The D'Addario company has done this already. They publish a string tension guide that has the tension of each of their strings for each instrument and scale length they are designed for, as well as the mathematical formula for figuring out what the tension would be for different scale lengths, for both electric instruments and classical instruments, including double bass, although the double bass chart is a separate pdf.
Now, of course, with the differences in double bass string manufacturing, not all strings will have the same tension, and one company's light might be more like another company's medium. The important thing is that once you know a string's tension for a given pitch and scale length, you can use the math to sort everything out. The only niggle I have with them is that they talk about "unit weight," when, more precisely, it should be "unit mass," but whatever. Notice it does NOT talk about string diameter, because depending on the manner of construction, the geometry of the wrap wire (flat, round, etc.), the amount of damping material, etc., two strings of the same diameter can have different mass, and two strings of the same mass can have different diameters.
From the D'Addario string tension guide (since pdf's won't post):
Understanding what determines string tension.
In order to determine the tension at which a string will vibrate, you need three pieces of
information: the Unit Weight, the Scale Length, and the Frequency of the string. You can use
the charts in this brochure to get a pre-calculated tension for the D’Addario strings listed or
you can use the formulas below to calculate the exact tension for any string using the scale
length of your particular instrument. All of the charts illustrate string tensions for each
string at a variety of pitches, in case you use alternative tunings.
UW-
Unit Weight. In all the charts and formulas in the brochure, unit weight is expressed in pounds per linear inch (lb/in).
L- Scale Length. This is the vibrating length of the string. This is determined by measuring the distance from the nut to the bridge of the instrument in inches (in).
F- Frequency or pitch. This is the pitch at which you will be tuning the string expressed in cycles per second (Hertz).
On the following page are two fingerboard graphics detailing the various
frequencies for the standard guitar and electric bass guitar.
To calculate the tension of a string in pounds use the formula below,inserting the three variables described above:
T - (Tension) = (UW x (2 x L x F)2) / 386.4
To convert the result into Newtons, simply multiply by 4.45.
If you know what tension you want the string to have, you can calculate the string unit weight. You can then use the charts in this guide to locate a string with approximately the same desired unit weight.
UW (unit weight) = (T x 386.4) / (2 x L x F)2
Now, after digesting that, then the differences in tone as a function of scale length have been researched by Ralph Novak, whose work I used in designing my fanned fret bass guitar and electric guitars. The following is, of course, for guitar, not bass or double bass, but the same principles apply: there is a difference in tone as a function of scale length, with all else being equal, the longer the scale length, the more and higher overtones a string can produce due to the tension increasing as the square of the scale length increasing.
Finally, several companies have posted their tension specs for their various double bass strings in various contexts and scale lengths: 4/4, 3/4, solo. Most notable are Thomastik Infeld, D'Addario, Velvet, and a few others. Most notable by its absence is Pirastro, who still refuse to publish anything but their subjective labelings as to general category.
And, as Ken says, it still comes down to what feels good for you. All these specs are meaningless in and of themselves. You can't use them like an engineer's reference manual to determine what string will be best for you. The best that can be said for them is that they are more like a naturalist's field guide to help you get in the general vicinity of a few possible selections based on an individual player's criteria, whether genre of music, cost, "feel," etc., and then do your own research to see what is best for you, consulting other players and teaching professionals.