Because the cognitive complexity levels of each of the parties and of the mediator can create either effective matches or unproductive clashes in conflict resolution, I recently have posted on my blogs several times about those levels. (See links below.)
Theories about what increases cognitive complexity are numerous. Most of the theorists seem to agree that developing higher complexity takes time; it also involves experiencing situations which enable a person to feel more and more comfortable with uncertainty and ambiguity. The benefits of complexity include the ability to take multiple perspectives, the already-mentioned comfort with ambiguity, skill in strong and complete analysis, and self-awareness. All of those benefits are helpful in conflict resolution; disparate levels of these traits in the people involved (including the mediator) can hamper or prevent resolution. Therefore it is important for mediators to understand these differences, assess them, and know what to do when they are driving behavior.
And now a surprise: Another method of promoting cognitive complexity may be reading fiction! If you want to learn more,