The Empyraeum is effectively a military state with one Emperor or Hegèmon at the head and the balance of power controlled by the unquestionable threat of the Kalshodar and the unspoken one of a dragon.
Alexander was educated by Aristotle, however, and democracy matters to him. Though he was raised in a monarchy, he was always certain that 'modern' theories of Athenian democracy held merit and were the ideal state of existence for a healthy and content society. Rumours that he became a devotee of Plato's ideas of Republic have never been confirmed.
What began as a purely military endeavour could not remain so for long, Alexander soon realised that. Soldiers can conquer but it is hearts and minds he needed to conquer in order to hold what he had taken because fear only motivates in the short term. Of course, some of his later decisions in Persia were unpopular with many of his more direct-minded soldiers. Politics will always make the ordinary man and women nervous but Alexander was raised and educated to be a politician; many say he was a both a natural and very much ahead of his time.
He developed the strategies he had used in Persia - of leaving the existing local officials in power or electing new ones with the assistance of the population, of marrying soldiers and functionaries into the local population among others - during the famous Bloodless Conquest and perfected it into the Empyraen Senate upon returning to Alexandria years later.
The Senate and attached political bodies was made up of members from every state, nation, kingdom, and territory within the Empyraeum. All decisions, all concerns, all laws went through them. All voices were heard and no one Senator or bloc could gain too much influence because Alexander had the final and irrefutable veto.
When Alexander vanished, the Stewards held all of his powers and continued his traditions. Most lacked his mind and native skills, though. That is until Lupernikes was unexpectedly elected.
It was Lupernikes who began to separate the military from politics and turn them into an independent body in their own right, at the call of all who needed them but answerable only to the Steward. He drew up the Constitution which, mostly, detailed the things he could not take it into his mind to do, like use the military inside of the Empyraeum without a two-thirds Senate vote or ever attack any member without a fair and lawful trial.
This is why, when Apatèon and his group began to gain influence, Lupernikes withdrew the Kalshodar. He still believed in the dream that was the Empyraeum even if the Empyraeum itself appeared to be forgetting.