 The definition uses a family of relations \(\{R_{i}\}_{i\in\mathcal{A}}\). In the literature, the same is denoted \((W,R_{i},V,w)_{i\in\mathcal{A}}\). Alternatively, R is taken to be a function sending agents to relations, i.e., \(R:\mathcal{A\rightarrow}\mathcal{P}(W\times W)\). Then for each \(i\in\mathcal{A}\), \(R(i)\) is a relation on W, often denoted \(R_{i}\). These are stylistic choices.