I’m a bioscientist with a background in cancer research, excitedly starting vaccine work at Pfizer. While I’m enthusiastic about many topics, my current side projects are rock climbing, reading (sci-fi and non-fiction), and D&D.
NathanDunkerley
Karma: 2
Very interesting post! I really enjoy simple, quantitative models of difficult-to-grasp problems. I have one question and one suggestion.
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.
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
XA/XB>YB/YA
$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(XA/XB)|>|log(YB/YA)|
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!