 Here it is a little more formally: Suppose \(\mathcal{O}\) is a set of options, \(\mathcal{W}\) is the set of possible worlds, and \(\mathfrak{U}\) is a disutility function. Then, if \(o^*\) is an option, and there is no \(w^*\) in \(\mathcal{W}\) such   \[\mathfrak{U}(o^*, w^*) = \min \{\mathfrak{U}(o, w) : o \in \mathcal{O}\ \&amp;\ w \in \mathcal{W}\}\] (when this minimum exists),  then \(o^*\) is irrational.