(Part 1) What the 4th Succession War Implies About Population Size

tl;dr? The size of Tikonov's garrison implies that the Successor States have a total population of no more than 516 billion to 539 billion people.

Let's talk about Tikonov.

Tikonov has 5.279 billion people, and (according to the NAIS Military Atlases) fielded 80 militia regiments in the 4th Succession War. That's one militia regiment per 66 million people. Capellan worlds typically have a two-battalion militia each; using the Tikonov ratio, two battalions would imply a typical population of 44 million per world.

The House Liao: The Capellan Confederation (hereafter HL:CC) Atlas contains forty major Capellan worlds totaling 138.502 billion people, and averaging 3.46255 billion each. If we estimate the Successor States to have 156 such major worlds totaling 450 billion people, then the 116 outside the Confederation average only 2.68533 billion each. (Remarkably close to Chesterton's average of 2.68444 billion, also from HL:CC.) That makes the major Capellan worlds about 1.29x as populous as major non-Capellan worlds. If we assume that 1.29x ratio also holds for lesser worlds, then the "typical" non-Capellan world should average about 34.12 million.

I count about 1892 star systems in the Successor States, claiming (probably on the lower end of) 1974 to 2654 inhabited worlds between them. Assuming the Chesterton systems have an average number of planets for a non-Capellan system, that makes 377 to 373 "typical" Capellan worlds vs. (respectively) 1441 to 2125 "typical" non-Capellan worlds. That totals 66 billion to 89 billion humans on top of the 450 billion from major worlds (i.e., 516 billion to 539 billion humans in all).

On the other hand, the ratio of two battalions per 44 million people is a pretty rough abstraction. The "typical" Capellan worlds could be quite a lot smaller and still be able to support the two battalions; typical non-Capellan worlds may be more populous in comparison.

I don't know why Tikonov has only two battalions per 44 million people, but the reason probably applies to any population of significant size in BattleTech, which makes it useful for calculating an upper limit on planetary populations.