We played around with taking learning algorithms designed for multi armed bandit problems (your action matters but not your policy) and placing them in Newcomblike environments (both your acctual action and your probability distribution over actions matters). And then we proved some stuf about their behaviour.
Not sure how usefull this is, but I think this counts as a selection theorem.
(Paper by Caspar Oesterheld, Joar Skalse, James Bell and me)
https://proceedings.neurips.cc/paper/2021/hash/b9ed18a301c9f3d183938c451fa183df-Abstract.html
We played around with taking learning algorithms designed for multi armed bandit problems (your action matters but not your policy) and placing them in Newcomblike environments (both your acctual action and your probability distribution over actions matters). And then we proved some stuf about their behaviour.
That is definitely a selection theorem, and sounds like a really cool one! Well done.