Mere addition paradox
The mere addition paradox is a problem in population ethics identified by Derek Parfit and discussed in his book Reasons and Persons. The paradox identifies the mutual incompatibility of four intuitively compelling assertions about the relative value of populations. Parfit’s original formulation of the repugnant conclusion is that "For any perfectly equal population with very high positive welfare, there is a population with very low positive welfare which is better, other things being equal."
The paradox
Parfit considers four populations, as depicted in the following diagram: A, A+, B− and B. Each bar represents a distinct group of people. The bars' width represents group size while the bar's height represents group happiness. Unlike A and B, A+ and B− are complex populations, each comprising two distinct groups of people. It is also stipulated that the lives of the members of each group are good enough that they would rather be alive than not exist.Parfit makes the following three suggestions regarding the value of the populations:
Together, these three comparisons entail that B is better than A. However, Parfit also observes the following:
Thus, there is a paradox. The following intuitively plausible claims are jointly incompatible: that A+ is no worse than A, that B− is better than A+, that B− is as good as B, and that B can be worse than A.
The repugnant conclusion
Parfit argues that this mere addition from A to B can be repeated over and over, eventually resulting in a much larger population Z with only slightly positive welfare. The assessment that such a population Z would be better is what Parfit calls the repugnant conclusion.Responses
Some scholars, such as Larry Temkin and Stuart Rachels, argue that inconsistencies between the four claims rely on the assumption that the "better than" relation is transitive. The inconsistency could then be resolved by rejecting the assumption. According to this view, although A+ is no worse than A, and B− is better than A+, it does not follow that B− is better than A.Another response is the conclusion that total utilitarianism must be rejected in favour of average utilitarianism, which would result in situation A+ being evaluated as worse than A, as the average happiness is lower. According to Parfit, this would however lead to an absurd conclusion, as it implies that adding people with lives worth living would make the world worse simply because they lower the average quality of life.
Torbjörn Tännsjö argues that the intuition that B is worse than A is wrong. While the lives of those in B are worse than those in A, there are more of them, and thus the collective value of B is greater than A. Michael Huemer also argues that the repugnant conclusion is not repugnant.
A number of philosophers have agreed that avoiding the repugnant conclusion is not a necessary criterion for a satisfactory theory of population ethics.
Other philosophers suggested that a universal theory of ethics may not exist. Gustaf Arrhenius proved that a theory of population ethics cannot simultaneously satisfy a number of plausible axioms.