A preference profile is a list \(\langle R_{1}, \ldots, R_{n}\rangle\) of weak orderings of the set \(X\) of alternatives, one for each of the people \(1, \ldots, n\). The list of three individual orderings in the paradox of voting is an example of a preference profile for the alternatives \(A\), \(B\), and \(C\) and people 1, 2, and 3. A profile is a representation of the individual preferences of everybody who will be consulted in the choice among the alternatives. It is in the form of profiles that Arrow’s aggregation procedures receive information about individual preferences. Often it is convenient to write \(\langle R_{i}\rangle\) instead of \(\langle R_{1}, \ldots, R_{n}\rangle\). Other profiles are written \(\langle R^*_{i}\rangle\), and so on.