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The Executive Committee Director is much like the President or Prime Minister of the Xenosaga universe. This person chairs the Executive Committee and is the most powerful person (politically) in the entire Universe. Because of the enormous influence this person has over federal policy making, he or she must be elected into office by a majority vote from the entier Federation Government, all 500,000 representative members. The Executive Committee Director runs the government from Fifth Jerusalem, the Federation's capital planet.
Wilhelm, the CEO of Vector Industries was once Executive Committee Director but steped down from the office several years before the start of Episode I. It is unknown whether he took a leave of absence from Vector while he chaired the Committee or not. It is hard to imagine that a sitting government would allow a corporate president to sit in an elected office while still running his corporation.