…probability is not about knowledge, it’s about belief. Read Ramsey.
That’s the setup. The setup wants you to accept that if you look at all the people who decided to one-box, most of them got $1,000,000, and if you look at all the people who decided to two-box, most of them got $1,000. So this isn’t the success rate, but it’s the spirit rather than the letter of the setup.
It would be akin to bickering that we know the success rate but we don’t know the detail about the success rate specifically for OB predictions and the success rate for TB predictions. Those could be different indeed but the spirit of the question implies that you should consider them to be the same.
Then the question is impossible to answer. It asks us to make a probability-based choice then tells us what we must believe.
As I said above, doing frequentist probability without knowing the probability space is not a paradox.
If anything it’s a good way to highlight how impoverished frequentist probability is.
Then the question is impossible to answer. It asks us to make a probability-based choice then tells us what we must believe.
What do you mean it’s impossible to answer?
I thought it was unspecified because not enough info, I tell you here’s how to read it and how to fill in the gaps and you tell me it’s impossible to answer because it tells us what we must believe?
That stuff doesn’t apply here. We are not in such a situation. It’s not like that weird Monty Hall thing.
This scenario is a departure from truth. Its ability contorts and bends what actually happens in the world. Ignoring that premise will not lead you to good results in this scenario.
In the real world, I don’t do things this way.
Just as, if I were playing D&D, and the way to put out fires is to yell “GO AWAY!!!” at it, that’s how I will put out a fire in the game. Asking me how that works out in the rest of life is meaningless.
The Newcomb setup is indeed contrived since structures that are formally similar to it seldom arise in everyday life. Nonetheless, a structurally similar analogy can help clarify what is really at stake. Consider a job interview with an employer who is skilled enough at reading candidates to predict, on the basis of their rational profile, not just their general dispositions but their actual behavior in specific situations, and makes their hiring decision accordingly. During the interview, the candidate discovers an opportunity to cheat in a way that would secure them a guaranteed bonus: either an additional hiring bonus if they are offered the job, or a financial compensation from the interviewer even if they are not. Since the bonus accrues regardless of the hiring outcome, taking it appears to be a dominating strategy. Whatever the interviewer has already decided before the interview took place, the candidate is always better off by that amount if they cheat. And yet the near-perfect interviewer has already predicted whether the candidate will yield to this temptation, and only hires candidates they have predicted will not cheat. The candidate who resists foregoes the bonus but walks away with the job; the one who cheats pockets the small gain but doesn’t get hired. CDT, applied naively, would say: the hiring decision is already made, so my behavior now is causally inert with respect to it. I might as well take the bonus. This is the CDT reasoning applied to the letter and it is worth pausing to see exactly where it leads us astray.
What makes this analogy imperfect (and what makes the version of the Newcomb setup where the predictor tracks the agent’s full rational profile especially striking) is the fact that the predictor tracks the agent’s reasoning process so closely that the candidate cannot “hide” behind a performance or a surface-level strategy, as one might in a real interview. It is as if the interviewer could read the candidate’s thoughts in real time, except that, in this Newcomb parallel, the reading is accomplished in advance. This might seem to suggest that the agent has a mysterious power to reach back and change the past. But that is not quite the right way to put it. Past physical events, including the predictor’s bodily motions of filling or not filling the opaque box, are indeed fixed in advance of the agent’s deliberation. But what makes those events count as the intended outcome of the agent’s rational decision is not fixed independently of that decision. The link between the predictor’s prior action and the agent’s eventual choice is irreducibly normative: it is a link between two exercises of rational agency that share the same intelligible source. The predictor did not cause the agent’s deliberation to unfold as it did, nor did past physical states of the universe do so. They merely foreshadowed it. What determines the rational significance of the predictor’s action, and hence what the agent actually walks away with, is the agent’s own deliberative process. CDT’s mistake is to treat the rational description of the outcome as already settled once the physical events are settled. But that is precisely what the Newcomb setup, in the version where the predictor reliably tracks rational agency, shows to be false.
