To state the next requirements it is convenient to use some shorthand. For any given individual ordering \(R_{i}\), let \(P_{i}\) be the strict or asymmetrical part of \(R_{i}: xP_{i}y\) if \(xR_{i}y\) but not \(yR_{i}x\). Intuitively, \(xP_{i}y\) means that \(i\) really does prefer \(x\) to \(y\), in that \(i\) is not indifferent between them. Similarly, let \(P\) be the strict part of \(f\langle R_{i}\rangle\). The next condition of Arrow’s theorem is: 