 Two common notational conventions should be mentioned. First, chains of relations can be contracted. Hence, \(A\succcurlyeq B\succcurlyeq C\) abbreviates \(A\succcurlyeq B \wedge B\succcurlyeq C\), and \(A\succ B\succ C\sim D\) abbreviates \(A\succ B \wedge B\succ C \wedge C\sim D\). Second, the ancestral symbol * is used to contract repeated uses of the same relation; hence \(\succ\)* stands for \(\succ\) repeated any finite non-zero number of times (and similarly for the other relations). Thus \(A\succ *C\) denotes that either \(A\succ C\) or there are \(B_1 \ldots B_n\) such that