Several philosophers of science have argued that epistemically rational individuals might form epistemically irrational groups and that, conversely, rational groups might be composed of irrational individuals. We call the conjunction of these two claims the Independence Thesis, as they entail that methodological prescriptions for scientific communities and those for individual scientists are logically independent. We defend the inconsistency thesis by characterizing four criteria for epistemic rationality and then proving that, under said criteria, individuals will be judged rational when groups are not and vice versa. We then explain the implications of our results for descriptive history of science and normative epistemology.Philosophers and social scientists have often argued (both implicitly and explicitly) that rational individuals can form irrational groups and that,

argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or "closeness to the truth" (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightlygeneralized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that there is no strictly proper scoring rule for imprecise probabilities.The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. 1 We argue instead that another Joycean assumptioncalled strict immodesty-should be rejected, and we prove a representation theorem that characterizes all "mildly" immodest measures of inaccuracy.

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