A Better Framing of Newcomb’s Problem

While I disagree with James M. Joyce on the correct solution to Newcomb’s problem, I agree with him that the standard framing of Newcomb’s problem (from Nozick 1969) can be improved upon. Indeed, I very much prefer the framing he gives in chapter 5.1 of The Foundations of Causal Decision Theory, which (according to Joyce) is originally due to JH Sobel:

Suppose there is a brilliant (and very rich) psychologist who knows you so well that he can predict your choices with a high degree of accuracy. One Monday as you are on the way to the bank he stops you, holds out a thousand dollar bill, and says: “You may take this if you like, but I must warn you that there is a catch. This past Friday I made a prediction about what your decision would be. I deposited $1,000,000 into your bank account on that day if I thought you would refuse my offer, but I deposited nothing if I thought you would accept. The money is already either in the bank or not, and nothing you now do can change the fact. Do you want the extra $1,000?” You have seen the psychologist carry out this experiment on two hundred people, one hundred of whom took the cash and one hundred of whom did not, and he correctly forecast all but one choice. There is no magic in this. He does not, for instance, have a crystal ball that allows him to “foresee” what you choose. All his predictions were made solely on the basis of knowledge of facts about the history of the world up to Friday. He may know that you have a gene that predetermines your choice, or he may base his conclusions on a detailed study of your childhood, your responses to Rorschach tests, or whatever. The main point is that you now have no causal influence over what he did on Friday; his prediction is a fixed part of the fabric of the past. Do you want the money?

I prefer this over the standard framing because people can remember the offer and the balance of their bank account better than box 1 and box 2. For some reason, I also find it easier to explain this thought experiments without referring to the thought experiment itself in the middle of the explanation. So, now whenever I describe Newcomb’s problem, I start with Sobel’s rather than Nozick’s version.

Of course, someone who wants to explore decision theory more deeply also needs to learn about the standard version, if only because people sometimes use “one-boxing” and “two-boxing” (the options in Newcomb’s original problem) to denote the analogous choices in other thought experiments. (Even if there are no boxes in these other thought experiments!) But luckily it does not take more than a few sentences to describe the original Newcomb problem based on Sobel’s version. You only need to explain that Newcomb’s problem replaces your bank account with an opaque box whose content you always keep; and puts the offer into a second, transparent box. And then the question is whether you stick with one box or go home with both.

Peter Thiel on Startup Culture

I recently read Peter Thiel’s Zero to One. All in all, it is an informative read. I found parts of ch. 10 on startup culture particularly interesting. Here’s the section “What’s under Silicon Valley’s Hoodies”:

Unlike people on the East Coast, who all wear the same skinny jeans or pinstripe suits depending on their industry, young people in Mountain View and Palo Alto go to work wearing T-shirts. It’s a chliché that tech workers don’t care about what they wear, but if you look closely at those T-shirts, you’ll see the logos of the wearers’ companies—and tech workers care about those very much. What makes a startup employee instantly distinguishable to outsiders is the branded T-shirt or hoodie that makes him look the same as his co-workers. The startup uniform encapsulates a simple but essential principle: everyone at your company should be different in the same way—a tribe of like-minded people fiercely devoted to the company’s mission.

Max Levchin, my co-founder at PayPal, says that statups should make their early staff as personally similar as possible. Startups have limited resources and small teams. They must work quickly and efficiently in order to survive, and that’s easier to do when everyone shares an understanding of the world. The early PayPal team worked well together because we were all the same kind of nerd. We all loved science ficion: Cryptonomicon was required reading, and we preferred the capitalist Star Wars to the communist Star Trek. Most important, we were all obsessed with creating a digital currency that would be controlled by individuals instead of governments. For the company to work, it didn’t matter what people looked like or which country they came from, but we needed every new hire to be equally obsessed.

In the section “Of cults and consultants” of the same chapter, he goes on:

In the most intense kind of organization, members hang out only with other members. They ignore their families and abandon the outside world. In exchange, they experience strong feelings of belonging, and maybe get access to esoteric “truths” denied to ordinary people. We have a word for such organizations: cults. Cultures of total dedication look crazy from the outside, partly because the most notorious cults were homicidal: Jim Jones and Charles Manson did not make good exits.

