A deontologist might refuse to kill one to save five, and yet take a one-in-a-million risk of killing one to avert a one-in-a-million risk of five dying. No prominent decision theory can accommodate this pair of preferences, as weighting outcomes by a uniform probability (or risk-weighted probability) preserves their ranking.
Risk-sensitive decision theories (which permit agents to have non-neutral attitudes towards risk) require them to have the same attitude towards all kinds of risk. But there are good reasons to think that if it can be rational to have a general risk attitude across all domains, then it can be rational to have domain-specific risk attitudes: to be, say, risk averse for epistemic goods, risk neutral for pleasure, and risk seeking for aesthetic value. I develop the formal resources to model these attitudes.
I argue that the characteristic feature of deontology is a particular kind of domain-specific risk attitude. Specifically, the deontologist thinks duty violations are worse than consequentialist harms, but is comparatively risk-seeking with respect to duty violations relative to consequentialist harms.
