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.
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.