> never seen a definition of utility which wasn't self referencing
It’s analogous to “holes” in semiconductors or virtual particles. You can’t directly observe it. But it’s an intuitive notion that makes many calculations easier.
Critically, there are several valid definitions of utility, e.g. the von Neumann–Morgenstern (VNM) utility theorem [1] and revealed preference [2]. Each has its own axioms, defined with varying rigour, that can be theoretically extended and practically applied.
> a highly unscientific concept
Sure, it’s unscientific in the way mathematics are unscientific: it starts with a set of axioms and extends from that. Determining whether the chosen axioms fit a particular situation is a separate, more scientific question.
That said, similar criticisms have been raised about e.g. auction theory and quantum physics, both of which (like utility-based models) make testable predictions.
"In economics, a utility representation theorem asserts that, under certain conditions, a preference ordering can be represented by a real-valued utility function, such that option A is preferred to option B if and only if the utility of A is larger than that of B."
You may challenge the assumptions but otherwise it's mathematics.
> It's "vibes" dressed up in sciency sounding language
This is pop economics. (And again, as mentioned, it’s not science-y. It’s applied mathematics. It’s only when you use the model to make predictions that it becomes science-y.)
Of course, if you’ve refuted von Neumann and Morgenstern, by all means, publish. Otherwise this is the “series of tubes” equivalent for economics.
> having multiple valid definitions of something that is foundational to a discipline
It’s foundational to one branch. Almost all of finance, for instance, doesn’t bother with utility functions.
One can similarly complain that mathematicians have different rules for parallel lines depending on geometry. Like, sure. But if you’re in the field it makes perfect sense why parallel lines don’t intersect in a Euclidean space but do in a curved one. Given utility functions are literally ordered sets of preferences, it strikes me as trivial that there would be a multitude of them. (If this bothers you, don’t look up Gödel.)
The economists who deal with utility functions are more or less applied game theoreticians. Some people have a problem with game theory and statistics because they’re unpure. Like, sure. Fine. I also have a small stable of useless opinions, e.g. raisins are trash fruit. That doesn’t mean raisins are themselves useless; it’s just my opinion that’s adding zero value in a world where raisins do.
> Almost all of finance, for instance, doesn’t bother with utility functions.
You need the concept of utility and some (reasonable) assumptions about the shape of the utility curve to derive CAPM - at least the way I was taught it and there may be an alternative I do not know of?
I do not think there being a multitude of utility curves is a problem. It seems to be there is a lack of a clear concept.
I do not think that your analogy with maths works. Maths is is more abstract and should change with different sets of axioms. Economics is supposed to be based on observations of the real world.
Utility of money is just how much value one (an individual or entity) can derive from having x amount of money. Utility and value might be defined by self referencing each other but that's true for many other concepts or words in a language for that matter. It doesn't make it problematic or unscientific.
The point is that it matters how much certain amount of money or wealth is worth for you not how much wealth you have. It's an important point as it explains why calculations purely in money terms are useless for making financial decisions (as seen in example of insurance)
It's not like that at all.
If you want to argue that one can't define value then I am out.
If you admit "value" has well understood meaning then utility function of wealth is just how much value one can derive from it. We usually measure wealth in money for convenience. I really don't know why you are so against it. There might be a lot of nonsense associate with it but the concept itself is pretty simple and useful.
It's a highly unscientific concept.