以理服人 To win people over with reason. A dictionary cites Lai Chuanzhu’s memoir of the time around the Gutian Conference. Mao, the Party representative, “took entirely the attitude of persuasion and education, of winning people over with reason.”
心服口服 Convinced in the heart and in words. To be sincerely persuaded.
有理走遍天下，无理寸步难行 With reason on one’s side, one can go anywhere. Without it, one cannot take a step.
秀才遇着兵，有理说不清 When a scholar meets a soldier, he has reason but cannot make it understood.