The Committee of Elders is the governing body in the community. They make the laws, organize the major events and ceremonies, and assign the jobs to the children who turn 12. The running joke among the citizens is that if you ever want a rule to be changed, the Committee of Elders will not change it, but instead let the idea rot in committee. Whenever the Elders need extra guidance, they ask the Receiver for his input on an issue.
They kill people, kind of
In addition to jessecreations' answer, the Committee of Elders is also responsible for pairing up matches based on compatibility for family units.