 Table 2  shows the result for the majority operator that minimizes the sum of the Hamming distances. In the first column are all the interpretations for the propositional variables p, q, and r. The interpretations that are not models of the IC have a shaded background. So, for example, \((1,0,1)\) cannot be selected as the collective outcome because it violates the legal doctrine. The numbers in the \(d_H (\cdot,K_1)\), \(d_H(\cdot,K_{2})\), and \(d_H(\cdot,K_{3})\) columns are the Hamming distances of each \(K_i\) from the corresponding interpretation. In the last column are the sums of the Hamming distances.