Most bradoon bits have loose rings, because the increased sensitivity that they afford is desirable for the upper level dressage horse typically being ridden in a double bridle arrangement.
Because the ring-shaped cheek pieces are attached to the bit by running through holes bored into the ends of the mouthpiece, the mouthpiece is able to move freely in relation to the rings. This allows the mouthpiece to move more independently with the tongue and jaw movements of the horse, even when the reins are maintaining pressure on the bit. This is an advantage in dressage in that it encourages a relaxed jaw and mobile tongue. The rings are also able to swivel freely in a lateral direction, allowing for clear transmission of direct rein aids.
As with its regular snaffle counterpart, the main drawback to the loose rings is that pinching of the lips between the rings and the mouthpiece can occur with some horses. In that case, an eggbutt style cheek is preferable.