Trade-Off Between Repugnant and Sadistic Conclusions Under the Separability of People’s Lives

Abstract

Population axiology includes two major arguments. The first is the repugnant conclusion, which was originally formulated by Derek Parfit to criticize total utilitarianism. The second is the sadistic conclusion. In this study, I demonstrate that no additively separable principle can avoid both repugnant and sadistic conclusions if individual moral values have no upper bound. This impossibility holds not only for utilitarian principles but also for any population principles that guarantee the separability of people’s well-being. I emphasize the importance of examining non-separable principles in population ethics.

Appendix

As mentioned earlier, our impossibility result does not rely on the minimal one-person trade-off. In this section, I illustrate that this is related to the definition of the repugnant conclusion. Blackorby et al., (2005; hereafter BBD) use the following version of the repugnant conclusion; see also Bossert, Cato, and Kamaga (2022, 2023) for the application of this version.

BBD’s repugnant conclusion: For all natural numbers $n$, a positive number $\zeta >0$, and a positive number $\varepsilon >0$ smaller than $\zeta$, there exists a natural number $m$ larger than $n$ such that the $m$-individual distribution where all the people obtain $\varepsilon$ is morally better than the $n$-individual distribution where all the people obtain $\zeta$.

First, this BBD version focuses on distributions where all individuals obtain the same well-being level. By contrast, a “population of at least ten billion people” (1984, p. 388) does not have to be egalitarian. Second, more importantly, unlike Parfit’s version, $n$ does not have to be at least ten billion. Note that the $n$-individual distribution where all the people obtain $\zeta$ corresponds to “population of at least ten billion people, all with a very high quality of life” (Parfit, 1984, p. 388).

The BBD version of the avoidance of repugnant conclusion becomes the following (Blackorby et al., 2005, p. 162):

BBD’s avoidance of repugnant conclusion: There exist a natural number $n$, a positive number $\zeta >0$, and a positive number $\varepsilon >0$ smaller than $\zeta$ such that, for all natural numbers $m$ larger than $n$, the $m$-individual distribution where all the people obtain $\varepsilon$ is not morally better than the $n$-individual distribution where all the people obtain $\zeta$.

If we use this version in the main theorem with additive separability, the minimal one-person trade-off needs to be added. To observe this point, let us consider the following principle:

For any two distributions, ${(u}_{1},...,{u}_{n})$ and ${(v}_{1},...,{v}_{m})$,

• (i) if $n=m=1$, the one with a higher utility level is morally better than the other (with a lower utility level);

• (ii) if $n=1$ and $m\ne 1$, ${u}_{1}$ is morally better than ${(v}_{1},...,{v}_{m})$;

• (iii) if $n\ne 1$ and $m= 1$, ${v}_{1}$ is morally better than ${(u}_{1},...,{u}_{n})$;

• (iv) if $n\ne 1$ and $m\ne 1$, ${(u}_{1},...,{u}_{n})$ is morally better than ${(v}_{1},...,{v}_{m})$ if and only if ${\sum }_{i=1}^{n}g({u}_{i})>{\sum }_{i=1}^{m}g({v}_{i})$, where $g$ is an increasing and concave function with no upper bound and $g\left(0\right)=0$.

This principle appears artificial but satisfies additive separability and the no-bliss-point of the moral value axiom, and avoids both BBD’s repugnant and sadistic conclusions. Notably, this does not avoid Parfit’s version of the repugnant conclusion. The argument in this section illustrates that the formulation of the repugnant conclusion can matter.