Normative population theory

Conclusion We have shown, contrary to the claims of Cowen, that average and critical-level utilitarianism, which do not suffer from the repugnant conclusion, do not recommend the killing of people with low but positive utilities. We have shown, in addition, that Methuselah's paradox and the repugnant conclusion do not stem from preferences that are represented by additive utility functions. Further, we have shown that Cowen's ideal participant method suffers from the repugnant conclusion.We believe that Parfit's 4] criticism of classical utilitarianism — that it satisfies the repugnant conclusion — should be taken seriously. That suggests that the ideal participant method should be rejected (along with classical utilitarianism) as a reasonable solution to the optimal population problem.We have benefited from private correspondence with T. Cowen, and the remarks of T. Hurka and an anonymous referee.