is the more appealing outcome. There's something about country B that makes it less likely for its citizens to be happy.
As a second example imagine you work in public health. City A has a population of 100,000 and no one has any chronic health concern. City B has 200,000 people and half of them have some low-level of arsenic in their systems. Which city are you more concerned about? Obviously city B. Despite the fact that both cities have the same number of perfectly healthy people, that does not mean they are the same. There's something in city B that is exposing its citizens to toxins.
We can go the other direction too, and often do. If we split the USA into male and female sub-populations we see that the female population has zero propensity to stockpile military weapons. The male half, however, does have this pathology. Should we be cheered that we're "no worse" than a gunless country half our size? Of course not, that would be silly. And yet that's what this argument hinges on.
So we see that total number of people is almost entirely irrelevant for how we actually evaluate populations as a whole. For measures like happiness, health, and wellbeing the statistics of the population -- the average, the mean, the standard deviation -- are much more meaningful than the sum. Even for measures that can be meaningfully aggregated, like wealth, the statistics of the distribution are still probably more interesting. With this in mind the paradox is easy to solve. Step 1 makes average happiness go way down, and then step 2 brings the average back up but not as high as before. Overall the transformation makes the situation worse overall, so C is worse than A. This is what our intuition tells us, so the paradox -- which was all based on intuition anyway -- is resolved.
Does this help us understand how to make utilitarian ethics work? Only a little. After all, making ethical decisions regarding diverse populations where everyone has human rights and a need for justice is going to take more than averaging a single self-reported number. But it might be a place to start.