This is not the post I was planning to write. Originally, it was going to be a heroic post where I showed my devotion to philosophical principles by reluctantly but fearlessly biting the bullet on the sadistic conclusion. Except... it turns out to be nothing like that, because the sadistic conclusion is practically void of content and embracing it is trivial.

Sadism versus repugnance

The sadistic conclusion can be found in Gustaf Arrhenius's papers such as "An Impossibility Theorem for Welfarist Axiologies." In it he demonstrated that - modulo a few technical assumptions - any system of population ethics has to embrace either the Repugnant Conclusion, the Anti-Egalitarian Conclusion or the Sadistic conclusion. Astute readers of my blog posts may have noticed I'm not the repugnant conclusion's greatest fan, evah! The anti-egalitarian conclusion claims that you can make things better by keeping total happiness/welfare/preference satisfaction constant but redistributing it in a more unequal way. Few systems of ethics embrace this in theory (though many social systems seem to embrace it in practice).

Remains the sadistic conclusion. A population ethics that accepts this is one where it is sometimes better to create someone whose life is not worth living (call them a "victim"), rather a group of people whose lives are worth living. It seems well named - can you not feel the top hatted villain twirl his moustache as he gleefully creates lives condemned to pain and misery, laughing manically as he prevents the intrepid heroes from changing the settings on his incubator machine to "worth living"? How could that sadist be in the right, according to any decent system of ethics?

Remove the connotations, then the argument

But the argument is flawed, for two main reasons: one that strikes at the connotations of "sadistic", the other at the heart of the comparison itself.

The reason the sadistic aspect is a misnomer is that creating a victim is not actually a positive development. Almost all ethical systems would advocate improving the victim's life, if at all possible (or ending it, if appropriate). Indeed some ethical systems which have the "sadistic conclusion" (such as prioritarianism or egalitarianism) would think it more important to improve the victim's life that some ethical systems that don't have the conclusion (such as total utilitarianism). Only if such help is somehow impossible do you get the conclusion. So it's not a gleeful sadist inflicting pain, but a reluctant acceptance that "if universe conspires to prevent us from helping this victim, then it still may be worth creating them as the least bad option" (see for instance this comment).

"The least bad option." For the sadistic conclusion is based on a trick, contrasting two bad options and making them seem related (see this comment). Consider for example whether it is good to create a large permanent underclass of people with much more limited and miserable lives than all others - but whose lives are nevertheless just above some complicated line of "worth living". You may or may not agree that this is bad, but many people and many systems of population ethics do feel it's a negative outcome.

Then, given that this underclass is a bad outcome (and given a few assumptions as to how outcomes are ranked) then we can find other bad outcomes that are not quite as bad as this one. Such as... a single victim, a tiny bit below the line of "worth living". So the sadistic conclusion is not saying anything about the happiness level of a single created population. It's simply saying that sometime (A) creating underclasses with slightly worthwhile lives can sometimes be bad, while (B) creating a victim can sometimes be less bad. But the victim isn't playing a useful role here: they're just an example of a bad outcome better than (A), only linked to (A) through superficial similarity and rhetoric.

For most systems of population ethics the sadistic conclusion can thus be reduced to "creating underclasses with slightly worthwhile lives can sometimes be bad." But this is the very point that population ethicists are disputing each other about! Wrapping that central point into a misleading "sadistic conclusion" is... well, the term "misleading" gave it away.

Consider the following facts:

1. For any population of people of happiness h, you can add more people of happiness less than h, and still improve things.
2. For any population of people, you can spread people's happiness in a more egalitarian way, while keeping the same average happiness, and this makes things no worse.

This sounds a lot like the mere addition paradox, illustrated by the following diagram:

This is seems to lead directly to the repugnant conclusion - that there is a huge population of people who's lives are barely worth living, but that this outcome is better because of the large number of them (in practice this conclusion may have a little less bite than feared, at least for non-total utilitarians).

But that conclusion doesn't follow at all! Consider the following aggregation formula, where au is the average utility of the population and n is the total number of people in the population:

au(1-(1/2)ⁿ)

This obeys the two properties above, and yet does not lead to a repugnant conclusion. How so? Well, property 2 is immediate - since only the average utility appears, the reallocating utility in a more egalitarian way does not decrease the aggregation. For property 1, define f(n)=1-(1/2)ⁿ. This function f is strictly increasing, so if we add more members of the population, the product goes up - this allows us to diminish the average utility slightly (by decreasing the utility of the people we've added, say), and still end up with a higher aggregation.

