I was considering writing something speculative about spin recovery that disagrees with the above: I would predict that anhedral would tend to delay upright spin recovery by reducing the amount of the rudder bottom exposed the the free airflow (the major anti-spin force). The opposite would be true in recovering from a negative spin. This compares two airplanes that are identical except that one has an anhedral stab, and the other doesn't. If you raised the attach point of the stab to compensate you might be able to mitigate this effect.

Another thing to consider is that few decent propeller-driven aerobatic airplanes have trouble recovering from spins, anhedral stab or not. Furthermore, any supposed advantage that might be gained by anhedral during a positive spin would be turned to a liability by the opposite effect during a negative spin, or vice versa. Since aerobatic airplanes need to recover precisely from both positive and negative spins, it seems unlikely that anhedral has as much to do with spin recovery as it does with appearance, except, as I mentioned in the earlier post, to re-distribute the effective center of horizontal tail area lower.

Again, this is all speculation based on my knowledge of physics and I have no experimentation to back any of this up. I might be missing something (like a brain). Perhaps Guille could illuminate me.

Anhedral wings are more efficient when producing positive lift because they reduce spanwise flow, converting more of the gas's overall momentum change to lift, rather than vortex generation. This would imply that while the anhedral stab is producing negative lift, while the airplane is positively loaded, it would be less efficient than a zero-hedral stab, and the opposite would be true while flying inverted or while the wing is negatively loaded. You can't get something for nothing. Whatever you gain from an anhedral stab in upright or inverted flight, you will lose during the opposite condition.

I think, in general, adding anhedral to a stab will increase yaw stability slightly, which isn't usually a good thing for an aerobatic plane, unless the fin/rudder/aft fuselage area is reduced proportionately to compensate.