Arrow established a convention that is still widely observed of using ‘\(R\)’ to denote the social preference derived from “\(\langle R_{i}\rangle\)”. The social welfare function used to derive it is, in his notation, left implicit. One advantage of writing ‘\(f\langle R_{i}\rangle\)’ instead of ‘\(R\)’ is that when we state the conditions of the impossibility theorem, in the next section, the social welfare function will figure explicitly in them. This makes it quite clear that what these conditions constrain is the functional relationship between individual and social preferences. Focusing attention on this was an important innovation of Arrow’s approach.