I think the key here is that threatening a guy with access to the police and the 800-lb gorilla of the state causes him to become defensive, and he likely won’t listen even if you’re right.

Appealing to his humanity and emotions in a calm and respectful way MIGHT have a better effect.

But crucial is appealing to his INCENTIVES. Simply put, he has a chance to be royally embarrassed by this case. Publicity could bring scorn on HIM for keeping someone who is engaging in peaceful civil disobedience in jail. While the hunger strike is Sam’s choice, it is a way to force this discussion into the media, where it can do damage to this judge.

As Chris pointed out in this post, people act in their perceived interest. I think this judge may not see that to back down in this case is in his interest, but it may be a very costly misjudgment if he’s wrong.

As with most things, it’s about personal incentives. If you make the judge understand that what you want is actually in his best interest, it’s win-win. If you try to fight him, it will inevitably be win-lose, and you can be sure the judge doesn’t want to be on the losing side of that battle.

You can’t say that it had zero effect. The fact he received it and likely read it has had some effect on the man though not in a way that is visible to us. Besides… what other options are there? You can be civil and inundate the people involved with requests to release him (legal and personally), break him out of jail or do nothing. Seems the middle of the road here is the most appropriate.