The answer is the path-goal theory of leadership.
This approach involves leaders making decisions based on a series of questions that help determine the best course of action. It does not specifically address the complications of personal relationships between former colleagues and now leader/subordinate.
Leader-member relations refer to the quality of the relationship between the leader and their subordinates. While this is relevant, it does not fully encompass the broader context of how leaders can influence their subordinates' motivation and performance, which is central to the path-goal theory.
The path-goal theory of leadership, developed by Robert House, focuses on how leaders can help their subordinates achieve their goals by providing direction, support, and removing obstacles. This theory considers the leader's behavior, the characteristics of the subordinates, and the work environment. Dean's discussion about the complications of personal relationships fits well within this theory, as it addresses how leaders can adapt their style to the needs of their subordinates and the situation.
This concept is more closely related to contingency theories of leadership, such as Fiedler's Contingency Model, which suggests that the effectiveness of a leader is contingent on the match between the leader's style and the situation. While relevant, it does not specifically address the dynamics of personal relationships between former colleagues and now leader/subordinate.
Therefore, the path-goal theory of leadership is the most appropriate answer.