Probability Adjusted Rank-Discounted Utilitarianism

We propose and axiomatize probability adjusted rank-discounted critical-level generalized utilitarianism (PARDCLU). We thus generalize rank-discounted utilitarianism (RDU) (proposed by Zuber and Asheim, 2012) to variable population and risky situations and thereby take important steps towards preparing RDU for practical use, e.g. for evaluation of climate policies and other policy issues with long-run consequences. We illustrate how PARDCLU yields rank-dependent expected utilitarianism - but with additional structure - in a special case, and show how PARDCLU can handle a situation with positive probability of human extinction.