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Mere addition paradox

The Mere Addition Paradox is a problem in ethics, due to Derek Parfit, and first appearing in his book, Reasons and Persons.

The paradox

The paradox appears to show that it is better to have a large population, where everyone has a life that is just barely worth living, than a small population where everyone is very happy.

The paradox arises from consideration of 3 different possibilities. The following diagrams show different populations, with population size on the x-axis, and the happiness of each individual on the y-axis.

A A Plus B

In population A, everyone is very happy.

Population A Plus consists of 2 groups - the same group as in A has had added to it a group that is moderately happy. As this is a mere addition of reasonably happy people, Parfit argues that it is no worse than the state of affairs in A.

Population B is the same size as population A Plus, but the average happiness is higher than A Plus, though slightly lower than in A. Since the average happiness is higher than in A Plus, Parfit argues that the state of affairs in B is no worse than that of A Plus, and therefore, no worse than that of A.

The paradox comes because this argument is repeatable until we reach something like Z, a huge population of people whose lives are only just worth living (on these graphs, negative values would indicate lives not worth living).

Z

Thus, the state of affairs in Z is no worse than the state of affairs in A. Parfit calls this the Repugnant Conclusion, and rejects it, but says he does not have a solution.

Objections

Some say that this paradox can be defeated by simply denying its first axiom: that adding people of less-than-average happiness into the world doesn't make the overall situation worse. This is by no means universally accepted, and there is a branch of utilitarianism that aims at maximising the average happiness. However, this position does involve the claim that it is actually bad for people of less-than-average happiness to be born, even if their lives are worth living.

Alternatively, one could deny that the redistribution of happiness in the move from A Plus to B makes things better. One could claim instead that A Plus is better than B. However, this would seem to involve the claim that what is most important is the happiness of the happiest people, and a small increase in that is worth a (bigger) decrease in the happiness of less happy people.