 The Condorcet winner criterion defines a social choice rule, where, for each profile \(\langle R_1, R_2 , \ldots ,R_n\rangle\), \(f(R_1, R_2 , \ldots ,R_n)\) contains every alternative in \(X\) that wins or at least ties with every other alternative in pairwise majority voting. As shown by Condorcet’s paradox, this may produce an empty choice set. By contrast, plurality rule and the Borda count induce social choice rules that always produce non-empty choice sets. They also satisfy the following basic conditions (the last for \(|X| \ge 3)\):