 The most convenient way to represent problems with multiple preference aspects is to introduce a vector \(\langle \succcurlyeq_1 ,\ldots ,\succcurlyeq_n \rangle\) whose elements are the preference relations we have to take into account. For simplicity, we can assume that all these preferences are complete (or we can treat incompleteness as indifference). We can call such a vector conflict free if and only if it has no elements \(\succcurlyeq_k\) and \(\succcurlyeq_m\) such that \(X \succ_k Y\) and \(Y \succ_m X\) for any alternatives \(X\) and \(Y\). If \(\langle \succcurlyeq_1 ,\ldots ,\succcurlyeq_n \rangle\) is conflict free, then we can define a combined preference relation \(\succcurlyeq\) such that (1) \(X\succ Y\) if there is some \(\succcurlyeq_k\) such that \(X\succ_k Y\), (2) \(Y\succ X\) if there is some \(\succcurlyeq_k\) such that \(Y\succ_k X\), and (3) otherwise \(X\sim Y\). This is a plausible construction for conflict free preferences, since the combined preference relation does not contradict any of the strict preferences expressed in the component vectors. 