 For each world w in W and agent a, we define the connected component of w, also called the a-connected component if emphasizing a is important, as follows:   \[ \cc_a(w) \coloneqq \{ v\in W \mid w({\geq_a}\cup{\leq_a})^*v\} . \]   If \(\cc_a(w)=\cc_a(w)\), then we say that w and v are informationally equivalent (or that they are a-informationally equivalent). The relation \(\geq_a\) must satisfy the property of Plausibility, which consists of the following three items: