Perhaps I'm misunderstanding your misunderstanding. Take you G&S points, apply your G&S bonuses. That tells you the max population your world will support at 100% approval. Once your population crosses that threshold, every 0.1 population beyond that max equal 1% less approval.
G&S points = 4 (Colony capital) + 2 (Entertainment center) = 6
G&S bonuses = 10% (Supportive population)
Max pop at 100% approval = 6 x (1 + 0.1) = 6.6
if your planet is at 12 population, approval = 100 - ((12 - 6.6) * 10) = 46%
This assumes the approval curve is linear. It holds true in the early game, not sure if it holds true for very high population worlds.
Unlike in GC2 and previous betas you can no longer use sliders to fix approval problems. You need to either build G&S improvements, build G&S starbase modules, research G&S techs, or offload people. Now that the production approval bonuses are no longer a step function, it's not a huge hit if you drop down to 99% approval. Building farms is a much tougher decision now. Does my planet have 2 more G&S points to support 2 more population? If I upgrade my farms do I have enough extra G&S on each planet to support the higher population? Is it better to have 2 more population at 80% approval, or just add a factory and maintain 100% approval? How might Stardock make these decisions more obvious, or perhaps that's the intended difference between a beginner and a pro?