Orri defends a weak version of the Pigou–Dalton principle for chances. The principle says that it is better to increase the survival chance of a person who is more likely to die rather than a person who is less likely to die, assuming that the two people do not differ in any other morally relevant respect. The principle justifies plausible moral judgements that standard ex-post views, such as prioritarianism and rank-dependent egalitarianism, cannot accommodate.

However, the principle can be justified by the same reasoning that has recently been used to defend the core axiom of ex-post prioritarianism and egalitarianism, namely, Pigou–Dalton for well-being. The arguably biggest challenge for proponents of Pigou–Dalton for chances is that it violates statewise dominance for social prospects. However, Orri argues that there is an independent reason for rejecting statewise dominance for social prospects, since on a standard interpretation of the principle (in particular, an interpretation that is inconsistent with Pigou–Dalton for chances), it prevents a "social planner" from properly respecting people’s attitudes to risk.