The population ethics literature has long focused on attempts to avoid the repugnant conclusion. We show that a large set of social orderings that are conventionally understood to escape the repugnant conclusion do not in fact avoid it in all instances. As we demonstrate, prior results depend on formal definitions of the repugnant conclusion that exclude some repugnant cases, for reasons inessential to any “repugnance” (or other meaningful normative properties) of the repugnant conclusion. In particular, the literature traditionally formalizes the repugnant conclusion to exclude cases that include an unaffected sub-population. We relax this normatively irrelevant exclusion, and others. Using several more inclusive formalizations of the repugnant conclusion, we then prove that any plausible social ordering implies some instance of the repugnant conclusion. This understanding—that it is impossible to avoid all instances of the repugnant conclusion—is broader than the traditional understanding in the literature that the repugnant conclusion can only be escaped at unappealing theoretical costs. Therefore, the repugnant conclusion provides no methodological guidance for theory or policy-making, because it does not discriminate among candidate social orderings. So escaping the repugnant conclusion should not be a core goal of the population ethics literature.
For example, the Stanford Encyclopedia of Philosophy entry on the repugnant conclusion ends its introductory paragraph with “Thus, the question as to how the Repugnant Conclusion should be dealt with and, more generally, what it shows about the nature of ethics has turned the conclusion into one of the cardinal challenges of modern ethics” (Arrhenius et al. 2017).
For example, Ng (1989) proves that any plausible social ordering must either imply the repugnant conclusion or violate one of two other conditions called Non-Antiegalitarianism and Mere Addition. Similarly, Asheim and Zuber (2014) prove that a family of social orderings “either leads to the Weak Repugnant Conclusion or violates the Weak Non-Sadism Condition.” Other important recent examples are the core contributions of Arrhenius (Population ethics: the challege of future generations (unpublished)) and Bossert (2017) and results in McCarthy et al. (2020).
Although without the same formalization, emphasis, or scope as our paper, prior arguments in this direction have been made in the philosophy literature by Anglin (1977) and Cowen (1996).
In the philosophical literature, for example, Temkin Larry (2014) considers denial of the transitive part of Axiom 1, Roberts (2011) denies Axiom 2, and Carlson (On some impossibility theorems in population ethics (forthcoming)) denies Axiom 3. Such issues are a focus of a companion working paper in the philosophy literature (Budolfson and Spears 2018), which does not contain the formal results of this paper.
Blackorby et al. (1995) use this observation to motivate an additively separable approach to population ethics, on the grounds that the utilities of past people should not influence the evaluation of policies that only impact future people; although our results include non-separable social orderings such as average utilitarianism, we further discuss separability in Sect. 4.3.
Arrhenius (Population ethics: the challege of future generations (unpublished)) uses an equivalent condition called the Strong Quality Addition Principle; Anglin (1977) shows that this principle is implied by both total and average utilitarianism, and Arrhenius extends this proof to Ng’s (1989) variable-value utilitarianism. Note that our theorem below uses a different condition, the unrestricted very repugnant conclusion.
The existence independence axiom holds that for all \(\mathbf {u},\mathbf {v}, \mathbf {w}\in \Omega\), \(\left( \mathbf {u},\mathbf {w}\right) \succsim \left( \mathbf {v},\mathbf {w}\right)\) if and only if \(\mathbf {u}\succsim \mathbf {v}\) (Blackorby et al. 1995, p. 159).
To see this, consider a case where \(\varepsilon = 10^{-6}\), \(n^\varepsilon = 10,000\), \(u^h = 9\), \(n^h = 10\), and \(\mathbf {v}\) is 10 lives at -10 (for simplicity, let \(n^\ell = 0\)). Average utilitarianism would choose the \(\varepsilon\) lives and total utilitarianism would choose the \(u^h\) lives. If \(\varepsilon = 0\), which would only increase any normative repugnance of such choice, average utilitarianism would continue to choose the \(\varepsilon\) lives as \(n^\varepsilon\) becomes ever larger, but total utilitarianism would continue to choose the \(u^h\) lives.
