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the rear axle bar for the most part stays parallel to the ground, the car body does not as it rolls with inertia through a turn. the sway bar will help resist that rolling force as the body twists it up on one side and down on the other. also, this will not increase the roughness of the ride dramatically as the entire axle moving up and down over say, a speedbump, will not engage the sway bar.
a stiffer rear sway bar will transfer more cornering load to the rear tires, as the bar will resist body roll more then the front bar, taking load off of the front tires and balancing the ff car more through a turn.
all i know of suspension tuning i learned from gran turismo

people here can confirm my above post though.
ahhhh i see your point, its bolting to the control arm, wtf? that seems less effective.
^^^ This all applies to a setup where the sway bar itself is bolted to the chassis/unibody of the car, as well as to a control arm or other moving part of the suspension. Like on a 240SX, or a Miata, or pretty much any car with an independent rear suspension (I've spent a lot of time under those cars!). In these setups, the sway bar acts like a "spring" that fights against the two sides of the independent suspension working against each other. However, I've also installed a rear sway bar onto a B15 Sentra SE-R, which has a solid rear beam setup similar to the Mirage's. It pretty much had no perceivable effect on handling.
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It would still work. As the body leans away from the inside of a turn the inside control arm will lift to follow the chassis and the outside control arm will drop. The sway bar being bolted to the control arms will fight that lifting/dropping of the control arms. So it might not be as effective as the sway bar being bolted to the chassis but it will still have an anti-roll affect on the chassis.
^^^ This is the part that I'm not grasping. How, exactly, is it fighting the lifting/dropping of the rear bar? If the rear bar tends to flex under hard cornering, and the sway bar would stop that flexing, I can understand that. But is that the case? It seems to me that the biggest difference that adding a rear sway bar to the CSM's solid rear bar would be that doing so adds 10-15lbs of unsprung weight to the lower back of the car, which could alter the car's handling characteristics.