Mere addition paradox

The mere addition paradox, also known as the repugnant conclusion, is a problem in ethics, identified by Derek Parfit, and appearing in his book Reasons and Persons (1984). The paradox identifies an inconsistency between four seemingly true beliefs about the relative value of populations.

Consider the four populations depicted in the following diagram: A, A+, B− and B. Each bar, within a population, represents a distinct group of people, whose size is represented by the bar's width and whose happiness is represented by the bar's height. Unlike A and B, A+ and B− are thus complex populations, each comprising two distinct groups of people. (For simplicity, we might imagine that everyone in a group has exactly the same level of happiness, although this is not essential to the argument. We might instead imagine that the height of a bar represents the average happiness within that group of people.)

How do these four populations compare in value? Let's start by making comparisons between pairs of populations.

First, it seems that A+ is no worse than A. This is because the people in A are no worse off in A+, while the additional people who exist in A+ are better off in A+ compared to A. (Arguably, existence is good for these additional people, assuming that they have lives which are worth living and preferable over non-existence.)

Second, it seems that B− is better than A+. This is because B− has greater total and average happiness than A+.

Finally, B seems equally as good as B− as the only difference between B− and B is that the two groups in B− are merged to form one group in B.

Put together, these three comparisons entail that B is better than A. (If y is no worse than z and x is better than y it follows that x is better than z.) However, when we directly compare A and B, it may seem that B is in fact worse than A.

Thus, we have a paradox—the mere addition paradox—because the following intuitively plausible claims are jointly inconsistent: (a) that A+ is no worse than A, (b) that B− is better than A+, (c) that B− is equally as good as B, and (d) that B is worse than A.

Some scholars, such as Larry Temkin and Stuart Rachels, argue that the apparent inconsistency between the four claims just outlined relies on the assumption that the "better than" relation is transitive. We may resolve the inconsistency, thus, by rejecting the assumption. On this view, from the fact that A+ is no worse than A and that B− is better than A+ it simply does not follow that B− is better than A.

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