Just in case anyone is interested, the torsional stiffness varies by the fourth power of the diameter. Put another way, if you keep everything else the same (bar length, material, etc.), and just vary the diameter of the bar, doubling the torsional stiffness of the bar requires only a 19% increase in the diameter.
Because the outside diameter has such a large influence on stiffness, a hollow bar doesn't lose as much stiffness as you'd think, because the material toward the center doesn't contribute very much. Using the example above, if a 1.19" bar is twice as stiff as a 1" bar, a hollow bar with 1.19"OD and 1"ID is just as stiff as a solid 1"OD bar, but only weighs 42% as much (if I did the math right).