A man convinced against his will
Is of the same opinion still.
It's been my experience that it's impossible to change someone else's mind. (The best you can do, in some cases, is inform someone when they're factually wrong, and even then you have to just hope for the best.) So what are arguments--or, to use the more civil term, "debates"--good for?
I've found that one of the best side effects of wholeheartedly debating something is that it helps to make very thoroughly clear to yourself what your own position is, and what you think supports it. Looking closely at this may help you change your own mind, but you'll never attribute this to the person you're debating with.
The following subjects are completely impervious to changing someone else's mind about:
Psk: I really do mean argument as in reasoned debate. If you can "sway" someone's mind they probably didn't have a rooted opinion for you to "change" to begin with.