# Who is the first one to equate "rational" with "complete and transitive preference"?

MWG taught that, suppose that the menu is finite, "rational" is the same as "complete and transitive". 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 "rationalizable" with "existence of utility function" or "complete and transitive preference". To be clearer about my question, I am most interested in learning the first literature which argue that the "existence of utility function" or "complete and transitive preference" is rational.

• I believe that was Ragnar Frisch, but I can't back up this claim. Nov 17 '20 at 15:35
• Wade Hands is a very good professor on the history of economic thought. He has a lot of work on modern microeconomic theory. I would recommend checking out some of his work, he will no doubt have something to say on it. Also, I know there is a philosopher Temkin, whose work is heavily focused on the history of transitivity. Nov 17 '20 at 15:58
• I am responding to the edit, I think this is problematic because transitivity and completeness are technical terms. People had some loose ideas of utility already in past and also some loose ideas about preference ordering and so forth. However, they would not call these completeness and transitivity axioms. If you are looking for background concept alone then that will be very difficult to prove given that pre 1900s economics was not very precise and rigorous
– 1muflon1
Nov 17 '20 at 21:11
• @1muflon1 Maybe I have to rephrase (or create new) the question? Who was the first economists arguing that utility maximization is the core of rationality and economic behavior? Nov 17 '20 at 21:19
• @HighGPA okay that is clear. By the way maybe you should consider making it a separate question - I do not think that would be duplicate of this current question.
– 1muflon1
Nov 17 '20 at 21:20

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

• Many thanks! I read several old papers by Frisch. I agree that Frisch might be one of the first economists who use completeness and transitivity; I am not sure if Frisch argued that completeness and transitivity are rational or normative. However, if you mean that completeness and transitivity is equivalent to the existence of utility function on some choice sets, then these representations result were proved by Cantor and Birkhoff before 1900. Also note that the original goal of Frisch's axiomatic approach is to axiomatize measurable utility. Nov 17 '20 at 21:04
• @HighGPA well yes you are right, I mean by using the axioms I meant to say that Frisch was first to formalize their use, some loose ideas about this might have existed before
– 1muflon1
Nov 17 '20 at 21:08
• @HighGPA that is good question, I would have to double check their book to be honest but if I remember correctly they argued that their EU is rational, not that any rational person must use their EU
– 1muflon1
Nov 17 '20 at 21:22
• A preference can be rational (as in complete and transitive) without being representable by a utility function. For instance, here economics.stackexchange.com/a/40807/11590 Nov 17 '20 at 23:07
• That was @HighGPA but reading the comment again, I think did not pay attention to "on some choice sets." Nov 17 '20 at 23:33