 In Savage’s framework, acts are modelled as functions that map possible states of the world to outcomes, the consequences, if you wish, of carrying out the relevant act in the relevant state of nature. The set of acts will be denoted by \(\mathcal{A}=\{f_1, f_2,\ldots g_1, g_2 \ldots\}\), the set of states by \(\mathcal{S}=\{s_1, s_2,\ldots\}\) and the set of outcomes by \(\mathcal{X}=\{x_1, x_2,\ldots,x_n\}\). For present purposes, it can be assumed that the acts considered are simple, i.e., that their range is finite. An act will be called “constant” if and only if it maps all states onto one same outcome. Sets of states, also known as events, will be denoted by upper-case letters \(A_1, A_2,\ldots, B_1, B_2, \ldots\) etc. The set of such events will be denoted by \(\mathcal{E}\). \(E_i^f\) will denote the set of states that the act \(f\) maps onto outcome \(x_i\), i.e., \(\{s\in\mathcal{S}: f(s)=x_i\}\). It will also be useful to denote by \(fAg\) the act that maps the states in \(A\) to the same outcomes that \(f\) does and the states outside of \(A\) to the same outcomes that \(g\) does.