Quorum of Twelve (TRS)
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The Quorum of Twelve is a unicameral deliberative body that grants each of the Twelve Colonies one elected representative, who votes on and brings issues to be discussed. The scope of these issues, in the aftermath of the Cylon attack, is likely to be quite broad due to the lack of any other organized political bodies.
In practice, the Quorum is the counterpoint to the President of the Twelve Colonies. While the executive branch has great power, the Quorum likely needs to ratify all laws devised by the president and the cabinet. It is also able to veto presidential provisions.
First Roslin Administration
Secluded in his lab, Gaius Baltar seems unaware that he has even been nominated for the Caprican post until he is made aware of the decision.
One of the primary issues of the new Quorum was the election of a vice president as the Quorum was responsible for the confirmation of the successor to that office. If there is a tie, as is the case during the campaign of Tom Zarek and Gaius Baltar, the president was the one who casts the tie-breaking vote (Colonial Day).
This Quorum of Twelve assembled on Cloud 9.
With the loss of Cloud 9 shortly after Gaius Baltar's inauguration, the Quorum's meeting place is destroyed. A number of delegates may also have died in the disaster. The Quorum continued to meet throughout the Baltar administration until at least its surrender to the Cylons a year later on New Caprica. It appears to have been dissolved at some point during the Cylon occupation.
Zarek/Second Roslin Administration
The representatives on this Quorum include:
Upon learning of Adama's plan to enter a permanent alliance with the Rebel Cylons in exchange for access to Cylon FTL technology to be installed on all civilian ships, Zarek takes advantage of Roslin's self-imposed absence from politics and agitates the Quorum into voting that no Cylon may board a civilian ship without the permission of its people (A Disquiet Follows My Soul).
Later, Zarek collaborates with Lieutenant Felix Gaeta of Galactica to stage a mutiny which quickly turns bloody (The Oath). When the Quorum (minus Lee Adama who is at large on Galactica) doesn't support him and Cantrell orders him to leave, pointedly addressing him as the Vice President, he orders their execution by the marines outside the door. After they carry out this order, Zarek summons Gaeta who is shaken out of his naievety about Zarek's motives and mourns the resulting loss of the rebellion's perceived moral high ground (Blood on the Scales).
Instead of forming the colony-based Quorum again with new representatives, Lee Adama proposes that the Colonials are no longer defined by their home colonies but rather the respective ships they live on. President Roslin supports the idea and tasks Lee with restructuring the civilian government accordingly (No Exit).
In "Someone to Watch Over Me", its revealed that a new Quorum is being formed, but this time made up of ship's captains. It is unknown how many captains are on this new Quorum, but a Cylon representative, a Six named Sonja, has also been elected to this Quorum to represent the Rebel Basestar.