Why is the evaluation using a condition that isn’t part of the problem?
For clarity. The fact that the ordinal ranking of decision theories remains the same regardless of how you fill in the unspecified variables is left (explicitly) as an exercise.
This doesn’t seem true, at least in the sense of strict ranking? In the EDT case: if Omega’s policy is to place a prime in Box 1 whenever Omicron chooses a composite number (instead of matching Omicron when possible), then it predicts the EDT agent will choose only Box 1 and so is a stable equilibrium. But since it also always places a different prime whenever Omicron chooses a prime, EDT never sees matching numbers and so always one-boxes, therefore its expected earnings are no less than FDT
The variables with no specified value in the template given aren’t the problem. The fact that the template has the form that it does is the problem. That form is unjustified.
The only information we have about Omega’s choices is that choosing the same number as Omicron is sometimes possible. Assuming that its probability is the same—or even nonzero—for all decision theories is unjustified, because Omega knows what decision theory the agent is using and can vary their choice of number.
For example, it is compatible with the problem description that Omega never chooses the same number as Omicron if the agent is using CDT. Evaluating how well CDT performs in this scenario is then logically impossible, because CDT agents never enter this scenario.
Like many extensions, variations, and misquotings of well-known decision problems, this one opens up far too many degrees of freedom.
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.
For clarity. The fact that the ordinal ranking of decision theories remains the same regardless of how you fill in the unspecified variables is left (explicitly) as an exercise.
This doesn’t seem true, at least in the sense of strict ranking? In the EDT case: if Omega’s policy is to place a prime in Box 1 whenever Omicron chooses a composite number (instead of matching Omicron when possible), then it predicts the EDT agent will choose only Box 1 and so is a stable equilibrium. But since it also always places a different prime whenever Omicron chooses a prime, EDT never sees matching numbers and so always one-boxes, therefore its expected earnings are no less than FDT
The variables with no specified value in the template given aren’t the problem. The fact that the template has the form that it does is the problem. That form is unjustified.
The only information we have about Omega’s choices is that choosing the same number as Omicron is sometimes possible. Assuming that its probability is the same—or even nonzero—for all decision theories is unjustified, because Omega knows what decision theory the agent is using and can vary their choice of number.
For example, it is compatible with the problem description that Omega never chooses the same number as Omicron if the agent is using CDT. Evaluating how well CDT performs in this scenario is then logically impossible, because CDT agents never enter this scenario.
Like many extensions, variations, and misquotings of well-known decision problems, this one opens up far too many degrees of freedom.
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.