To state the last condition of Arrow’s theorem, another piece of shorthand is handy. For any given relation \(R\), and any set \(S\), let \(R|S\) be the restriction of \(R\) to \(S\). It is that part of \(R\) concerning just the elements of  \(S\).[3]  The restriction of \(\langle R_{1}, \ldots, R_{n}\rangle\) to \(S\), written \(\langle R_{1}, \ldots, R_{n}\rangle|S\), is just \(\langle R_{1}|S, \ldots, R_{n}|S\rangle\). Take for instance the profile from the paradox of voting in Section 1: