Who is the first one to equate "rational" with "complete and transitive preference"? MWG taught that, suppose that the menu is finite, &quot;rational&quot; is the same as &quot;complete and transitive&quot;. But it seems that it does not cite any sources. Who said this first?
vNM said in 1944 that their EU is rational behavior, which is followed by computer scientists, statistician, and Finance literature. Why didn't MWG also follow this?

MWG equate &quot;rationalizable&quot; with &quot;existence of utility function&quot; or &quot;complete and transitive preference&quot;. To be clearer about my question, I am most interested in learning the first literature which argue that the &quot;existence of utility function&quot; or &quot;complete and transitive preference&quot; is rational.
As pointed in the comments this was done by  Ragnar  Frisch.  At least Barten and  Böhm. (1982) as well as Johansen (1969) attribute these axioms to one of these two publications:

Frisch, Ragnar (1926). &quot;Sur un problème d'économie pure [On a problem in pure economics]&quot;. Norsk Matematisk Forenings Skrifter, Oslo. 1 (16): 1–40
Frisch,(1926). &quot;Kvantitativ formulering av den teoretiske økonomikks lover [Quantitative formulation of the laws of economic theory]&quot;. Statsøkonomisk Tidsskrift. 40: 299–334.

Also I think this question has a misconception.
Von Neumann and Morgenstern (1944) indeed in their Theory of Games and Economic Behavior equate maximization of expected utility $E(u)$, with rational behavior.
However, note that the $E(u)$ of vNM is already based on axiom of transitivity and completeness. The issue here is that vNM were not just deriving utility of rational person. They were deriving cardinal utility of rational person.
The assumption of transitivity and completeness is only condition for preferences to be rational in general (see MWG pp 6.).