The Mere Addition Paradox

In this post, I formulate the Mere Addition Paradox, a paradox in so-called "population ethics". I would like to know what others think of the paradox.

Consider the following three possible populations:
Population A: A population of 10,000 people each of whose level of well-being is +100,000
Population A+: A population of 20,000 people, 10,000 of whom have a level of well-being of
+100,000 and the other 10,000 of whom have a level of well-being of +90,000
Population B: A population of 20,000 people each of whose level of well-being is +95,000
(I should explain what I mean by "well-being" here. The well-being of an individual is simply how well things go for that individual. The well-being of one individual is greater than the well-being of another individual just in case things go better for the first individual than they do for the second individual.)

There are then two versions of the Mere Addition Paradox:

Mere Addition Paradox (Version 1)
1. The existence of Population A+ is better than the existence of Population A.
2. The existence of Population B is better than the existence of Population A+.
3. If (1) and (2), then the existence of Population B is better than the existence of Population A.
4. Therefore, the existence of Population B is better than the existence of Population A.

Mere Addition Paradox (Version 2)
1*. The existence of Population A+ is just as good as the existence of Population A.
2. The existence of Population B is better than the existence of Population A+.
3*. If (1) and (2), then the existence of Population B is better than the existence of Population A.
4. Therefore, the existence of Population B is better than the existence of Population A.

Premise (3) is justified by appeal to the transitivity of being better than: For all x, y, and z, if x is better than y and y is better than z, then x is better than z. Premise (3*) is justified by appeal to the slightly different principle that for all x, y, and z, if x is just as good as y and z is better than y, then z is better than x. On the assumption that both of these principles are true, the two versions of the Mere Addition Paradox show that whether we accept premise (1) or premise (1*), so long as we accept premise (2) we get the conclusion that the existence of Population B is better than the existence of Population A.

I have already stated why one might accept premises (3) and (3*). Why might one accept premises (1), (1*), and (2)?

Let's begin with (2). The reasoning for two goes as follows: The existence of Population B is better than the existence of Population A+ because the average level of well-being does not differ between the two populations and Population B is more equitable than Population A+. Assuming that equality is a good-making feature of a population, then, the existence of Population B is better than the existence of Population A+.

What about premises (1) and (1*)? Few have attempted to argue for one of these over the other, preferring to argue instead for disjunction. But arguing for their disjunction is good enough, since which of the disjuncts is true doesn't matter for the success of the argument. If (1) and (2) are true, then (given (3)), the conclusion follows and if (1*) and (2) are true, then (given (3*)), the conclusion follows. So, why believe the disjunction of premises (1) and (1*)? Well, it seems that merely adding some people with high well-being to a population each of whose members has even higher well-being can't make the existence of the resultant population worse than the existence of the original. After all, presumably the existence of people with high well-being is a good thing and so cannot detract from an already good thing. Thus, either the existence of Population A+ is better than the existence of Population A or the existence of Population A+ is just as good as the existence of Population A.

Let me end by saying why the Mere Addition Paradox is supposed to be paradoxical. Consider Population B+, a population of 40,000, 20,000 of whom have a level of well-being +95,000 and 20,000 of whom have a level of well-being of +85,000. By reasoning similar to the reasoning in favor of the disjunction of premises (1) and (1*), the existence of Population B+ is either better than or just as good as the existence of Population B. But then, by reasoning similar to the reasoning in favor of premise (2), the existence of Population C (a population of 40,000 people each of whose level of well-being is +90,000) is better than the existence of Population B+. So, by reasoning similar to the reasoning in favor of premises (3) and (3*), the existence of Population C is better than the existence of Population B and hence, since the existence of Population is better than the existence of Population A, the existence of Population C is better than the existence of Population A. By repeated applications of the same sort of argument, then, we reach the conclusion (sometimes called "The Repugnant Conclusion") that the existence of a large population each of whose members has the same very low positive level of well-being is better than the existence of Population A.

So, what do you all think of this paradox? What should one say to the arguments? Should one accept that the existence of a very large population each of whose members has a very low positive level of well-being (described by some as having a life barely worth living) is better than the existence of a smaller population each of whose members has a very high level of well-being? If not, what should one say against the reasoning in favor of that conclusion?

[I should note before closing that the premises and conclusion of the arguments should probably include ceteris paribus clauses. That is, we are wondering about whether the existence of Population B is better than the existence of Population A assuming that the only relevant difference between the two populations is how many people they contain and the level of well-being each person has. I should also note that if you want to find out more about the Mere Addition Paradox and potential solutions to it, you should look at the SEP's entry entitled "The Repugnant Conclusion": http://plato.stanford.edu/entries/repugnant-conclusion/]