The concept known as Rational irrationality was introduced in The Myth of the Rational Voter. It was developed by economist Bryan Caplan to reconcile the widespread existence of irrational behavior with the assumption of rationality made by mainstream economics and game theory. The original purpose of the concept was to explain how (allegedly) detrimental policies could be implemented in a democracy, and unlike conventional public choice theory, Caplan posited that bad policies were selected by voters themselves.
Essentially Rational Irrationality is a term used to describe a state in which a decision, of minimal immediate impact on a person, such as voting allows that person to make a decision which benefits him by adhering to his own rational adherence to personal belief without regard to the irrationality of the decisions cost-benefit analysis in the big picture.
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A voter has very small chance of influencing policy. Therefore, the vote he casts is of little consequence to him. There is no incentive for a voter to invest time and energy analyzing the consequences of a policy. However, a voter derives some benefits from voting. It allows him to signal the kind of person he is, who he associates with. If there are no consequences in being mistaken about the effect of a policy, it becomes "rational" to hold the most pleasant opinion, or the one most conducive to socialization.