The horse biological mechanism is extraordinarily effcient but not simple . It cannot be explained with simple formulas. The complexity is in fact worse when actual knowledge of the equine physciology is explained in respect of old theories. JLC
The ridden horse's spine does not move according to the dressage theories since Baroque Dressage (Duke of Newcastle.) The horse's spine is very rigid, does not flex much either side to side or up and down, and the horse uses his spine muscles to stiffen his spine so that the spinal cord is protected. Because of this, the modern dressage theory of the use of the seat as a driving aid provokes bruising in the horse's back, leading to lesions that manifest as lameness, you need to fix the horse's back to cure a lot of the lameness.
Use of the seat as a driving aid is bad for the horse's back. The problems that the driving seat aid cause seriously affect the purity of the gaits.
A way out of this dilemna is to keep your pelvis vertical at all times using the curves of your spine to absorb the shocks. Tilting the rider's pelvis back drives the seat bones of the rider into the horse's back, well what often happens is that protrusions on the underside of the tree of improperly made saddles are forced down into the muscles of the horse's back and harm it. To feel these protrusions you have to feel between the panels and the tree, often they are 2 inches wide, at the top end of the saddle flap Most dressage saddles have these protrusions, supposedly to strengthen the rider's seat aids. One of my other GP saddles has a pyramid shaped protrusion, point down, at the same place.
Personally I only use a driving seat aid when the horse balks at every other driving aid. I consider it severe, more severe that properly used spurs. 40-50 years ago it became a fashion to use the driving seat at the start of every move and every aid in hunt seat and dressage. I was taught to do this in the British system, luckily I went to Forward Seat which does not use the driving seat so I did not mess up my horses' backs too bad.
What I say above is a combination of Jean Luc's articles and what I learned on the Corrector pad site and what I've observed. Hope it helps, this can be a complicated subject. I by no means understand this as much as Jean Luc!