Leadership is not a popularity contest it is about accomplishing the mission.
You clearly articulate your expectations, you set the standard, and you set the example for performance. Frankly, you don’t care what they think of you because you are leading them where they need to go.
Should you be concerned about what your subordinates think and say about your leadership?
Does your subordinates opinion of your leadership have an impact on their effectiveness?
Does your subordinates opinion of your leadership have an impact on your effectiveness as a leader?
Does your opinion of your boss’ leadership impact your effectiveness?
