Negative Reflection.For prospects X and Y and a question Q, if X is not better than Y conditional on any possible answer to Q, then X is not better than Y unconditionally.
Background Independence is a weaker version of Separability. I think someone who denies Separability doesn’t have much reason to satisfy Background Independence, because I expect intuitive arguments for Background Independence (like the Egyptology objection) to generalize to arguments for Separability.
But still, either way, Russell, 2023 proves the following:
Theorem 6. Stochastic Dominance and Negative Reflection together imply that Fanaticism is false.
This rules out expected utility maximization with unbounded utility functions.
There’s also a reflection argument in Wilkinson, 2022, in his Indology Objection. Russell, 2023 generalizes the argument with a theorem:
and Russell, 2023 defines Negative Reflection based on Wilkinson, 2022′s more informal argument as follows:
Background Independence is a weaker version of Separability. I think someone who denies Separability doesn’t have much reason to satisfy Background Independence, because I expect intuitive arguments for Background Independence (like the Egyptology objection) to generalize to arguments for Separability.
But still, either way, Russell, 2023 proves the following:
This rules out expected utility maximization with unbounded utility functions.