Often used to describe a gradual process in which someone is convinced over time. It wasn't easy, but I eventually brought him round to my way of thinking.
Pro Tip 2/3
Changing Stance
Suggests a shift from a firm stance, stressing the effort involved in changing someone's mind. After much debate, she was finally brought round to the new policy.
Pro Tip 3/3
Emotional Appeal
Can imply using emotional arguments to sway someone's opinion or decision. He was adamant, but the heartfelt stories from the community brought him round.