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The rule determines which members of Congress will serve as chairs and which as members of each committee is Seniority. 

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The correct answer to this open question is the following.

The rule that determines the members of Congress that will serve as chairs and which as members of each committee is the Seniority Rule.

Seniors have privileges everywhere and Congress is not the exception.  

In US politics, the Seniority Rule or Seniority system refers to the practice in Congress that gives special treatment and privileges to senior members of the Senate or the House of Representants. This means the congressmen that have served the country in Congress for a long time. These members -through the years- have become very powerful men and women that influence legislation, pick their offices in Congress and their assignments in the different committees.