Sensitivity is likely something that can be measured objectively, but first it has to be defined more precisely. In other words, what exactly is sensitivity? From the angling perspective, we may say it is the ability to manually detect acceleration that occurs at the end of the fishing line. In the realm of materials science it may have some relationship to vibration transmission, and that will vary in any one particular rod with the frequency of the vibration. Perhaps if we can identify the frequency (probably low frequency) of the transmitted vibrations that we would encounter in bass fishing, and duplicate those vibrations in the lab upon a line extending from the end of a rod, we can easily (by means of a simple vibration meter placed at the reel seat) measure the amplitude of the transmitted vibrations. We could then compare it between rods.
The problem remains, though, whether such measurement will reveal any valuable information that relates to the subjective feel, effectiveness, or fishing enjoyment of any rod.
I have always wondered what parameters are used by rod blank manufacturers, and by the major rod makers who chose the blanks. Probably trade secrets that we will never be privy to.
My favorite rods, out of the three or four brands that I have fished with extensively, are the Dobyns Champion series, which seem to me light and sensitive, and give me a sense of liveliness, fun, and confidence when fighting a fish. But, who knows?, it's probably all in my head.