All of the committees are in my sig, but I'll list them again here:
Assembly Leader: One nation, executive function that ensures the charter is upheld and the game runs smoothly.
Board of First Nations (3):
Holds significant power, especially in the electing of delegates to other committees, and in the veto. Must have 3 nations for a tie-breaker.
Security Council (5):
Admits and ejects nations from the Assembly, punishes delegates for misdeeds and exerts the influence of the Assembly's reputation on non-member nations. Must have an odd number for tiebreaker, must have more than 3 so that the Board of First Nations can't elect itself to be the only ones in this committee.
Policy Committee (5):
Makes changes to the charter and elects nations to the Board of First Nations if there is a vacancy. Must have an odd number for tiebreaker, must have more than 3 so that the Board of First Nations can't elect itself to be the only ones in this committee.
Economic Council (5):
Handles trade agreements, and creates agencies and advisory boards. No reason for it to have fewer members than the previous committees because it is less prestigious.
Humanitarian Committee (6):
Creates programs, deploys EC-created agencies, and creates resolutions that member nations must abide by. Has more members than the other committees because it is less prestigious.
Committee to Promote Justice (7):
Issues legal opinions and rules on cases submitted to the UA. Must have an odd number for tiebreaker. Has 7 instead of 5 because it is less prestigious, and because the U.S. Supreme Court has 9.
General Assembly:
Every nation is a member of this committee. It passes budgets and submits suggestions to other committees. It also has veto power on some resolutions made by other committees.
The idea of the structure is thus: The committees are supposed to be made up of different people, so that a nation has power in some areas and relies on other nations in others. No nation is in more than 4 of the 6 committees, and most nations are only in 2 or 3. Resolutions are supposed to be drafted by small committees, and then argued out in the General Assembly chamber by every nation, just like in the House. This ensures a balance of powers. It could, conceivably, work with only 10 nations, but it simply doesn't work with anything lower, and I firmly believe that 12 is the minimum optimal number. Ideally, every nation would only be on one or two committees, and diplomacy between nations would become more important as each nation would only have sway over a few things that the UA is capable of doing.
It has nothing to do with realism. This is game play. It's how the game is meant to be played.