The usual Newcomb setup introduces an unusual causal chain to link the agent’s deliberative process with the intended outcome, enabling the predictor to set up the outcome in advance. This is why it appears to challenge CDT and also why it appears to vindicate naive evidentialism. But the medical variations (like the smoker’s lesion case) where a gene independently causes both a craving and a disease show why evidentialist reasoning is generally unreliable, since in that case the agent’s deliberation is bypassed entirely rather than tracked. Once you attend carefully to this distinction in causal structure, you can have the best of both worlds: act rationally and secure the intended outcome. And you gain a practically useful diagnostic tool. To choose correctly between one-boxing and two-boxing, you need to ask precisely what it is that the predictor is tracking: raw dispositions that bypass reasoning (where two-boxing is correct) or the exercise of rational agency itself (where one-boxing is correct).
Do I know whether I am the clone or not? And do I care about the other version of myself? Answer those two questions, and I will respond to your game 1. I have not looked at the other games yet, because I must understand this one first.
I’ll simplify again.
If your decision counts as evidence of the predictor’s choice, then you should take box B since deciding to do so is confirmation that there will be £1,000,000 in it.
If your decision now is independent of the predictor’s prior choice then you should take both boxes since this maximises outcomes given uncertainty.
So the only relevant probability is the probability that your decision is evidence of the predictor’s prior choice.
This depends on the mechanism by which this choice is made (since we’re told it’s not 100%)
Probability is about one’s degree of belief in the absence of knowledge (otherwise all probabilities would be either 1 or 0).
We have a degree of belief about absolutely everything, even if 50/50.
Therefore whether or not we’re told the mechanism makes no difference at all to whether or not we have degrees of belief about what it might be.
And our degree of belief is what determines the rationality of CDT vs EDT.
If your decision now is independent of the predictor’s prior choice then you should take box boxes since this maximises outcomes given uncertainty.
What do you mean by ‘independent’ and by ‘count as evidence’? I could see strong interpretation and weak interpretations of both.
If independent just means your decision now can go both ways whatever the predictor predicted, which is just saying the predictor isn’t perfect then yes that’s the Version 1 or the original version of the problem and as you say you should TB.
No, and neither does the clone.
You ought care that if you’re not the clone then the clone’s decision factors into your reward.
Note that the clone doesn’t receive any reward; it is destroyed after making a choice. It’s choice is just used to predict your choice in Game 1 and influences your reward in Games 2 and 3.
If (3) is rejected, then unobserved events that are associated with Player’s past can be regarded in some way as being determined by Player’s present observations, as per delayed choice experiments in Quantum Mechanics.
Provided Player and Opponent cannot utilise information from the future to create logical contradictions, all is good. This is the case here, since Player is unaware of what Opponent predicted; hence Player cannot act in such a way as to contradict Opponent’s “earlier” decision; nonetheless, Player can regard his present decision as influencing Opponent’s earlier decision without implying a contradiction.
The outcome of our strange Newcomb game without counterfactual definiteness can be simulated by repeatedly playing trials of a Newcome game in the ordinary fashion until as and when Opponent successfully predicts Player’s action, and using only the outcome of this final round as the result of our game.
Notice that in the final round, Player’s action “caused” the Opponent’s prediction in the sense that Player’s action contributed to the termination of the game that in turn decided what Opponent’s prediction was. The actions of Player and Opponent in the final round illustrate the meaning of “Quantum Handshake” in Transactional Quantum Mechanics.
I didn’t read the entirety of your post because it reduces to the above.
It doesn’t matter what he is tracking. What matters is, has he already tracked it, or not? And if he has tracked it, then I must ask: in what direction does causality flow?
You may say that, in a way, it kind of flows both ways. You may say that future and past states are entangled in a mutually causative way, which is a form of retrocausality. I would say that determinism is necessarily a view of causality as flowing in both directions of time.
Because determinism reduces causality to logic, and logical biconditional implications go both ways. So, if you believe in a perfect predictor and thus determinism, and/or you believe in bi-directional causality with predictors whose past states are entangled with your present/future actions, then yes, of course, one-boxing is right.
But I don’t have that view of causality. I believe in indeterminism, and I believe in the strict unidirectionality of causality. I think this is true, and therefore rational and typically beneficial to believe. In V1 of the Newcomb Game, this happens to be a losing belief in Phase 1. In Phase 2 however, it is a winning belief.
