Intergenerational justice when future worlds are uncertain

Let there be a positive (exogenous) probability that, at each date, the human species will disappear. We postulate an Ethical Observer (EO) who maximizes intertemporal welfare under this uncertainty, with expected-utility preferences. Various social welfare criteria entail alternative von Neumann Morgenstern utility functions for the EO: utilitarian, Rawlsian, and an extension of the latter that corrects for the size of population. Our analysis covers, first, a cake-eating economy (without production), where the utilitarian and Rawlsian recommend the same allocation. Second, a productive economy with education and capital, where it turns out that the recommendations of the two EOs are in general different. But when the utilitarian program diverges, then we prove it is optimal for the extended Rawlsian to ignore the uncertainty concerning the possible disappearance of the human species in the future. We conclude by discussing the implications for intergenerational welfare maximization in the presence of global warming.