Guarantee half the room guesses their hat right

Eight people each wear a black or white hat, assigned by an adversary who wants as many wrong as possible. Everyone sees all the other seven hats but not their own. At a signal, all eight simultaneously write down a guess for their own hat color. There is no communication once the hats are on.

Devise a plan that guarantees at least four of the eight are correct, no matter how the hats are assigned.