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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 MAJ_k ∘MAJ_k. We observe that the minimum value of k for which there exists a MAJ_k ∘MAJ_k 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 MAJ_k ∘MAJ_k circuit computing thearXiv:1610.02686v1 fatcat:74xhlc3drncynhzp4v7nnitiry