Accordingly, the preferences of individual people are represented in Arrow’s framework by binary relations \(R_{i}\) among the alternatives: \(xR_{i}y\) means that individual \(i\) weakly prefers alternative \(x\) to alternative \(y\). That is, either \(i\) strictly prefers \(x\) to \(y\), or else \(i\) is indifferent between them, finding them equally good. Each individual preference relation \(R_{i}\) is assumed to be connected (for all alternatives \(x\) and \(y\), either \(xR_{i}y\), or \(yR_{i}x\), or both) and transitive (for all \(x\), \(y\) and \(z\), if \(xR_{i}y\) and \(yR_{i}z\), then \(xR_{i}z\)). That these relations have these structural properties was, for Arrow, a matter of the “rationality” of the preferences they represent; for further discussion, see the entries on Preferences and Philosophy of Economics. Connected, transitive relations are called weak orderings. They are “weak” in that they allow ties—in this connection, indifference. 