 The present way of representing an aggregation rule helps us see how many possible aggregation rules there are. Suppose there are \(k\) profiles in the domain of admissible inputs (in the present example, \(k = 2^n\), since each of the \(n\) individuals has two choices, with abstention disallowed). Suppose, further, there are \(l\) possible social decisions for each profile (in the example, \(l = 3\), allowing ties). Then there are \(l^k\) possible aggregation rules: the relevant table has \(k\) rows, and in each row, there are \(l\) possible ways of specifying the final entry (the collective decision). Thus the number of possible aggregation rules grows exponentially with the number of admissible profiles and the number of possible decision outcomes.