This is fun! I agree with others that the added question of Is it better to kill an ally with probability P or die myself with probability Q makes the whole problem slightly less straightforward. In an extreme case, if I just want to survive, I might as well always call an airstrike, missing the whole teaching of this problem. Maybe you could tweak the scenario a bit to remove this dilemma?
The jankiness here is deliberate (which doesn’t preclude it from being a mistake). My class on Bayesianism is intended to also be a class on the limitations thereof: that it fails when you haven’t mapped out the entire sample space, that it doesn’t apply ‘cleanly’ to any but the most idealised use cases, and that once you’ve calculated everything out you’ll still be left with irreducible judgement calls.
This is fun! I agree with others that the added question of Is it better to kill an ally with probability P or die myself with probability Q makes the whole problem slightly less straightforward. In an extreme case, if I just want to survive, I might as well always call an airstrike, missing the whole teaching of this problem. Maybe you could tweak the scenario a bit to remove this dilemma?
The jankiness here is deliberate (which doesn’t preclude it from being a mistake). My class on Bayesianism is intended to also be a class on the limitations thereof: that it fails when you haven’t mapped out the entire sample space, that it doesn’t apply ‘cleanly’ to any but the most idealised use cases, and that once you’ve calculated everything out you’ll still be left with irreducible judgement calls.