A different conjunction fallacy

Because the conjunction p-and-q implies p, the value of a bet on p-and-q cannot exceed the value of a bet on p at the same stakes. We tested recognition of this principle in a betting paradigm that (a) discouraged misreading p as p-and-not-q, and (b) encouraged genuinely conjunctive reading of p-and-q. Frequent violations were nonetheless observed. The findings appear to discredit the idea that most people spontaneously integrate the logic of conjunction into their assessments of chance.