I’d love to know if there are established formal approaches to this.
You should probably look at Jaynes’s book “Probability Theory: the Language of Science”. In particular, I think that the discussion there dealing with the Widget Problem and with Laplace’s Rule of Succession may be relevant to your question.
And just as it gets really interesting, that chapter ends. There is no solution provided for stage 4 :/
Odd. The printed book has another page and a half for that chapter, including the solution to Stage 4. (No surprises in the solution—same as stage 3 except you start with 40 fewer Green widgets.)
You should probably look at Jaynes’s book “Probability Theory: the Language of Science”. In particular, I think that the discussion there dealing with the Widget Problem and with Laplace’s Rule of Succession may be relevant to your question.
And just as it gets really interesting, that chapter ends. There is no solution provided for stage 4 :/
Odd. The printed book has another page and a half for that chapter, including the solution to Stage 4. (No surprises in the solution—same as stage 3 except you start with 40 fewer Green widgets.)