 A combination of preference orderings across the individuals, \(\langle R_1, R_2 , \ldots ,R_n\rangle\), is called a profile. A preference aggregation rule, \(F\), is a function that assigns to each profile \(\langle R_1, R_2 , \ldots ,R_n\rangle\) (in some domain of admissible profiles) a social preference relation \(R = F(R_1, R_2 , \ldots ,R_n)\) on \(X\). When \(F\) is clear from the context, we simply write \(R\) for the social preference relation corresponding to \(\langle R_1, R_2 , \ldots ,R_n\rangle\).