But entrepeneurs should take cultures of extreme dedication seriosuly. Is a lukewarm attitude to one’s work a sign of mental health? Is a merely professional attitude the only sane approach? The extreme opposite of a cult is a consulting firm like Accenture: not only does it lack a distinctive mission of its own, but individual consultants are regularly dropping in and out of companies to which they have no long-term connection whatsover.


The best startups might be considered slightly less extreme kinds of cults. The biggest difference is that cults tend to be fanatically wrong about something important. People at a successful startup are fanatically right about something those outside it have missed. You’re not going to learn those kinds of secrets from consultants, and you don’t need to worry if your company doesn’t make sense to conventional professionals. Better to be called a cult—or even a mafia.

Is it a bias or just a preference? An interesting issue in preference idealization

When taking others’ preferences into account, we will often want to idealize them rather than taking them too literally. Consider the following example. You hold a glass of transparent liquid in your hand. A woman walks by, says that she is very thirsty and would like to drink from your glass. What she doesn’t know, however, is that the water in the glass is (for some reason not relevant to this example) poisoned. Should you allow her to drink? Most people would say you should not. While she does desire to drink out of the glass, this desire would probably disappear upon gaining knowledge of its content. Therefore, one might say that her object-level preference is to drink from the glass, while her idealized preference would be not to drink from it. There is not too much literature on preference idealization, as far as I know, but, if you’re not already familiar with it, anyway, consider looking into “Coherent Extrapolated Volition“.

Preference idealization is not always as easy as inferring that someone doesn’t want to drink poison, and in this post, I will discuss a particular sub-problem: accounting for cognitive biases, i.e. systematic mistakes in our thinking, as they pertain to our moral judgments. However, the line between biases and genuine moral judgments is sometimes not clear.

Specifically, we look at cognitive biases that people exhibited in non-moral decisions, where their status as a bias to be corrected is much less controversial, but which can explain certain ethical intuitions. By offering such an error theory of a moral intuition, i.e. an explanation for how people could erroneously come to such a judgment, the intuition is called into question. Defendants of the intuition can respond that even if the bias can be used to explain the genesis of that moral judgment, they would nonetheless stick with that moral intuition. After all, the existence of all our moral positions can be explained by non-moral facts about the world – “explaining is not explaining away”. Consider the following examples.

Omission bias: People judge consequences of inaction as less severe than those of action. Again, this is clearly a bias in some cases, especially non-moral ones. For example, losing $1,000 by not responding to your bank in time is just as bad as losing $1,000 by throwing them out of the window. A business person who judges the two equivalent losses equally will ceteris paribus be more successful. Nonetheless, most people distinguish between act and omission in cases like the fat man trolley problem.

Scope neglect: The scope or size of something often has little or no effect on people’s thinking when it should have. For example, when three groups of people were asked what they would pay for interventions that would affect 2,000, 20,000, or 200,000 birds, people were willing to pay roughly the same amount of money irrespective of the number of birds. While scope neglect seems clearly wrong in this (moral) decision, it is less clearly so in other areas. For example, is a flourishing posthuman civilization with 2 trillion inhabitants really twice as good as one with 1 trillion? It is not clear to me whether answering “no” should be regarded as a judgment clouded by scope neglect (caused, e.g., by our inability to imagine the two civilizations in question) or a moral judgment that is to be accepted.

Contrast effect (also see decoy effect, social comparison bias, Ariely on relativity, mere subtraction paradox, Less-is-better effect): Consider the following market of computer hard drives, from which you are to choose one.

