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I think that, in the end, even Juror #3 was convinced of reasonable doubt.
He seems almost to give in at the end simply because everyone else has changed their votes. When the others realize that some of his disdain for the boy is based on the fact that his relationship with his own son is dysfunctional, he simply folds under the pressure. He does not want to give in, but he has no real reason to fight against the rest of the jury once they have all changed their votes.