The aggregation of individual sets of judgments over interconnected propositions can yield inconsistent collective sets of judgments, even when the individual sets of judgments are themselves consistent. A doctrinal paradox occurs when majority voting on a compound proposition (such as a conjunction or disjunction) yields a different result than majority voting on each of the elements of the proposition. For example, when most individuals accept proposition X ; most individuals accept proposition Y ; but only a minority of individuals accept the compound proposition “X and Y”. Conducting two elemental votes would lead to accept X and Y, but conducting one compound vote would lead to reject X and Y. In such a situation, do people manifest a stable preference as to which voting procedure should be applied? This research reports the results of two behavioral experiments using a within-participant design, which show that procedural preferences can be upturned by framing either positively or negatively the set of judgments to be aggregated. This shift in procedural preference leads to large swings in the final collective judgment endorsed by participants.