I guess you should give the same reward, to the most convincing argument, regardless of whether it really convined you or not. It motivates the other people to do their best, and does not influence you in making the decision.

I don't like the idea of overcompensating for biases. I understand the reason behind it, but I am afraid that this approach creates its own specific problems. For example, how much should you overcompensate? I mean, if overcompensating is good, then the more you overcompensate, the more virtuous you are...