Hard drive model Model 1 Model 2 Model 3 (decoy)
Price $80 $120 $130
Capacity 250GB 500GB 360GB

Generally, one wants to expend as little money as possible while maximizing capacity. In the absence of model 3, the decoy, people may be undecided between models 1 and 2. However, when model 3 is introduced into the market, it provides a new reference point. Model 2 is better than model 3 in all regards, which increases its attractiveness to people, even relative to model 1. That is, models 1 and 2 are judged by how they compare with model 3 rather than by their own features. The effect clearly exposes an instance of irrationality: the existence of model 3 doesn’t affect how model 1 compares with model 2. When applied to ethical evaluation, however, it calls into question a firmly held intrinsic moral preference for social equality and fairness. Proponents of fairness seem to assess a person’s situation by comparing it to that of Bill Gates rather than judging each person’s situation separately. Similar to how the overpriced decoy changes our evaluation of the other products, our judgments of a person’s well-being, wealth, status, etc. may be seen as irrationally depending on the well-being, wealth, status, etc. of others.

Other examples include peak-end rule/extension neglect/evaluation by moments and average utilitarianism; negativity bias and caring more about suffering than about happiness; psychological distance and person-affecting views; status-quo bias and various population ethical views (person-affecting views, the belief that most sentient beings that already exist have lives worth living); moral credential effect; appeal to nature and social Darwinism/normative evolutionary ethics.

Decision Theory and the Irrelevance of Impossible Outcomes

(This post assumes some knowledge of the decision theory of Newcomb-like scenarios.)

One problem in the decision theory of Newcomb-like scenarios (i.e. the study of whether causal, evidential or some other decision theory is true) is that even the seemingly obvious basics are fiercely debated. Newcomb’s problem seems to be fundamental and the solution obvious (to both sides), and yet scholars disagree about its resolution. If we already fail at the basics, how can we ever settle this debate?

In this post, I propose a solution. Specifically, I will introduce a very plausible general principle that decision rules should abide by. One may argue that settling on powerful general rules (like the one I will propose) must be harder than settling single examples (like Newcomb’s problem). However, this is not universally the case. Especially in decision theory, we should expect general principles to be especially convincing because a common defense of two-boxing in Newcomb’s scenario is that Newcomb’s problem is just a weird edge case in which rationality is punished. By introducing a general principle that CDT (or, perhaps, EDT) violates, we can prove the existence of a general flaw.

Without further ado, the principle is: The decisions we make should not depend on the utilities assigned to outcomes that are impossible to occur. To me this principle seems obvious and indeed it is consistent with expected value calculations in non-Newcomb-like scenarios: Imagine having to deterministically choose an action from some set A. (We will ignore mixed strategies.) The next state of the world is sampled from a set of states S via a distribution P and depends on the chosen action. We are also given a utility function U, which assigns values to pairs of a state and an action. Let a be an action and let s be a possible state. If P(s,a) = 0 (or P(s|a)=0 or P(s given the causal implications of a)=0 – we assume all of these to be the equivalent in this non-Newcomb-like scenario), then it doesn’t matter what U(s,a) is, because in an expected value calculation, U(s,a) will always be multiplied with P(s,a)=0. That is to say, any expected value decision rule gives the same outcome regardless of U(s,a). So, expected value decision rules abide by this principle at least in non-Newcomb-like scenarios.

Let us now apply the principle to a Newcomb-like scenario, specifically to the prisoner’s dilemma played against an exact copy of yourself. Your actions are C and D. Your opponent is the “environment” and can also choose between C (cooperation) and D (defection). So, the possible outcomes are (C,C), (C,D), (D,C) and (D,D). The probabilities P(C,D) and P(D,C) are both 0. Applied to this Newcomb-like scenario, the principle of the irrelevance of impossible alternatives states that our decision should only depend on the utilities of (C,C) and (D,D). Evidential decision theory behaves in accordance with this principle. (I leave it as an exercise to the reader to verify this.) Indeed, I suspect that it can be shown that EDT generally abides by the principle of the irrelevance of impossible outcomes. The choice of causal decision theory on the other hand does depend on the utilities of the impossible outcomes U(D,C) and U(C,D). Remember that in the prisoner’s dilemma the payoffs are such that U(D,x)>U(C,x) for any action x of the opponent, i.e. no matter the opponent’s choice it is always better to defect. This dominance is given as the justification for CDT’s decision to defect. But let us say we increase the utility of U(C,D) such that U(C,D)>U(D,D) and decrease the utility of U(D,C) such that U(D,C)>U(C,C). Of course, we must make these changes for the utility functions of both players so as to retain symmetry. After these changes, the dominance relationship is reversed: U(C,x)>U(D,x) for any action x. Of course, the new payoff matrix  is not that of a prisoner’s dilemma anymore – the game is different in important ways. But when played against a copy, these differences do not seem significant, because we only changed the utilities of outcomes that were impossible to achieve anyway. Nevertheless, CDT would switch from D to C upon being presented with these changes, thus violating the principle of the irrelevance of impossible outcomes. This is a systematic flaw in CDT: Its decisions depend on the utility of outcomes that it can already know to be impossible.

