Survey says: Like Hell!
If
predestination is caused/enforced by a
higher power, then the
existence/non-existence of
free will should be observed from the
viewpoint of that higher power, in which case it becomes
obvious that we have no free will.
Assuming, of course, that you believe in predestination in the
above form. I don't. If there is a sort of predestination, I prefer to think of it in terms of
prediction, like looking at a
basketball mid-air and calling whether or not it's going in the
basket. With that
paradigm, we get predestination AND free will,
best of both worlds. :-)