I don’t see this contradiction. In a timeless decision theory, the diagram and parameters are not the same when X is in control of resource A (at “time” T) and when X is not in control of resource A (at time T+1).
The “timeless” of the decision theory doesn’t mean that the decision theory ignores the effects of time and past decisions. Rather, it refers to a more technical (and definitely more confusing) abstraction about predictions and kind of subtly hints at a reference to the (also technical) concept of symmetry in physics.
Mainly, the point is to deflect naive reasoning in problems involving predictions or similar “time-defying” situations. The classic example is newcomblike problems, specifically Newcomb’s Problem. In these situations, acting as if your current decision were a partial cause of the past prediction, and thus of whether or not Omega/The Predictor put a reward in a box, leads to better subjective chances of finding a reward in said box. The “timeless” aspect here is that a phenomenon (the decision you make) is almost looks like it’s a cause of another (the prediction of your decision) that happened “in the past”.
In fact, however, they have a common prior cause: the state of the universe and, particularly, of the brain / processor / information of the entity making the decision, prior to the prediction. Treating it as, and calling it, “timeless” helps avoid issues where this will turn into a debate about free will and determinism.
In newcomblike problems, an event B happenes where Omega predicts whether A1 or A2 will happen, based on whether C1 or C2 is true (two possible states of the brain of the player, or outcomes of a simulation). Then, either A1 or A2 happens, based on whether C1 or C2 is true, as predicted by Omega. Since the player doesn’t have the same means as Omega to know C or B, he must decide as if A caused C which caused B, which could be roughly described as a decision causing the result of a prediction of this decision in the past.
So, back to the timeless VS sunk costs “contradiction”: In a sunk costs situation, there is no Omega, there is no C, there is no prediction (B). At the moment of decision, the state of the game in abstract is something more like: “Decision A caused Resource B to go from 5 to 3, 1B can be paid to obtain 2 utilons by making decision C1, 2B can be paid to obtain 5 utilons by making decision C2″. There’s no predictions or fancy delusions of affecting events that caused the current state. A caused B(5->3) caused (NOW) caused C. C has no causal effect on (NOW), which has no causal effect on B, which has no causal effect on A. No amount of removing the timestamps and pretending that your future decision will change how it was predicted is going to change the (NOW) state.
I could go on at length and depth, but let’s see how much of this makes sense first (i.e. that you understand and/or that I mis-explained).
I don’t see this contradiction. In a timeless decision theory, the diagram and parameters are not the same when X is in control of resource A (at “time” T) and when X is not in control of resource A (at time T+1).
The “timeless” of the decision theory doesn’t mean that the decision theory ignores the effects of time and past decisions. Rather, it refers to a more technical (and definitely more confusing) abstraction about predictions and kind of subtly hints at a reference to the (also technical) concept of symmetry in physics.
Mainly, the point is to deflect naive reasoning in problems involving predictions or similar “time-defying” situations. The classic example is newcomblike problems, specifically Newcomb’s Problem. In these situations, acting as if your current decision were a partial cause of the past prediction, and thus of whether or not Omega/The Predictor put a reward in a box, leads to better subjective chances of finding a reward in said box. The “timeless” aspect here is that a phenomenon (the decision you make) is almost looks like it’s a cause of another (the prediction of your decision) that happened “in the past”.
In fact, however, they have a common prior cause: the state of the universe and, particularly, of the brain / processor / information of the entity making the decision, prior to the prediction. Treating it as, and calling it, “timeless” helps avoid issues where this will turn into a debate about free will and determinism.
In newcomblike problems, an event B happenes where Omega predicts whether A1 or A2 will happen, based on whether C1 or C2 is true (two possible states of the brain of the player, or outcomes of a simulation). Then, either A1 or A2 happens, based on whether C1 or C2 is true, as predicted by Omega. Since the player doesn’t have the same means as Omega to know C or B, he must decide as if A caused C which caused B, which could be roughly described as a decision causing the result of a prediction of this decision in the past.
So, back to the timeless VS sunk costs “contradiction”: In a sunk costs situation, there is no Omega, there is no C, there is no prediction (B). At the moment of decision, the state of the game in abstract is something more like: “Decision A caused Resource B to go from 5 to 3, 1B can be paid to obtain 2 utilons by making decision C1, 2B can be paid to obtain 5 utilons by making decision C2″. There’s no predictions or fancy delusions of affecting events that caused the current state. A caused B(5->3) caused (NOW) caused C. C has no causal effect on (NOW), which has no causal effect on B, which has no causal effect on A. No amount of removing the timestamps and pretending that your future decision will change how it was predicted is going to change the (NOW) state.
I could go on at length and depth, but let’s see how much of this makes sense first (i.e. that you understand and/or that I mis-explained).