The principle of the irrelevance of impossible outcomes can be used beyond arguing against CDT. As you may remember from my post on updatelessness, sensible decision theories will precommit to give Omega the money in the counterfactual mugging thought experiment. (If you don’t remember or haven’t read that post in the first place, this is a good time to catch up, because the following thoughts are based on the ideas from the post.) Even EDT, which ignores the utility of impossible outcomes, would self-modify in this way. However, the decision theory resulting from such self-modification violates the principle of the irrelevance of impossible outcomes. Remember that in counterfactual mugging, you give in because this was a good idea to precommit to when you didn’t yet know how the coin came up. However, once you know that the coin came up the unfavorable way, the positive outcome, which gave you the motivation to precommit, has become impossible. Of course, you only give in to counterfactual mugging if the reward in this now impossible branch is sufficiently high. For example, there is no reason to precommit to give in if you lose money in both branches. This means that once you have become updateless, you violate the principle of the irrelevance of impossible outcomes: your decision in counterfactual mugging depends on the utility you assign to an outcome that cannot happen anymore.

Omoto and Snyder (1995) on motivations to volunteer

Omoto and Snyder (1995) is only a single study on volunteerism with a sample of 116 AIDS volunteers, but the results are quite interesting nonetheless. In a Snyder, Omoto and Crain (1999) they summarize:

Motivations [..] foreshadow the length of time that volunteers stay active (Omoto and Snyder, 1995). In one longitudinal study, volunteers who were more motivated […] when they began their work were more likely to still be active 2.5 years later. Interestingly, relatively self-focused motivations (i.e., personal development, understanding, esteem enhancement) were more predictive of volunteers’ duration of service than those that were more other-focused (i.e., values and beliefs, community concern). That is, volunteers remained active to the extent that they more strongly endorsed relatively self-focused motivations for their work. Other-focused motives, even though they may provide considerable impetus for people to become volunteers, may not sustain volunteers faced with the tough realities and personal costs of volunteering.

The study also has other interesting results. For instance, “90% of respondents expected to continue volunteering with the agency for at least another year. In actuality, 54% of the volunteers were still active 1 year later, whereas only 16% of them were still active 2.5 years later.” (Omoto and Snyder 1995, p. 677)

I haven’t looked into the literature much more but this seems to be exactly the kind of research one should turn to if I wanted to design a successful social movement.

Thoughts on Updatelessness

[This post assumes knowledge of decision theory, as discussed in Eliezer Yudkowsky’s Timeless Decision Theory.]

One interesting feature of some decision theories that I used to be a bit confused about is “updatelessness”. A thought experiment suitable for explaining the concept is counterfactual mugging: “Omega [a being to be assumed a perfect predictor and absolutely trustworthy] appears and says that it has just tossed a fair coin, and given that the coin came up tails, it decided to ask you to give it $100. Whatever you do in this situation, nothing else will happen differently in reality as a result. Naturally you don’t want to give up your $100. But Omega also tells you that if the coin came up heads instead of tails, it’d give you $10000, but only if you’d agree to give it $100 if the coin came up tails.”

There are various alternatives to this experiment, which seem to illustrate a similar concept, although they are not all structurally isomorphic. For example Gary Drescher discusses Newcomb’s problem with transparent boxes in ch. 6.2 and retribution in ch. 7.3.1 of his book Good and Real. Another relevant example is Parfit’s hitchhiker.

