Voting power in Parliament is proportionate to the tax base of your province (minimum of one vote). The provinces marked on the map (minus Ohren and Zion, which aren't listed on HM:FWL page 62) total 320 votes across 125 star systems, which is about 3x as many votes per system (320/125 vs 180/208) as the smaller provinces. This means more than 3x the tax base, since many single-vote provinces would be rounded up to one vote.
So, on a scale of 100 to 200 star systems, population correlates pretty well with tax base.
Smaller scales are difficult to gauge because some provinces (especially disproportionate ones like Gibson, Tamarind and Sirius) are no doubt leveraging populations outside their borders.
It's very interesting how most of the gigapop worlds follow a clear sinusoidal curve--and that the average of Andurien and Lopez (which lie close together in the Duchy of Andurien) would fall right on the curve, and that the average of Oriente and Calloway IV (which lie close together in the Duchy of Oriente) would also fall right on the curve. The average of Marik and Angell II stands ~33% above the curve, but perhaps that's to be expected, since Atreus (capital of the FWL) stands ~66% above the curve.
It makes sense for the population curve to dip near the periphery, but why it would dip between Terra and Andurien is less clear. Perhaps a combination of proximity to enemy borders, to Terra, and to other gigapop worlds?
I'm curious to see how Capellan and Draconis gigapops compare; if there's a consistent pattern, I may be able to estimate Davion and Steiner gigapops. (The Atlases in the old Davion and Steiner sourcebooks didn't include population figures.)
It's also interesting that there are [(radius/14.5)-2] gigapop worlds within [radius] Light Years of Terra. Instead of being spread across regular intervals of area (like the FWL's other star systems are), gigapop worlds show up at regular intervals of linear distance from Terra, which means the ratio of gigapop worlds to regular worlds falls dramatically the further out you go.
A few posts ago I calculated that, for small provinces, the average number of votes per system also falls geometrically the further out you go. Big provinces--which generally have more gigapop worlds--don't change with distance.
Perhaps each gigapop world (or pair of gigapop worlds) is the dense center of a population spread across half a dozen to a dozen worlds, such that the value of any given world would depend on its distance from a population center? This will require more thought.
