Why does the chief continue his pretend that he is deaf and mute, even afer his vote at the group meeting? How does this help his role as a narrator?

Pretending to be deaf and mute gives the Chief the ability to listen to everything that everyone says. People talk openly around him and so he has an almost omniscient feel in his narration. While he cannot be completely omnisicent since he cannot see into the minds of the other characters, he does bring a wider knowledge of everyone's behavior as he lives through each day that he then later describes.