Boolean functions assign an aggregate binary output to any vector of binary components. We study (j,k)-functions, which assign an aggregate output, among k choices, to any vector with j choices for each index or component. The binary case, achieved for j=2 and k=2, reduces to the Boolean context. Simple games are particular examples of Boolean functions, and (j,k)-functions can be seen as extensions of simple games. We consider distinguished subclasses of monotonic (j,k)-functions: regular, thr...
Boolean functions assign an aggregate binary output to any vector of binary components. We study (j,k)-functions, which assign an aggregate output, among k choices, to any vector with j choices for each index or component. The binary case, achieved for j=2 and k=2, reduces to the Boolean context. Simple games are particular examples of Boolean functions, and (j,k)-functions can be seen as extensions of simple games. We consider distinguished subclasses of monotonic (j,k)-functions: regular, threshold and anonymous and establish some relations among them. The case of anonymous (j,k)-functions deserves special attention: we get a closed formula to count them for j=2 and any value of k, and for k=3 and any value of j we prove an extension of May’s theorem.