 These and similar examples can be used to show that actual human beings may have cyclic preferences. It does not necessarily follow, however, that the same applies to the idealized rational agents of preference logic. Perhaps such patterns are due to irrationality or to factors, such as lack of knowledge or discrimination, that prevent actual humans from being rational. There is a strong tradition, not least in economic applications, to regard full \(\succcurlyeq\)-transitivity as a necessary prerequisite of rationality.