Judgment aggregation by quota rules

It is known that majority voting among several individuals on logically interconnected propositions may generate irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds some (proposition-specific) threshold. After characterizing quota rules, we prove necessary and sufficient conditions under which their outcomes satisfy various rationality conditions. We also consider sequential quota rules, which adjudicate propositions sequentially, letting earlier judgments constrain later ones. While ensuring rationality, sequential rules may be path-dependent. We characterize path-independence and prove its equivalence to strategy- proofness under mild conditions. Our results generalize earlier (im)possibility theorems.