Very interesting post! I really enjoy simple, quantitative models of difficult-to-grasp problems. I have one question and one suggestion.

Here, $X$ is the criterion that A is better on, $Y$ is the criterion that B is better on, and $c$ is the aggregate of all other criteria that A and B are identical on.

Is the claim here that X and Y are the only variables with respect to which A and B differ, and that they share the same value for all other variables, which are multiplied together to equal c? That would mean that this model only represents an all-else-being-equal case, right? To Arepo's comment, I think this all-else-being-equal model is a good starting place but not the final word e.g. doesn't capture flow-through effects.

Higher-frequency information is valuable, but a quarterly survey is 4x more expensive than an annual survey, and its information is probably not 4x more valuable. So the cost advantage of less frequent surveys is more important, and thus we should fund the survey annually rather than quarterly.

If we're applying the given formula as written, you get a weird result when you want to minimize one variable and maximize the other. Using the survey example, say A is an annual survey, B is a quarterly survey, X is annual survey cost, and Y is data quality (indicated by total citations of all surveys conducted over a year). When we plug in some toy-values, we get the following

$X_A/X_B>Y_B/Y_A$

$\$1000/\$4000>22/10$

$0.25>2.20$

which isn't true even though the range of X is larger than Y. A representation that captures this scenario could be

$|log\left(X_A/X_B\right)|>|log\left(Y_B/Y_A\right)|$

In this case, instead of $0.25>2.20$ for the above example, you get $0.60>0.34$, which is true.

Disclaimer: I'm a chemist, not a mathematician. Please take my math with a grain of salt!