As explained in the section on Mars' political structure, the most important pan-Association organisation is the Martian Senate. There is also a Grand Council, but this serves mostly as a talking shop. A fuller picture of the sometimes complex interrelationship between the Quadrants and the various interstellar organisations is available here.
The Senate is responsible for oversight of government departments and the Martian Star Navy. There are a variety of senate sub-committees, but undoubtedly the most important of these is the Senate Interstellar Coordination Committee. Via the participation of the President of the Martian Union and Supreme Councillor of Q0 (see the section of Quadrant 0) as Chairman of the Committee, the ICC has become a de facto 'cabinet' and executive branch of Martian government, with the President of the Martian Union serving as a sort of 'Martian President' .
The Senate oversees the Navy and the Association Courts, while the ICC has direct oversight of the new Martian AI Detection Service (MAIDS).
Although Martian politics tends to be more personal than party political, various loose political groupings have a variety of influence throughout the different sections of the MAFC. The Liberal Welfare Party currently holds sway, but the Central Democratic Party and the Colonial Growth Faction are also strong.