 To fit this into the framework of partial belief we assume that the set of acts \(A_1, A_2, \ldots, A_n\) partition \(W\). We also assume the set of states \(S_1, S_2, \ldots, S_m\) partition \(W\). We assume that the subjective probability function assigns a probability to every state given every act. We assume that acts and states are logically independent, so that no state rules out the performance of any act. Finally, we assume that given a state of the world \(S_j\) and an act \(A_i\) there is exactly one outcome \(O_{ij}\) which is assigned a utility \(U(O_{ij})\). The ultimate counsel of rational choice theory is that agents ought to perform only those acts that maximize  expected utility. The expected utility of an act is defined as: