 When the preference relation over \(\mathcal{A}\) is cyclical, neither \(\mathbf{C}^B\) nor \(\mathbf{C}^L\) may be a relational choice function for \(\mathcal{A}\). In the simplest case, with a cyclical preference \(A\succ B\succ C\succ A\), \(\mathbf{C}^B(A,B,C) = \mathbf{C}^L(A,B,C) = \varnothing\). Schwarz (1972) therefore proposes a third relational choice function, which operates even on the basis of cyclical preferences.  Its basic idea is to select elements that are not dominated by non-cyclical preference.