If there's any kernel to the concept of rationality, it's the idea of proportioning beliefs to evidence (Hume). Everything really flows from that, and the sub-variations (like epistemic and instrumental rationality) are variations of that principle, concrete applications of it in specific domains, etc.

"Ratio" = comparing one thing with another, i.e. (in this context) one hypothesis with another, in light of the evidence.

(As I understand it, Bayes is the method of "proportioning beliefs to evidence" par excellence.)