Mere addition paradox
The mere addition paradox is a problem in ethics, identified by Derek Parfit, and appearing in his book, Reasons and Persons. The paradox identifies apparent inconsistency between three seemingly true beliefs about population ethics.
The Paradox
The paradox arises from consideration of three different possibilities. The following diagrams show different populations, with population size represented by column width, and the population's happiness represented by column height. Note that for each group of people represented, everyone in the group has exactly the same level of happiness.
| File:Mere Addition A.png | File:Mere Addition A Plus.png | File:Mere Addition B.png |
| A | A+ | B |
|---|---|---|
In population A, everyone is very happy.
Population A+ consists of 2 groups - the same group as in A, and another population which is less happy, but whose lives are nevertheless worth living. The two populations are entirely separate, that is, they cannot communicate and are not even aware of each other. As this is a mere addition of people with lives worth living, it seems that, all things considered:
1) A+ is not worse than A.
Population B is the same size as population A+, and its average happiness is higher than A+, though slightly lower than A. Since A+ and B have the same number of people and because there is a greater level of equality and average happiness in B, it seems that, all things considered:
2) B is better than A+.
Finally, Parfit argues that, all things considered:
3) B is worse than A.
The argument for (3) is as follows: If B is better than A, then seemingly a larger population, C, standing in the same relation to B as B does to A, would be better still. Population D, twice as large and with a somewhat lower level of happiness would then be better than C, and so on, until reaching the Repugnant Conclusion that the best outcome is Z, an enormous population with all members having lives barely worth living. Claim (3) follows if we reject the Repugnant Conclusion and hold that Z is worse than A.
A paradox results. (1), (2), and (3) each seem true. However, it seems that all three claims cannot be true. For instance, (1) and (2) imply that B is not worse than A. But this conflicts with (3), which states that B is worse than A.
| File:Mere Addition Z.png |
| Z |
|---|
Objections and resolutions of the paradox
Some argue that the paradox can be defeated by denying claim (1), that adding people of less-than-average happiness into the world does not make the overall situation worse. Claim (1) is not universally accepted; for example one branch of utilitarianism aims at maximizing average happiness. However, rejecting claim (1) commits one to the position that it is actually bad for people of less-than-average happiness to be born, even if their lives are worth living. A more sophisticated rejection of claim (1) might argue for some threshold above the level at which lives become worth living but below which additional lives would nonetheless make the situation worse. Parfit argues that for this position to be plausible, such a threshold would be so low as to apply only to lives that are "gravely deficient" and which, "though worth living ... must be crimped and mean." Parfit calls this hypothetical threshold the "bad level," and argues that its existence would not resolve the paradox because population A would still be better than an enormous population with all members having lives at the "bad level."
Alternatively, one could attempt to resolve the paradox by rejecting claim (2), that B is better than A+. However, rejecting claim (2) implies that what is most important is the happiness of the happiest people, and commits one to the view that a small increase in the happiness of the happiest people outweighs a (bigger) decrease in the happiness of less happy people.
Some have rejected the conclusion in claim (3) by arguing that Z may not be worse than A, because we can not rely on our intuition as a sound picture of the moral weight of billions upon billions of lives "barely worth living". Reversing the reasoning for (3) one can discover that the best choice is a single person with enormous happiness. Some also argue that we must consider that life in Z would not be terrible, but perhaps not much different from a normal privileged one and therefore the repugnancy of Z is not established.
Some have taken the approach of denying the paradox altogether by arguing for the intransitivity of the "better than" relation.
It has also been observed[who?] that nowhere in Parfit's many works on this subject does he explain why doubling the size of the population is guaranteed to always produce a population where each person has a level of happiness at least half that of the original population. It is easy to defend this assumption in the limit that there are very few people with many times the resources or wealth that they need (or, perhaps, even want). Doubling the population in this case won't materially affect the happiness of the original population much at all, and all the individuals in the new population will therefore be almost as happy as individuals in the original. However in the limit of very large populations this is no longer so obvious. A pertinent example being a population having just enough food to survive. Doubling this population and sharing out resources equally would mean that everyone would starve. Surely each individual's happiness would then be less than half that of the well-fed people in the original population. With this unwritten assumption removed the Mere Addition Paradox ceases to exist, and the common sense notion that there is some happy compromise of a finite population which maximises the total happiness returns.