EDIT: No one was doing what the post suggests, so I accepted an idea from one of the comments, and embedded my response in a comment, not the post itself
I'd like to ask this question to you, and I'll respond it myself as well.
What Is The Worst Problem You've Ever Encountered and Solved? And the One You Didn't, Yet!
Some prior considerations:
1) I mean "problem" in a very general sense, it could be a math problem, an existential problem, a social problem, an akrasia problem, a disease problem etc...
2) I'd like people to give informative/didactic responses. Try not only to state the facts, but also to help someone who'd encounter similar situations to be able to deal with them.
3) When talking about the one you didn't, give enough specifics that someone would actually be able to help you.
The general idea is to teach people how to Win by example, taking in consideration all the shortcomings of biases etc...
Well, that is all. One solved, one not yet solved. State your own issues and help others here. Someone else's rationality is always welcome.
Ok, after your clarifications: Yes, this does have a manipulative character to it. It just strikes me as a situation where the ideal honesty is simply not achievable. A group will have tacit beliefs and assumptions, there is nothing you can do about it. First come, first served. So better that you, with your rational beliefs make the case for something before someone else absent mindedly cites a cached thought created by their moralist/super irrational aunt 15 years ago, setting the moral ground into an awful downward spiral.
Also, my recommendation is to use this for beliefs in which you are the first one to believe something in a group (cryonics as a classic case), so frequently people don't even have prior believes about the matters at hand.
Finally, at an emotional level, maybe you can fathom what is it like to be 17 and different from everyone around you, think that reality is fundamentally different from what they think, and that life should be lived according to different principles than the ones that guide them, every single one of them. Every human being you have ever encountered. If you do, I think you know as well as I do how arrogance, specially in the form of disrespect for authority, may come in handy as a survival technique.
If you don't, take my word for it. Sometimes arrogance is not a weapon of choice, but a weapon of lack of choice.