The veil of ignorance argument was used by John C. Harsanyi to defend Utilitarianism and by John Rawls to defend the absolute priority of the worst off. In a recent paper, Lara Buchak revives the veil of ignorance argument, and uses it to defend an intermediate position between Harsanyi's and Rawls' that she calls Relative Prioritarianism. None of these authors explore the implications of allowing that agent's behind the veil are averse to ambiguity. Allowing for aversion to ambiguity---which is both the most commonly observed and a seemingly reasonable attitude to ambiguity---however supports a version of Egalitarianism, whose logical form is quite different from the theories defended by the aforementioned authors. Moreover, it turns out that the veil of ignorance argument neither supports standard Utilitarianism nor Prioritarianism unless we assume that rational people are insensitive to ambiguity.