 Two points about the concept of an aggregation rule are worth noting. First, under the standard definition, an aggregation rule is defined extensionally, not intensionally: it is a mapping (functional relationship) between individual inputs and collective outputs, not a set of explicit instructions (a rule in the ordinary-language sense). Different sets of instructions could in principle give rise to the same mapping from inputs to outputs. Secondly, an aggregation rule is defined for a fixed set of individuals \(N\) and a fixed decision problem, so that majority rule in a group of two individuals is a different mathematical object from majority rule in a group of three. One potential disadvantage of this way of defining an aggregation rule is that it makes it harder to determine how a given aggregation rule is to be extended to inputs outside the function’s formal domain. By contrast, if we were given an explicit set of instructions, it might be easier to infer, for instance, how these are to be extended from the case of \(n\) individuals and three alternatives to the case of \(n + 1\) individuals and four alternatives.