Of course, you win by refusing to pay. To strengthen the intuition that this is the case, imagine that the whole world just consists of one instance of counterfactual mugging and that you already know for certain that the coin came up tails. (We will assume that there is no anthropic uncertainty about whether you are in a simulation used to predict whether you would give in to counterfactual mugging. That is, Omega used some (not necessarily fully reliable) way of figuring out what you’d do. For example, Omega may have created you in a way that implies giving in or not giving in to counterfactual mugging.) Instead of giving money, let’s say thousands of people will be burnt alive if you give in while millions could have been saved if the coin had come up heads. Nothing else will be different as a result of that action. I don’t think there is any dispute over what choices maximizes expected utility for this agent.

The cause of dispute is that agents who give in to counterfactual mugging win in terms of expected value as judged from before learning the result of the coin toss. That is, prior to being told that the coin came up tails, an agent better be one that gives in to counterfactual mugging. After all, this will give her 0.5*$10,000 – 0.5*$100 in expectation. So, there is a conflict between what the agent would rationally want her future self to choose and what is rational for her future self to do. (Another example of this is the absent-minded driver.) There is nothing particularly confusing about the existence of problems with such inconsistency.

Because being an “updateless” agent, i.e. one that makes the choice based on how it would have wanted the choice to be prior to updating, is better for future instances of mugging, sensible decision theories would self-modify into being updateless with regard to all future information they receive. (Note that being updatelessness doesn’t mean that one doesn’t change one’s behavior based on new information, but that one goes through with the plans that one would have committed oneself to pursue before learning that information.) That is, an agent using a decision theory like (non-naive) evidential decision theory (EDT) would commit to giving in to counterfactual mugging and similar decision problems prior to learning that it ended up in the “losing branch”. However, if the EDT agent already knows that it is in the losing branch of counterfactual mugging and hasn’t thought about updatelessness, yet, it wouldn’t give in, although it might (if it is smart enough) self-modify into being updateless in the future.

One immediate consequence of the fact that updateless agents are better off is that one would want to program an AI to be updateless from the start. I guess it is this sense in which people like the researchers of the Machine Intelligence Research Institute consider updatelessness to be correct despite the fact that it doesn’t maximize expected utility in counterfactual mugging.

But maybe updateless is not even needed explicitly if the decision theory can take over epistemics. Consider the EDT agent, to whom Omega explains counterfactual mugging. For simplicity’s sake, let us assume that Omega explains counterfactual mugging and only then states which way the coin came up. After the explanation, the EDT agent could precommit, but let’s assume it can’t do so. Now, Omega opens her mouth to tell the EDT agent how the coin came up. Usually, decision theories are not connected to epistemics, so upon Omega uttering the words “the coin came up heads/tails”, Bayesian updating would run its due course. And that’s the problem, since after Bayesian updating the agent will be tempted to reject giving in, which is bad from the point of view of before learning which way the coin came up. To gain good evidence about Omega’s prediction of oneself, EDT may update in a different way to ensure that it would receive the money if the coin came up heads. For example, it could update towards the existence of both branches (which is basically equivalent to the updateless view of continuing to maintain the original position). Of course, self-modifying or just using some decision theory that has updatelessness built in is the much cleaner way to go.

Overall, this suggests a slightly different view of updatelessness. Updatelessness is not necessarily a property of decision theories. It is the natural thing to happen when you apply acausal decision theory to updating based on new information.

Environmental and Logical Uncertainty: Reported Environmental Probabilities as Expected Environmental Probabilities under Logical Uncertainty

[Readers should be familiar with the Bayesian view of probability]

Let’s differentiate between environmental and logical uncertainty, and, consequently, environmental and logical probabilities. Environmental probabilities are the ones most of my readers will be closely familiar with. They are about the kinds of things that you can’t figure out even if you have infinite amounts of computing power until you have seen enough evidence.

Logical uncertainty is a different kind of uncertainty. For example, what is the 1,000th digit of the mathematical constant e? You know how e is defined. The definition uniquely implies what the 1,000th digit of e is and yet you’re uncertain as to the value of the 1,000th digit of e. Perhaps, you would assign logical probabilities: the probability that the 1,000th digit of e is 0 is 10%. For more detail, consider the MIRI paper Questions of Reasoning Under Logical Uncertainty by Nate Soares and Benja Fallenstein.

