Variety among preferences is the result, in Arrow’s account, of the different standards by which we assess our options. Our preferences depend on our “tastes” in personal consumption but importantly, for social choice, they also depend on our socially directed “values”. Now, we are to some extent free to have various tastes, values, and preferences; and we are free, also, to have these independently of one another. Any individual can have a range of preferences, then, and for any given sets of people and alternatives there are many possible preference profiles. One profile \(\langle R_{i}\rangle\) represents the preferences of these people among their alternatives in, if you will, one possible world.  Another profile \(\langle R^*_{i}\rangle\) represents preferences of the same people, and among the same alternatives, but in another possible world where their tastes and values are different.