I believe causality runs one way. Therefore, I believe the following things:
- Applying CDT is always best.
- Believing in CDT is usually best.
The case when believing in CDT is not best is when that belief is itself punished, unbeknownst to the believer. This is what is happening in Version 1 of the Newcomb Game. In Version 2, believing in CDT is still punished, but not as harshly. As a believer in CDT in V2, my punishment is that I need to do extra work, to set up a contract that allows me to one-box in a way that is logically consistent with my beliefs. There is no way for me to reliably one-box non-consistently with my beliefs, because my beliefs to a great degree determines my actions.
Note that the application of CDT is always beneficial in this framework. Even when I find a way to one-box in V2 of the game, I am still applying CDT. And the extra cost I incur due to this is not due to my application of CDT, but rather my belief in it. The predictor punishes me for my belief in, not my application of, CDT. Or well, this is the view that follows from the unidirectionality of causality. Drop that that view of unidirectionality, and the boundaries between Phase 1 and Phase 2 become blurry.
@Sime I am tagging you here because you seem to be suggesting the same thing. If you depart from the unidirectionalty of causality, then one-boxing is right. And I actually respect that position far more than the position of believing in the unidirectionality of causality, and yet nonetheless subscribing to one-boxing. The former position is an esoteric one requiring extraordinary evidence. The latter is, however, simply incoherent and illogical. Irrational, in fact.
Consider a job interview with an employer who is skilled enough at reading candidates to predict, on the basis of their rational profile, not just their general dispositions but their actual behavior in specific situations, and makes their hiring decision accordingly. During the interview, the candidate discovers an opportunity to cheat in a way that would secure them a guaranteed bonus: either an additional hiring bonus if they are offered the job, or a financial compensation from the interviewer even if they are not. Since the bonus accrues regardless of the hiring outcome, taking it appears to be a dominating strategy. Whatever the interviewer has already decided before the interview took place, the candidate is always better off by that amount if they cheat. And yet the near-perfect interviewer has already predicted whether the candidate will yield to this temptation, and only hires candidates they have predicted will not cheat. The candidate who resists foregoes the bonus but walks away with the job; the one who cheats pockets the small gain but doesn’t get hired. CDT, applied naively, would say: the hiring decision is already made, so my behavior now is causally inert with respect to it. I might as well take the bonus. This is the CDT reasoning applied to the letter and it is worth pausing to see exactly where it leads us astray.
CDT here is entirely correct if we accept the interviewer has already decided before the interview. You might be conflating phase 1 (before the interview, when we may be able to change our rational profile) and phase 2 (during the interview).
The thing that causes the employer not to hire is not the fact that they cheated, but his rational profile. So the three following things are true all at once and recommended by CDT:
- Once in the interview, all the candidates win more by cheating, so cheating is the rational decision. (considering phase 2 alone)
- Before the interview, every candidate should change their rational profile to appear as one who doesn’t cheat if possible. (considering phase 1 alone)
- If for some reason, the only way to successfully appear as one who doesn’t cheat in phase 1 requires that one doesn’t cheat in phase 2, then the rational choice is indeed to appear as one who doesn’t cheat and to not cheat.
The cloning just adds an extra layer of our beliefs about mechanisms because now we have to consider our beliefs about the mechanism by which the cloning took place.
So, consider the cloning perfect and we’re back to square one with the ‘real’ you (as if such a thing made any sense at all with perfect cloning), having some belief about how this game really works.
What I’m saying is that it’s that belief which determines the rationality of choosing EDT or CDT, and once you’ve chosen EDT or CDT, the course of action is trivially obvious from there.
If one truly believes the pub is at the end of the road, it is rational to go to the end of the road to get there. This is independent of whether the pub actually is at the end of the road.
Nonsense. CDT is a methodology one chooses to employ. Despite what the ‘T’ stands for, it isn’t a theory that has a truth value or not, something that is open to a falsification test like any actual theory is.
An example where it wins over EDT would be nice. There must be some, similar to how this Newcomb was designed to distinguish the opposite.
Again the assertion of it having a truth value, and that we deny it.
@Michael’s post 169 outlines a pure local causal scenario that implements Newcomb’s thing, all without paradox or any weird backwards causation or mere correlation.
