 The only information contained in an ordinal utility representation is how the agent whose preferences are being represented orders options, from least to most preferable. This means that if \(u\) is an ordinal utility function that represents the ordering \(\preceq\), then any utility function \(u'\) that is an ordinal transformation of \(u\)—that is, any transformation of \(u\) that also satisfies the biconditional in (1)—represents \(\preceq\) just as well as \(u\) does. Hence, we say that an ordinal utility function is unique only up to ordinal transformations.