Sometimes saying why you changed your mind can help. In more detail than "his position seemed better than mine". But sometimes it takes doing some action that is in line with the new idea in order for other people to think you may be serious.
Another thing that may help is to wait some time before telling the person. "Later that day" makes it seem like a quick turnaround. Waiting until the next day to say something like "I've had some time to think about it, and I think you were right about X" might make more sense to the other person and lessen the incredulity.
Also, it depends on what your past history has been with this person, and what they have observed in your behaviour.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.