How do we know that there is no repugnant conclusion? Well, f(n) is bounded above by 1. So let au and n be the average utility and size of a given population, and au' and n' those of a population better than this one. Hence au(f(n)) < au'(f(n')) < au'. So the average utility can never sink below au(f(n)): the average utility is bounded.

So some weaker versions of the mere addition argument do not imply the repugnant conclusion.

I want to thank Irgy for this idea.

As people generally know, total utilitarianism leads to the repugnant conclusion - the idea that no matter how great a universe X would be, filled without trillions of ultimately happy people having ultimately meaningful lives filled with adventure and joy, there is another universe Y which is better - and that is filled with nothing but dull, boring people whose quasi-empty and repetitive lives are just one tiny iota above being too miserable to endure. But since the second universe is much bigger than the first, it comes out on top. Not only in that if we had Y it would be immoral to move to X (which is perfectly respectable, as doing so might involve killing a lot of people, or at least allowing a lot of people to die). But in that, if we planned for our future world now, we would desperately want to bring Y into existence rather than X - and could run great costs or great risks to do so. And if we were in world X, we must at all costs move to Y, making all current people much more miserable as we do so.

The repugnant conclusion is the main reason I reject total utilitarianism (the other one being that total utilitarianism sees no problem with painlessly killing someone by surprise, as long as you also gave birth to someone else of equal happiness). But the repugnant conclusion can emerge from many other population ethics as well. If adding more people of slightly less happiness than the average is always a bonus ("mere addition"), and if equalising happiness is never a penalty, then you get the repugnant conclusion (caveat: there are some subtleties to do with infinite series).

But repugnant conclusions reached in that way may not be so repugnant, in practice. Let S be a system of population ethics that accepts the repugnant conclusion, due to the argument above. S may indeed conclude that the big world Y is better than the super-human world X. But S need not conclude that Y is the best world we can build, given any fixed and finite amount of resources. Total utilitarianism is indifferent to having a world with half the population and twice the happiness. But S need to be indifferent to that - it may much prefer the twice-happiness world. Instead of the world Y, it may prefer to reallocate resources to instead achieve the world X', which has the same average happiness as X but is slightly larger.

Of course, since it accepts the repugnant conclusion, there will be a barely-worth-living world Y' which it prefers to X'. But then it might prefer reallocating the resources of Y' to the happy world X'', and so on.

This is not an argument for efficiency of resource allocation: even if it's four times as hard to get people twice as happy, S can still want to do so. You can accept the repugnant conclusion and still want to reallocate any fixed amount of resources towards low population and extreme happiness.

It's always best to have some examples, so here is one: an S whose value is the product of average agent happiness times the logarithm of population size.

Related: Taking ideas seriously

Let us say hypothetically you care about stopping people smoking. 

You were going to donate $1000 dollars to givewell to save a life, instead you learn about an anti-tobacco campaign that is better. So you chose to donate $1000 dollars to a campaign to stop people smoking instead of donating it to a givewell charity to save an African's life. You justify this by expecting more people to live due to having stopped smoking (this probably isn't true, but for the sake of argument)

The consequences of donating to the anti-smoking campaign is that 1 person dies in africa and 20 live that would have died instead live all over the world. 

Now you also have the choice of setting fire to many tobacco plantations, you estimate that the increased cost of cigarettes would save 20 lives but it will kill likely 1 guard worker. You are very intelligent so you think you can get away with it. There are no consequences to this action. You don't care much about the scorched earth or loss of profits.

If there are causes with payoff matrices like this, then it seems like a real world instance of the trolley problem. We are willing to cause loss of life due to inaction to achieve our goals but not cause loss of life due to action.

What should you do?

Killing someone is generally wrong but you are causing the death of someone in both cases. You either need to justify that leaving someone to die is ethically not the same as killing someone, or inure yourself that when you chose to spend $1000 dollars in a way that doesn't save a life, you are killing. Or ignore the whole thing.

This just puts me off being utilitarian to be honest.

Edit: To clarify, I am an easy going person, I don't like making life and death decisions. I would rather live and laugh, without worrying about things too much.

This confluence of ideas made me realise that we are making life and death decisions every time we spend $1000 dollars. I'm not sure where I will go from here.