On the randomized complexity of functions that approximate a voting function

We consider the complexity of the realization of partial Boolean functions that approximate a Boolean function of $n$ variables, which is the Boolean voting function (by majority) $M(x_1,\dots,x_n)$. The functions are computed on a computer with arbitrary memory capacity and equipped with a random number generator. We show that the use of random number generators allows us to compute functions that roughly approximate $M(x_1,\dots,x_n)$ in constant time. In computing functions that are sufficiently close to $M(x_1,\dots,x_n)$ the use of random number generators does not allow the complexity of computation to be lowered more than a constant number of times.