The next condition ensures that social preferences are not based entirely on the preferences of any one person. Person \(d\) is a dictator of \(f\) if for any alternatives \(x\) and \(y\), and for any profile \(\langle\ldots, R_{d},\ldots\rangle\) in the domain of \(f\): if \(xP_{d}y\), then \(xPy\). When a dictator strictly prefers one thing to another, the society always does as well. Other people’s preferences can still influence social preferences. So can “non-welfare” features of the alternatives such as, in the case of social states, the extent to which people are equal, their rights are respected, and so on. But all these can make a difference only when the dictator is indifferent between two alternatives, having no strict preference one way or the other. The condition is now simply: