Limited Aggregation and Risk

Many of us believe (1) Saving a life is more important than averting any number of headaches. But what about risky cases? Surely: (2) In a single choice, if the risk of death is low enough, and the number of headaches at stake high enough, one should avert the headaches rather than avert the risk of death. And yet, if we will face enough iterations of cases like that in (2), in the long run some of those small risks of serious harms will surely eventuate. And yet: (3) Isn't it still permissible for us to run these repeated risks, despite that knowledge? After all, if it were not, then many of the risky activities that we standardly think permissible would in fact be impermissible. Nobody has yet offered a principle that can accommodate all of 1-3. In this paper, I show that we can accommodate all of these judgements, by taking into account both ex ante and ex post perspectives. In doing so, I clear aside an important obstacle to a viable deontological decision theory.