Whether ratios multiply is a mathematical question, not a psychological one, so your comment doesn’t make sense. The only relevance human rationality has is whether ratios are an accurate model for humans. Furthermore, the OP said “If a microeconomist had a list of 120 ratios between each value, she could describe a great deal of a rational agent’s behavior in a wide new variety of contexts.” so humans are being modeled as rational beings, both explicitly (the OP outright says it) and implicitly (the use of ratios implies a certain level of rationality, no pun intended).
Once you choose a model, you can only model systems as being consistent with your model. If you model people as having a well defined utility function, then you are modeling them as having preference ratios that multiply. If the ratio between the utilitons that A gives you and the utilitons B gives you is X, and the ratio between the utilitons that B gives you and the utilitons C gives you is Y, then the ratio between the utilitons that A gives you and the utilitons C gives you must be XY. If U(A)/U(B) = X and U(B)/U(C) = Y, then U(A)/U(C) = XY. Saying “Well, people are irrational, so their utility function might not make sense” isn’t a valid response to this. U(A) is a real number, so it must follow the rules of real numbers. The fact that it the domain of U is a set of things that doesn’t have to follow those rules doesn’t change the fact that its codomain does have to follow those rules.
If you want to propose some other model, maybe come up with some mathematical structure that doesn’t follow these rules, then you are welcome to try. But you should be clear in properly formalizing this model, and not put it in terms of things that have to follow rules that your model doesn’t follow.
They ought to for a perfectly rational being, but humans aren’t.
Whether ratios multiply is a mathematical question, not a psychological one, so your comment doesn’t make sense. The only relevance human rationality has is whether ratios are an accurate model for humans. Furthermore, the OP said “If a microeconomist had a list of 120 ratios between each value, she could describe a great deal of a rational agent’s behavior in a wide new variety of contexts.” so humans are being modeled as rational beings, both explicitly (the OP outright says it) and implicitly (the use of ratios implies a certain level of rationality, no pun intended).
Once you choose a model, you can only model systems as being consistent with your model. If you model people as having a well defined utility function, then you are modeling them as having preference ratios that multiply. If the ratio between the utilitons that A gives you and the utilitons B gives you is X, and the ratio between the utilitons that B gives you and the utilitons C gives you is Y, then the ratio between the utilitons that A gives you and the utilitons C gives you must be XY. If U(A)/U(B) = X and U(B)/U(C) = Y, then U(A)/U(C) = XY. Saying “Well, people are irrational, so their utility function might not make sense” isn’t a valid response to this. U(A) is a real number, so it must follow the rules of real numbers. The fact that it the domain of U is a set of things that doesn’t have to follow those rules doesn’t change the fact that its codomain does have to follow those rules.
If you want to propose some other model, maybe come up with some mathematical structure that doesn’t follow these rules, then you are welcome to try. But you should be clear in properly formalizing this model, and not put it in terms of things that have to follow rules that your model doesn’t follow.
Good point.