Sorry to bring in MWI - it is how I model actions and decisions, but it's not necessary to the conversation.

you want to win such a debate

Agreed, and I was unclear above. Many times you want to "win" by convincing people to follow you, even if you are encouraging untruth in them. You still benefit by knowing the truth, as it will help you manipulate them. I'd argue that this drifts from rationality to ethics pretty quickly, but you're absolutely right: the point of debate may not be rational truth-seeking in the first place.