 Some agendas have two or more of these properties. The agendas in our ‘doctrinal paradox’ and ‘discursive dilemma’ examples are both non-simple and pair-negatable. To illustrate, take the agenda from the expert-panel example, \(X = \{p, \neg p, p\rightarrow q, \neg(p\rightarrow q), q, \neg q\}\). It is non-simple, because it has a minimal inconsistent subset of size 3, namely \(\{p, p\rightarrow q, \neg q\}\), and it is pair-negatable, because it has a minimal inconsistent subset, namely \(Y = \{p, p\rightarrow q, \neg q\}\), in which we can find a pair of propositions, namely \(\{p, \neg q\}\), such that if we replace these with their negations in \(Y\), the resulting set is consistent (note that \(\{\neg p, p\rightarrow q, q\}\) is consistent). An example of an agenda which has all three combinatorial properties is the preference agenda, \(X = \{\)‘\(x\) is preferable to \(y\)’, ‘\(y\) is preferable to \(x\)’, ‘\(x\) is preferable to \(z\)’, ‘\(z\) is preferable to \(x\)’, \(\ldots \}\), assuming preferability is transitive and complete and there are three or more alternatives \(x, y, z, \ldots\), over which preferability is defined. The following result holds: