 Balinski and Laraki propose several conditions that a satisfactory grade aggregation rule should satisfy. In particular, they suggest that \(f\) should be (i) defined for the universal domain of all possible profiles of individual grade assignments; (ii) neutral in the familiar sense of treating all alternatives equally; (iii) anonymous in the equally familiar sense of treating all voters equally; (iv) unanimous in the sense that if all individuals assign the same grade to an alternative, this becomes the collective grade; (v) monotonic in the sense that if some individuals raise their grade for an alternative (other grades remaining equal), this doesn’t lower the resulting collective grade, and if all individuals raise the grade, this correspondingly raises the collective grade; (vi) independent of irrelevant alternatives in the sense that the collective grade for any alternative depends only on the individual grades for that alternative, not on the individual grades for other alternatives, and (vii) continuous (which becomes relevant when \(S\) is a subset of the real numbers) in the sense that small changes in the individual grades for an alternative lead only to small changes in the collective grade. A grade aggregation rule that satisfies conditions (i) to (vii) is called a social grading function.