The Confederacy (and the Umojans for that matter) were ruled by councils. I suppose those councils acted as a sort of cabinet and exercised authority collectively. However usually bodies such as these would be headed by a president since after all the term president comes from one who
presides over a body such as a council. Not to mention there would probably one or more people who would effectively lead such a body, often by reducing the others to mere ciphers, such as in many modern parliamentary governments. Doesn't seem they were too interested in who was actually running the Confederate government, especially since now that is been destroyed and replaced by an autocratic monarchy.