 Approval voting only modifies rather than enriches the informational basis of social choice. Here, individuals indicate which alternatives they approve of, where ‘approving’ can mean something like saying ‘yes’ to an alternative, or ‘good’, or ‘satisfactory’. Each individual can approve of as many or as few alternatives as he or she wishes. This partitions the set of alternatives into two subsets: the approved and the non-approved ones. Alternatives are not fully ranked from top to bottom. Formally, for each individual \(i \in N\), let \(A_i\) be the subset of \(X\) consisting of those alternatives which individual \(i\) approves of. Then the set \(X\setminus A_i\) contains the non-approved alternatives. Call \(A_i\) individual \(i\)’s approval ballot. The task is to find a way of aggregating any given profile of approval ballots, \(\langle A_1, A_2 , \ldots ,A_n\rangle\), into a collective outcome, which also takes the form of a subset of \(X\), consisting of the collectively approved or winning alternatives. Thus an aggregation rule is a function \(f\) that assigns to each profile \(\langle A_1, A_2 , \ldots ,A_n\rangle\) (typically in the domain of all possible approval ballots) a subset of \(X\), denoted \(f(A_1, A_2 , \ldots ,A_n)\).