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 <italic>utilitarian</italic> 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 <italic>ex ante</italic> and <italic>ex post</italic> evaluations for such prospects. We examine the relationship between the <italic>ex ante</italic> and the <italic>ex post</italic> in this restrictive framework: There are more possibilities to respect <italic>ex ante</italic> and <italic>ex post</italic> objectives simultaneously than in the general framework, i.e. without the restriction to binary utilities (<italic>cf</italic>. Harsanyi's aggregation theorem). We extend our results to <italic>n</italic> 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 <italic>pro-poorly off</italic> (or <italic>prioritarian</italic>) value functions (Diamond 1967; Rabinowicz 2002; Fleurbaey 2010) for the evaluation of risky prospects.
