This might have already been said in inadequate equilibria however it was definitely not clear enough for me to understand it from their so it's not plagiarism. The outside asks, what evidence do you have that you are right and the other person is wrong. The fact that you think your right does not constitute evidence because he also thinks he's right.
My counter is that their are different levels of sureness about being correct. I can be pretty sure or absolutely certain. And the more sure I am of something the more likely it is to be true. So if I knew that I was more sure than the other person I know that it is more likely that I am right and he is wrong. However how do I know that I'm more sure than he is on this topic. The answer is simple, you don't. However you don't need to know that. Let's say that if you are more sure than you are 100 percent correct however if your exactly as sure than you are 5o percent likely to be correct. And you are 50 percent certain that you are more sure than he is. Then it is 75 percent likely that you are correct.
Even if you are both the same sure about it you can look at how often are you this sure and how often is he that sure. Let's say your this sure 1 out of 50 times and he is this sure 1 out of 30 times then its more likely that you are correct because you being sure constitutes more evidence than his being sure.
This argument is at its most powerful when you conserve it for those few times that you're absolutely sure. Where your at the most possible clarity about a thing. Because when that happens you are way more likely to be correct since you are the most possibly sure and its really unlikely he is as sure as you or even if he is its really unlikely that he is rarely as sure as this so its way more likely that you are correct
I'm my experience this feeling of absolute correctness rarely manifests but when it does i've always been correct ( I had these arguments before I learned anything about logic or philosophy and after I learned a little I found out that I had mainstream views so that's my correct metric). Its a feeling of absolute clarity, in the moment you understand it perfectly and you feel the confusion and lack of understanding of your opponent.
From here I usually find things that I set in stone are and if you disagree with them I lower you in my outside calibration but that is for another post.