A power relation is a binary relationship between coalitions that is transitive.
For coalitions \(a, b, c \in 2^N\), this means that if \(a \succ b\) and
\(b \succ c\), then \(a \succ c\).
A power relation with cycles is not transitive. A transitive closure over a power relation removes all cycles and turns it into a
transitive relation, placing all coalitions within a cycle in the same equivalence class.
If \(a \succ b \succ a\), from the symmetric definition in PowerRelation() we
therefore assume that \(a \sim b\). Similarly, if
\(a \succ b_1 \succ b_2 \succ \dots \succ b_n \succ a\), the transitive closure turns it into
\(a \sim b_1 \sim b_2 \sim \dots \sim b_n\).
transitiveClosure() transforms a PowerRelation object with cycles into a PowerRelation object without cycles.
As described above, all coalitions within a cycle then are put into the same equivalence class
and all duplicate coalitions are removed.