Mere addition paradox

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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.

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[edit] The Paradox

The paradox arises from consideration of four different possibilities. The following diagrams show different situations, with each bar representing a population. The group's size represented by column width, and the group's happiness represented by column height. For simplicity, in each group of people represented, everyone in the group has exactly the same level of happiness, though Parfit did not consider this essential to the argument.

In situation A, everyone is happy.

In situation A+, there are the extra people. There is the same population as in A, and another population of the same size, 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. Parfit gives the example of a possible state of the world before the Atlantic was crossed, and says that Situation A, in that case, represents a state of the world in which the Americas were unpopulated.

In situation B-, there are again two separate populations, of the same size as before, but now of equal happiness. The increase in happiness of the right-hand population is greater than the decrease in happiness of the left-hand population.

Finally in situation B, there is a single population whose size is the sum of the two populations in situation B-, and at the same level of happiness.

[edit] Going from A to B

The difference between the situations A and A+ is only in the existence of extra people at a lower level of happiness. If the two populations were known to each other, and were aware of the inequality, this would arguably constitute social injustice. However as they do not, Parfit says this represents a Mere Addition, and it seems implausible to him that it would be worse for the extra people to exist. Thus A+ is not worse than A.

Furthermore there are the same numbers of people on both sides of the divide in situation B- as there are in situation A+. The average happiness in B- is higher than A+ (though 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, B- is better than A+. But the situations B- and B are the same, except the communication gap is removed. It seems that B is at least as good as B-.

[edit] The Repugnant Conclusion

We can then repeat the argument, and imagine another divide, and ask if it would be better for more extra people to exist, unknown to the people in B, and so on, as before. We then arrive at a situation C, in which the population is even larger, and less happy, though still with lives worth living. And if we agree that B is not worse than A, then we would conclude in the same fashion that C is not worse than B. But then we could repeat that argument again, finally arriving at a situation Z, in which there are an enourmous number of people whose lives are worth living, but only just barely. Parfit calls this the Repugnant Conclusion, and says that Z is in fact worse than A, and that it goes against what we believe about overpopulation to say otherwise. This is a contradiction, but it is not clear how to avoid it.

[edit] Objections and resolutions of the paradox

The paradox can be defeated by asserting that A+ is actually worse than A, in other words, that adding people of less-than-average happiness into the world makes the overall situation worse. For example one branch of utilitarianism aims at maximizing average happiness, and so this assertion would follow. However, this assertion 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 position 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."

Parfit also considers an objection where the comparison between A+ and B- is attacked. The comparison between A and A+ was partly dependent on their separation. Thus A+ and B- might simply be incomparable. Parfit gives the Rich and Poor example, in which two people live in separate societies, and are unknown to each other, but are both known to you, and you have to make a choice between helping one or the other. Thus, despite their separation, it is meaningful to ask whether A+ is better than B- or not. One could deny that B- is better than A+, and therefore neither is B. But this rejection implies that what is most important is the happiness of the happiest people, and commits one to the view that a smaller increase in the happiness of the happiest people outweighs a bigger decrease in the happiness of less happy people. Parfit calls this the Elitist view.

Temkin has taken the approach of resolving the paradox by arguing for the intransitivity of the "better than" relation, and even the "all things considered better than" relation. That is, it is entirely possible that indeed, at the same time, B is, all things considered, better than A+, which is, all things considered, better than A, which is, all things considered, better than B.

Of course one can simply accept the Repugnant Conclusion. Torbjörn Tännsjö argues that we have a false intuition of the moral weight of billions upon billions of lives "barely worth living". He argues that we must consider that life in Z would not be terrible, and that in our actual world, most lives are actually not far above, and often fall below the level of "not worth living". Therefore the Repugnant Conclusion really isn't so repugnant.

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