This paper presents a new kind of problem in the ethics of distribution. The problem takes the form of several 'calibration dilemmas', in which intuitively reasonable aversion to small-stakes inequalities requires leading theories of distribution to recommend intuitively unreasonable aversion to large-stakes inequalities. We first lay out a series of such dilemmas for prioritarian theories. We then consider a widely endorsed family of egalitarian views and show that they are subject to even

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... forceful calibration dilemmas than prioritarian theories. Finally, we show that our results challenge common utilitarian accounts of the badness of inequalities in resources.