We consider a special set of risky prospects in which the outcomes are either life or death (or, more generally, binary utilities). There are various alternatives to the utilitarian objective of minimizing the expected loss of lives in such prospects. We start off with the two-person case with independent risks and construct taxonomies of ex ante and ex post evaluations for such prospects. We examine the relationship between the ex ante and the ex post in this restrictive framework: There are more possibilities to respect ex ante and ex post objectives simultaneously than in the general framework, i.e. without the restriction to binary utilities (cf. Harsanyi's aggregation theorem). We extend our results to n persons and to dependent risks. We study optimal strategies for allocating risk reductions given different objectives. We place our results against the backdrop of various pro-poorly off (or prioritarian) value functions (Diamond 1967; Rabinowicz 2002; Fleurbaey 2010) for the evaluation of risky prospects.
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