Will people follow their intuition even when they explicitly recognize that it is irrational to do so? Dual-process models of judgment and decision making are often based on the assumption that the correction of errors necessarily follows the detection of errors. But this assumption does not always hold. People can explicitly recognize that their intuitive judgment is wrong but nevertheless maintain it, a phenomenon known as acquiescence. Although anecdotes and experimental studies suggest that acquiescence occurs, the empirical case for acquiescence has not been definitively established. In four studies—using the ratio-bias paradigm, a lottery exchange game, blackjack, and a football coaching decision—we tested acquiescence using recently established criteria. We provide clear empirical support for acquiescence: People can have a faulty intuitive belief about the world (Criterion 1), acknowledge the belief is irrational (Criterion 2), but follow their intuition nonetheless (Criterion 3)—even at a cost.