 How do impossibility results in judgment aggregation conciliate with the fact that IC merging operators can ensure a consistent collective outcome? The reason is that merging operators violate the independence conditions, one of the requirements imposed on aggregation functions in the impossibility theorems. Independence turned out to be an instrumentally attractive condition because it protects an aggregation function from strategic manipulation (Dietrich 2006; Dietrich and List 2007b). This means that an individual has no interest in submitting an insincere judgment set in order to get a better outcome for her. However, independence has been criticized in the literature as a not suitable desideratum to aggregate propositions that are logically interconnected (Chapman 2002; Mongin 2008). Clearly, paradoxical results are avoided by resorting to IC, which blocks unacceptable outcome. However, it is worth noting that in judgment aggregation the collective rationality condition (that requires logically consistent outputs) plays an analogous role as IC in belief merging, that is, blocks unacceptable outcomes like inconsistent majority judgments. Moreover, judgment aggregation impossibility results persist even if we explicitly import additional integrity constraints into the judgment aggregation framework (see Dietrich and List 2008b; Grandi 2012).