BTW South Song of the Day
Vertical Horizon, "Everything You Want" from Everything You Want (Mt. Love)

The Empire of Pictus
I'm an idiot. Erixish society has no legacy of hierarchical leadership, but some manner of government is required for accession into the Empire. What better model of (relatively) leaderless governance than the Athenian democracy, especially in its 5th and 4th century B.C. flowering before the coming of Alexander the Great's Macedonian barbarism. Modifications are of course necessary, but I feel like a dunderhead for not realizing this sooner. It's perfect!

The Privy Council
The Parliamentary Prefectures
The Emperor of Pictus - The sovereign of every world in the Empire; the other members of the Privy Council serve at the Emperor's pleasure. Since the Emperor is also Lord Prinzlo and thus holds a seat in the Parliament, she serves the dual role of monarch to whom the Council serves as advisor and the representative to the Council of the Empire's Pic and Tehl Larian populations.

The Commonwealth of Phythria
The Ambassador of the College of Abbots - Each abbot is sovereign within his cloister-laboratory (scientist-monk is the highest calling in Phythrian society, all outside labor is undertaken to subsidize scientific research) and the surrounding territory. The College is a deliberative body with no executive; the Ambassador is just that, an authorized speaker for the Abbots superior in rank to no abbot of the College in good standing.

The Shogunate of Enkariworld
The Shogun of the Enkari - The Shogun is just that, the supreme warlord of the Enkari. There is an arguable degree of democracy in Enkari society as each chieftain needs the support of his warriors and each shogun relies upon the loyalty of enough of the chieftains to maintain his supremacy.

The Aepyrian Kingdom
The King of All the Nations - The King of All the Nations sits at the head of a consultative body made up of the Kings of the Nations, each of whom sits at the head of a consultative body made up of officials in a descending and extremely formalized hierarchy of consultative bodies pertaining to any number of national, tribal, clannish, and familial loyalties. Modern Aepyrian society is very egalitarian except for the rituals of the the hierarchy leading to the King of All the Nations, who wields both executive and legislative power.

The Hsi Church
The Archbishop of the Supreme Mystery - The religious and temporal head of the Hsi Church, the Archbishop commands his people body (state) and soul (church). He is elected by the Supreme Mystery, a collegial body of the Church's highest vicars from whose ranks he is chosen.

The Republic of Jurai
The High Trustee of the Republic of Jurai - The High Trustee is elected directly by the people, separately from the legislative Chamber of Trustees, each of whom represents a specific constituency of the planet Jurai. Both the High Trustee and the Chamber fulfill specific constitutional roles, unchanged since before the Republic's accession to the Empire with one significant exception: sovereign power once resided in the Jurai people and now radiates exclusively from the Emperor.

The Democracy of the Erixish
The Archon Eponymous - Lots are drawn from a pool of volunteers who are then seconded on to a smaller pool from whom lots are again drawn up and up and up the ladder until you reach the 5,000-member Council of Archons, from whom lots are drawn to determe the Archon Eponymous, who wields no executive power but is a plenipotentiary emissary for the Archons, each of whom speaks for the pool from which his name was drawn all the way back down the ladder.

The Rylander Palatinate
The Proxy-Palatine of the Presidium - The Presidium rules the Palatinate as an elected and oligarchic despotism. In Rynlander law, the Presidum's political power is virtually absolute, the scheduling and conduct of elections being the only prominent exception. As the name Palatinate implies, the Presidium reigns at the Emperor's sufferance; since accession to the Empire, other limits on the Presidium's power have arisen, but they have been limited by the Imperial reluctance to dictate cultural mores (outside of the preservation of the sentient rights inherent to every subject of the Empire). The Proxy-Palatine is a Presidium member empowered to speak in the name of his fellows, but not ranked above them, similar to the Phythrian Ambassador.

The Empire of Many Nations
The populations of the constituent species of the Empire, in descending order (I do not have specific numbers):
Rynlander
Aepyrian
Hsi
Pic
Erixish
Enkari
Tehl Larian (so-called "Pic Larian")
Phythrian
Jurai