When times are good and the ship of state only needs to sail straight, mentally healthy people function well as political leaders. But in times of crisis and tumult, those who are mentally abnormal, even ill, become the greatest leaders. We might call this the Inverse Law of Sanity.

Consider Neville Chamberlain. Before the Second World War, he was a highly respected businessman from Birmingham, a popular mayor and an esteemed chancellor of the exchequer. He was charming, sober, smart—sane.

Winston...