You don't need to bring irrational individual behavior into it: you can get rock-paper-scissors group cycles even when every voter has a well-ordered list of preferences.

As a basic example, imagine voters prefer whoever is closer to them on some 2-dimensional politics. 3 candidates form a triangle. Draw the altitudes to form six regions, and put a voter in alternating ones. That's a rock-paper-scissors cycle, with very simple rational voters.