1 is not stated. It is explicity that the predictor is nearly infallible, quite compatible with the clone scenario from post 169.
2. also seems kind of irrelevant. The exercise can be played just fine with or without whatever one considers ‘free choice’ as distinct from ‘choice’. I will admit that the clone thing doesn’t work if the agent isn’t physical and thus lacking in the clone. So we can assume naturalism say.
3. I don’t buy into counterfactuals, but in a classical scenario, it doesn’t seem to have any relevance. The exercise seems totally classical and doesn’t seem to involve anything funny like the box being in superposition of having money or not. I challenge you to come up with a workable example for the predictor leveraging that to get his result.
I can thwart the predictor by using uncaused quantum effects to make my choice, but there’s no utility in that strategy.
We are concluding that, yes, even if 3 is false. As I said, this is a classical exercise.
I suspect that your argument is used to prove that the predictory cannot be completely infallible, but the OP correctly says “near-perfect”.
I agree that CDT could be falsified if we could prove retro-causality is present at the macroscopic level. We make decisions at the macroscopic level, so if retro-causality is completely restricted to the nanoscopic level, it is irrelevant.
Anyways, CDT is just pure logic, assuming the unidirectionality of causality at the macroscopic level.
If you assume the contrary, then EDT becomes correct and one-boxing becomes correct. If that is your position, then we can instead discuss macroscopic retro-causality. That’s a great discussion!
But if you believe in macroscopic unidirectional causality, then you have no choice but to adhere to CDT, lest you have a self-contradictory view of reality.
Agreed, but this isn’t a marginal qualification. It is the standard Newcomb case. A predictor whose reliability rests on tracking the agent’s rational profile as it bears on the specific decision just is a predictor for whom the only way to successfully appear as one who doesn’t cheat requires actually not cheating. Your “if for some reason” framing treats this as an exotic edge case, but it is the central case: what makes the predictor reliable in the non-medical Newcomb scenario is precisely their sensitivity to how the agent will actually deliberate when the moment arrives.
So I agree with your point 3 but I want to stress its implications. The predictor’s anticipation tracks the agent’s actual decision with some significant degree of reliability, in a manner that anticipates it. But the crucial point is that this foreknowledge is not the causal ground of the agent’s decision. The causal ground rather is the agent’s own rational assessment of whether cheating (or two-boxing) is warranted in their actual circumstances. Rational considerations are genuinely efficacious in producing action. An agent’s deliberative judgment, in my view, is a real causal contributor to the outcome, not something epiphenomenal that merely accompanies it. This is what I mean by rational causation. It is not the implausible claim that whatever rationally ought to happen will happen, but the more modest claim that when an agent acts for reasons those reasons are part of what brings the action about. The predictor’s success, in Newcomb’s scenario, is parasitic on this. They can anticipate the outcome only because the agent’s reasoning genuinely determines it.
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I was asking for why my ‘proof’ of the incompatibility of (1) and (2) failed in regards to (3).
Provided Player and Opponent cannot utilise information from the future to create logical contradictions, all is good. This is the case here, since Player is unaware of what Opponent predicted; hence Player cannot act in such a way as to contradict Opponent’s “earlier” decision; nonetheless, Player can regard his present decision as influencing Opponent’s earlier decision without implying a contradiction.
I am not sure to understand this. Even assuming (3), player is still unaware of what Opponent predicted so (1) and (2) aren’t incompatible with (3).
The outcome of our strange Newcomb game without counterfactual definiteness can be simulated by repeatedly playing trials of a Newcome game in the ordinary fashion until as and when Opponent successfully predicts Player’s action, and using only the outcome of this final round as the result of our game.
Can it? Cause here there is a chance the game doesn’t stop. This shows that even in the “meta” game, the predictor isn’t infallible. There isn’t necessarily a final round.
why are you talking about cloning? Am I missing something?
What I’m saying is that it’s that belief which determines the rationality of choosing EDT or CDT, and once you’ve chosen EDT or CDT, the course of action is trivially obvious from there.
What belief? My previous message asked you to clarify some terms.
Michael’s post 169 outlines a pure local causal scenario that implements Newcomb’s thing, all without paradox or any weird backwards causation or mere correlation.
Indeed and the rational choice is (b) in other words TB.