We study the following computational problem: for which values of k, the majority of n bits 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 MAJk ∘ MAJk. We observe that the minimum value of k for which there exists a MAJk ∘ MAJk circuit that has high correlation with the majority of n bits is equal to Θ(n^1/2). We then show that for a randomized MAJk ∘ MAJk 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 MAJk ∘ MAJk circuit computes the majority of n bits correctly on all inputs, then k ≥ n^{13/19 + o(1)}.