I think this is true. The whole argument about people who do the opposite
of what you predict doesn't shed much light on free will, in my opinion.
Imagine a computer program which outputs a 0 or 1. You are supposed to
type in your prediction of what it will output, and then it prints out
its choice. Now write the program so that regardless of what you input,
it prints out the opposite value. This is a trivial program, about three
lines long. Most people would agree that it does not have free will.
Or, imagine an even simpler system, a pendulum which swings from left
to right in one second. Back and forth it goes. You are supposed to
predict where it will be in one second. If you think it will be at the
right, you "tell" the pendulum this by setting the bob to the right,
and similarly if you think it will be at the left. But, it appears that
your prediction is wrong, because whichever side you set the bob at,
after one second it is at the opposite side.
This does not reflect any true inability to predict the future of these
systems. It simply means that the system has the property that when the
prediction is input in a certain way, it affects the output. Even quite
trivial systems have this property, and it doesn't have anything to do
with free will.
Hal