Here \(C(S)\) is the set of those options from \(S\) that are, in the sense of the social ordering \(f\langle R_{i}\rangle\), as good as any other; and \(C^*(S)\) stands for the maxima by \(f\langle R^*_{i}\rangle\). This is Arrow’s Condition 3 (Arrow 1951 [1963]: 27).[8] 