dysrationalia
n. The tendency to think or act irrationally in certain situations, despite having sufficient intelligence.
dysrational adj.

Example Citations:
In 1994, Stanovich began comparing people's scores on rationality tests with their scores on conventional intelligence tests. What he found is that they don't have a lot to do with one another. On some tasks, there is almost a complete dissociation between rational thinking and intelligence. You might, for example, think more rationally than someone much smarter than you. Likewise, a person with dysrationalia is almost as likely to have higher than average intelligence as he or she is to have lower than average intelligence.
—Kurt Kleiner, "Why Smart People Do Stupid Things," University of Toronto Magazine, June 1, 2009

Even so, this recent article's explicit study of the persistently dysrational (a better term than "arational" or "dysreasonal") feels like a useful way to reframe the discussion. From Bush to Rumsfeld to Climate change deniers we've seen some fairly smart to brilliant people stuck in dysrational modes. If we can understand what produces dysrationalia, and how to intervene in early life, we may take a big step towards enlightenment 2.0 and rational discourse though not universal agreement.
—John Gordon, "Reason — it's more than IQ," Gordon's Notes, November 10, 2009

Earliest Citation:
The new disability is called dysrationalia. The proposed definition of the disability is as follows: Dysrationalia is the inability to think and behave rationally despite adequate intelligence.
—Keith E. Stanovich, "Dysrationalia: A new specific learning disability" (PDF document), Journal of Learning Disabilities, October 1, 1993

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