We study the following computational problem: for which values of k, the majority of n bits \text{MAJ}_n can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by \text{MAJ}_k \circ \text{MAJ}_k. We observe that the minimum value of k for which there exists a \text{MAJ}_k \circ \text{MAJ}_k circuit that has high correlation with the majority of n bits is equal to \Theta(n^{1/2}). We then show that for a randomized \text{MAJ}_k \circ \text{MAJ}_k circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n^{2/3+o(1)}. We show a worst case lower bound: if a \text{MAJ}_k \circ \text{MAJ}_k circuit computes the majority of n bits correctly on all inputs, then k\geq n^{13/19+o(1)}. This lower bound exceeds the optimal value for randomized circuits and thus is unreachable for pure randomized techniques. For depth 3 circuits we show that a circuit with k= O(n^{2/3}) can compute \text{MAJ}_n correctly on all inputs.