"Thanks for listening" strikes me as about right: they're taking an effort to seriously consider what you have to say, which is worth thanking regardless of whether they eventually agree with you. Thanking them for coming to a particular conclusion seems like it could disincentivize honest truth-seeking.
(Do make a point of thanking people if they listen to you, consider your ideas seriously, and eventually decide that they still disagree.)
This only works in the case where Alice went to considerable effort to provide a well-organized argument, as in your example. I'm not sure what to do in casual conversation.
Would it be supercilious to thank someone for updating? I know I would feel uncomfortable doing it, but I often feel the urge to do so anyway.
There seems to be something vicious about thanking them. My own estimation of my own belief has not changed in these situations. I feel fairly satisfied that the other has considered my view and has shakily come to agree with it. I worry it would be a little like saying 'screw your opinion, now you see I'm right.'
However:
It is both rational and polite to thank them. The gentlemen's agreement of rationality allows for one person to be wrong and not lose face at all. When someone concedes something to me (a point) I typically feel the need to thank them.
What do you think?