I agree that the problem is not fully specified, and that this is a common feature of many decision problems in the literature. On my view, the ability to notice which details are missing and whether they matter is an important skill in analyzing informally-stated decision problems. Hypothesizing that the alleged circumstances are impossible, and noticing that the counterfactual behavior of various agents is uncertain, are important parts of operating FDT at least on the sorts of decision problems that appear in the literature.
At a glance, it looks to me like the omitted information is irrelevant to all three decision algorithms under consideration, and doesn’t change the ordinal ranking of payouts (except to collapse the rankings in some edge cases). That said, I completely agree that the correct answer to various (other, afaict) decision problems in the literature is to cry foul and point to a specific piece of decision-relevant underspecification.
The omitted information seems very relevant. An EDT agent decides to do the action maximizing
Sum P(outcomes | action) U(outcomes, action).
With omitted information, the agent can’t compute the P() expressions and so their decision is undetermined. It should already be obvious from the problem setup that something is wrong here: equality of Omega and Omicron’s numbers is part of the outcomes, and so arguing for an EDT agent to condition on that is suspicious to say the least.
The claim is not that the EDT agent doesn’t know the mechanism that fills in the gap (namely, Omega’s strategy for deciding whether to make the numbers coincide). The claim is that it doesn’t matter what mechanism fills the gap, because for any particular mechanism EDT’s answer would be the same. Thus, we can figure out what EDT does across the entire class of fully-formal decision problems consistent with this informal problem description without worrying about the gaps.
I agree that the problem is not fully specified, and that this is a common feature of many decision problems in the literature. On my view, the ability to notice which details are missing and whether they matter is an important skill in analyzing informally-stated decision problems. Hypothesizing that the alleged circumstances are impossible, and noticing that the counterfactual behavior of various agents is uncertain, are important parts of operating FDT at least on the sorts of decision problems that appear in the literature.
At a glance, it looks to me like the omitted information is irrelevant to all three decision algorithms under consideration, and doesn’t change the ordinal ranking of payouts (except to collapse the rankings in some edge cases). That said, I completely agree that the correct answer to various (other, afaict) decision problems in the literature is to cry foul and point to a specific piece of decision-relevant underspecification.
The omitted information seems very relevant. An EDT agent decides to do the action maximizing
Sum P(outcomes | action) U(outcomes, action).
With omitted information, the agent can’t compute the P() expressions and so their decision is undetermined. It should already be obvious from the problem setup that something is wrong here: equality of Omega and Omicron’s numbers is part of the outcomes, and so arguing for an EDT agent to condition on that is suspicious to say the least.
The claim is not that the EDT agent doesn’t know the mechanism that fills in the gap (namely, Omega’s strategy for deciding whether to make the numbers coincide). The claim is that it doesn’t matter what mechanism fills the gap, because for any particular mechanism EDT’s answer would be the same. Thus, we can figure out what EDT does across the entire class of fully-formal decision problems consistent with this informal problem description without worrying about the gaps.