If the judge knows that you are trying to convince him, then there should be nothing you can do which convinces him short of committing to a penalty cost if you take a different action (which is the same as changing the payoff matrix); If I manage to commit to giving $1500 to a charity that I hate (e.g. Westboro) if I take both boxes, and communicate that commitment to the judge, then I can convince the judge that I will take one box.

I don't have to convince him of my decision process, only of my actions.