Now, I would like to draw attention to what happens when an agent is forced to quantify its environmental uncertainty, for example, when it needs to perform an expected value calculation. It’s good to think in terms of simplified artificial minds rather than humans, because human minds are so messy. If you think that any proper artificial intelligence would obviously know the values of its environmental probabilities, then think again: Proper ways of updating environmental probabilities based on new evidence (like Solomonoff induction) tend to be incomputable. So, an AI usually can’t quantify what exact values it should assign to certain environmental probabilities. This may remind you of the 1,000th digit of e: In both cases, there is a precise definition for something, but you can’t infer the exact numbers from that definition, because you and the AI are not intelligent enough.

Given that computing the exact probabilities is so difficult, the designers of an AI may fail with abandon and decide to implement some computable mechanism for approximating the probabilities. After all, “probabilities are subjective” anyway… Granted, an AI probably needs an efficient algorithm for quantifying its environmental uncertainty (or it needs to be able to come up with such a mechanism on its own). Sometimes you have to quickly compute the expected utility of a few actions, which requires numeric probabilities. However, any ambitious artificial intelligence should also keep in mind that there is a different, more accurate way of assigning these probabilities. Otherwise, it will forever and always be stuck with the programmers’ approximation.

The most elegant approach is to view the approximation of the correct environmental probabilities as a special case of logical induction (i.e. reasoning over logical uncertainty) possibly without even designing an algorithm for this specific task. On this view, we have logical meta-probability distributions over the correct environmental probabilities. Consider, for example, the probability P(T|E) that we assign to some physical theory T given our evidence E. There is some objectively correct subjective probability P(T|E) (assuming, for example, Solomonoff’s prior probability distribution), but the AI can’t calculate its exact value. It can, however, use logical induction to assign probabilities to statements like P(T|E) probabilities densities to statements like P(T|E)=0.368. These probabilities may be called logical meta-probabilities – they are logical probabilities about the correct environmental probabilities. With these meta-probabilities all our uncertainty is quantified again, which means we can perform  expected value calculations.

Let’s say we have to decide whether to taking action a. We know that if we take action a, one of the outcomes A, B and C will happen. The expected value of a is therefore

E[a] = P(A|a)*u(A) + P(B|a)*u(B) + P(C|a)*u(C),

where u(A), u(B) and u(C) denote the utilities an agent assigns to outcomes A, B and C, respectively. To find out the expected value of a given our lack of logical omniscience, we now calculate the “expected expected value”, where the outer expectation operator is a logical one:

E[E[a]] = E[P(A|a)*u(A) + P(B|a)*u(B) + P(C|a)*u(C)] = E[P(A|a)]*u(A) + E[P(B|a)]*u(B) + E[P(C|a)]*u(C).

The expected values E[P(A|a)], E[P(B|a)] and E[P(C|a)] are the expected environmental probabilities of the outcomes given a and can be computed using integrals. (In practice, these will have to be subject to approximation again. You can’t apply logical induction if you want to avoid an infinite regress.) These expected probabilities are the answers an agent/AI would give to questions like, “What probability do you assign to A happening?”

This view of reported environmental probabilities makes sense of a couple of intuitions that we have about environmental probabilities:

  • We don’t know which probabilities we assign to a given statement, even if we are convinced of Bayes’ theorem and a certain prior probability distribution.
  • We can update our environmental probability assignments without gathering new evidence. We can simply reconsider old evidence and compute a more accurate approximation of the proper Bayesian updating mechanism (e.g. via logical induction).
  • We can argue about probabilities with others and update. For example, people can bring new explanations of the data to our attention. This is not Bayesian evidence (ignoring that the source of such arguments may reveal its biases and beliefs through such argumentation). After all, we could have come up with these explanations ourselves. But these explanations can shift our logical meta-probabilities. (Formally: what external agents tell you can probably be viewed as (part of) a deductive process, see MIRI’s newest paper on logical induction.)

Introducing logical uncertainty into assigning environmental probabilities doesn’t solve the problem of assigning appropriate environmental probabilities. MIRI has described a logical induction algorithm, but it’s inefficient.