An action, or sequence of actions is rational for a decision maker if, when the decision maker is confronted with an analysis of the decisions involved, but with no additional information, she does not regret her choices.
Stated differently, a decision is rational if it is immune to logical introspection, but no new or different assumptions. Thus, you could show someone not following Bayes's rule they are wrong in real time if all they understood was logic, which is independent of empirical data. People who think 'shy librarians' are more common than 'librarians' are thinking irrationally, whereas people who think tax cuts are good/bad for the economy are rational as long as they understand how their assumptions relate to their conclusion.
Many of Kahneman and Tversky's famous behavioral biases are not robust to instrospection, and people realize that anchoring, framing, and representativeness biases are 'wrong', and thus change their opinions upon learning about their errors.
Interestingly, this implies that bees, lions, babies or morons can never be rational, because they don't understand logic, their instincts simply dominate in certain cases. But that's not most people, so if an educated group of adults believes something, and defends their beliefs vigorously, it's rational even if it's wrong.
You could not show people that NINJA loans were toxic back in 2003--there were academic conferences that basically all agreed Alicia Munell was right and Stan Liebowitz was wrong, so smart people all agreed that the historical data showed trivial mortgage risk from such changes (See Papademetriou and Ray, 2004, which highlights no doc, teaser rate, low down payment loans as efficient and just). We now know they were wrong, but the point is, they argued about this in academic journals, and they all agreed previous underwriting standards were discriminatory. Thus, it wasn't irrational, just wrong.
That's important, because it's trivial to prevent irrational bubbles, but rational ones are by definition immune to greater examination.