 Universal domain requires the aggregation rule to cope with any level of ‘pluralism’ in its inputs. Ordering requires it to produce ‘rational’ social preferences, avoiding Condorcet cycles. The weak Pareto principle requires that when all individuals strictly prefer alternative \(x\) to alternative \(y\), so does society. Independence of irrelevant alternatives requires that the social preference between any two alternatives \(x\) and \(y\) depend only on the individual preferences between \(x\) and \(y\), not on individuals’ preferences over other alternatives. Non-dictatorship requires that there be no ‘dictator’, who always determines the social preference, regardless of other individuals’ preferences. (Note that pairwise majority voting satisfies all of these conditions except ordering.)