Abstract: This paper presents a new kind of problem for prioritarian, egalitarian, and utilitarian approaches to the ethics of distribution. The problem takes the form of several “calibration dilemmas,” in which intuitively reasonable aversion to small-stakes inequality-increasing tradeoffs entails intuitively unreasonable aversion to large-stakes tradeoffs—e.g., tradeoffs in which half the population would gain an arbitrarily large quantity of well-being or resources. We lay out these dilemmas, explain how they bear on the leading theories in distributive ethics, and consider what a theory might have to look like in order to evade both horns of the dilemmas. Such a theory would have some strange features, which many philosophers will find implausible. We conclude by offering suggestions for further research.