Further examples include (Palivos and Yip 1993; Dasgupta 2005; Boucekkine and Fabbri 2013; Spears 2017; Scovronick et al. 2017), and Lawson and Spears (2018).
In this paper we distinguish between prioritarianism and egalitarianism using the definitions of Broome (2015). Both functional forms use concave g transformations and same-number risk-free additive separability, but the prioritarian social welfare function is additively separable, while egalitarianism follows (Fleurbaey 2010) in inverting g to use the EDE, so average egalitarianism is \(W^{AE}(\mathbf {u})=g^{-1}\left( \frac{1}{n(\mathbf {u})}\sum _{i = 1}^{n(\mathbf {u})}g(u_i)\right)\) and total egalitarianism is \(W^{TE}(\mathbf {u})= n(\mathbf {u}) g^{-1}\left( \frac{1}{n(\mathbf {u})}\sum _{i = 1}^{n(\mathbf {u})}g(u_i)\right)\). Total prioritarianism satisfies mere addition but total egalitarianism does not; both satisfy the conditions of the Theorem and therefore imply the very repugnant conclusion. Nothing hinges on our use of this terminology from the literature, however.
Broome (2004) advances a case for CLGU which he “standardizes” by setting the critical level equal to zero, adjusting g to match. (In this case, zero may or may not be a neutral life for the person.) Broome interprets his resulting social ordering to imply the repugnant conclusion, which he argues is unintuitive but ultimately acceptable. What Broome there calls “the repugnant conclusion,” Arrhenius (Population ethics: the challege of future generations (unpublished)) names “the weak repugnant conclusion,” a further example of simultaneous debate in the prior literate about the extent and acceptability of the repugnant conclusion.
To see this, for RDGU, choose y that is very close to x, let \(n=1\) and let \(m>1\). For CLGU let \(c> x> y > 0\) and n be much larger than m (a violation for CLGU of our Axiom 5).
Fleurbaey and Tungodden (2010) prove the incompatibility of their similar Minimal Aggregation and Minimal Non-Aggregation axioms. As the names suggest, their Minimal Aggregation axiom is weaker than our Aggregation axiom. Yet, their Minimal Aggregation and Minimal Non-Aggregation only conflict in the presence of their Reinforcement axiom, which they call a “basic consistency requirement.” However, this is not sufficient to cover all candidates for population ethics because RDGU—which was introduced by Asheim and Zuber (2014) after Fleurbaey and Tungodden’s (2010) theorem—does not satisfy Reinforcement.
This quotation is from a collaboration of 29 authors from economics and philosophy, asking “What should we agree on about the Repugnant Conclusion?”. Further related conclusions include those of Adler (2009) (“Perhaps the best solution, on balance, is to revert to ‘total’ prioritarianism and accept the repugnant conclusion.”) and Cowen (2018) (concluding an appendix about the repugnant conclusion by dismissing its relevance: “I say full steam ahead”).
Our weak sign axioms play a part similar to mere addition (but only apply to perfectly equal populations); our Aggregation axiom has a role similar to Ng’s Non-Antiegalitarianism; and we use an unrestricted repugnant conclusion.
One question is what Parfit himself might have thought of our observation that we misunderstand the lesson of the repugnant conclusion if we impose the normatively irrelevant restriction that \(n(\mathbf {v}) = 0\). Late in his career, in a remarkable final paper, Parfit (2017) wrote about a plurality of related conditions: “such repugnant conclusions” (p. 124) he wrote there, just as also in 2016 he wrote about multiple repugnant conclusions (we cite above). In this final paper, although he still sought to escape the repugnant conclusion, Parfit came to a revised understanding of the repugnant conclusion that resonates with ours: “Because the Repugnant Conclusion seemed to me very implausible, I claimed that we ought to reject this Wide Collective Principle. This claim made two mistakes. We cannot justifiably reject strong arguments merely by claiming that their conclusions are implausible” (p. 154).