Why does the Cognitive Reflection Test (sometimes) predict utilitarian moral judgment (and other things)?

The Cognitive Reflection Test (CRT) is thought to correlate with measures of utilitarian moral judgment because it measures system-2 correction of an initial intuitive response. And some theories of moral judgment hold that the same thing often happens when people arrive a utilitarian judgments. We find, however, that CRT-type items (using logic as well as arithmetic) can work just as well when they do not have obvious intuitive answers at predicting utilitarian moral judgment, assessed with self-report questionnaires as well as with hypothetical scenarios, and also at predicting a measure of actively open-minded thinking (AOT). Moreover, long response times, as well as high accuracy, also predict moral judgment and other outcomes. The CRT might thus be considered a test of reflection-impulsivity (RI). However, RI is only part of AOT, because RI is concerned only with the amount of thinking, not its direction. Tests of AOT also predict utilitarian moral judgments. Individual differences in AOT and moral judgments are both strongly (negatively) associated with belief that morality comes from God and cannot be understood through thought. The correlation of CRT and utilitarian judgment, when found, is thus likely due to the (imperfect) correlation of AOT and CRT. Intuition in these domains is thus not necessarily something that people overcome through additional thinking, but rather what they rely on when they do not think very much.