  In this paper we consider the computational complexity of the following
problem. Let $f$ be a Boolean polynomial. What value of $f$, 0 or 1, is taken
more frequently? The problem is solved in polynomial time for polynomials of
degrees 1,2. The next case of degree 3 appears to be PP-complete under
polynomial reductions in the class of promise problems. The proof is based on
techniques of quantum computation.
