If this institution is totally honest, and extremely accurate in making predictions, so that obeying the laws it enforces is like one-boxing in Newcomb’s problem, and somehow an institution with this predictive power has no better option than imprisonment, then yes I would be OK with it.
Please see the edit I just added to the post; it seems like my wording wasn’t precise enough. I had in mind statistical treatment of large groups, not prediction of behavior on an individual basis (which I assume is the point of your analogy with Newcomb’s problem).
I would also be ok with this… however by your own definition it would never happen in practice, except for extreme cases like cults or a rage virus that only infects redheads.
Sell patents.
(or more specifically, patent your invention and wait until someone else wants to use it. If this seems unethical, remember you will usually be blocking big evil corporations, not other inventors, and that the big evil corporations would always do the same thing to you if they could.)