The law of effect, randomization and Newcomb’s problem

The law of effect (LoE), as introduced on p. 244 of Thorndike’s (1991) Animal Intelligence, states:

Of several responses made to the same situation, those which are accompanied or closely followed by satisfaction to the animal will, other things being equal, be more firmly connected with the situation, so that, when it recurs, they will be more likely to recur; those which are accompanied or closely followed by discomfort to the animal will, other things being equal, have their connections with that situation weakened, so that, when it recurs, they will be less likely to occur. The greater the satisfaction or discomfort, the greater the strengthening or weakening of the bond.

As I (and others) have pointed out elsewhere, an agent applying LoE would come to “one-box” (i.e., behave like evidential decision theory (EDT)) in Newcomb-like problems in which the payoff is eventually observed. For example, if you face Newcomb’s problem itself multiple times, then one-boxing will be associated with winning a million dollars and two-boxing with winning only a thousand dollars. (As noted in the linked note, this assumes that the different instances of Newcomb’s problem are independent. For instance, one-boxing in the first does not influence the prediction in the second. It is also assumed that CDT cannot precommit to one-boxing, e.g. because precommitment is impossible in general or because the predictions have been made long ago and thus cannot be causally influenced anymore.)

A caveat to this result is that with randomization one can derive more causal decision theory-like behavior from alternative versions of LoE. Imagine an agent that chooses probability distributions over actions, such as the distribution P with P(one-box)=0.8 and P(two-box)=0.2. The agent’s physical action is then sampled from that probability distribution. Furthermore, assume that the predictor in Newcomb’s problem can only predict the probability distribution and not the sampled action and that he fills box B with the probability the agent chooses for one-boxing. If this agent plays many instances of Newcomb’s problem, then she will ceteris paribus fare better in rounds in which she two-boxes. By LoE, she may therefore update toward two-boxing being the better option and consequently two-box with higher probability. Throughout the rest of this post, I will expound on the “goofiness” of this application of LoE.

Notice that this is not the only possible way to apply LoE. Indeed, the more natural way seems to be to apply LoE only to whatever entity the agent has the power to choose rather than something that is influenced by that choice. In this case, this is the probability distribution and not the action resulting from that probability distribution. Applied at the level of the probability distribution, LoE again leads to EDT. For example, in Newcomb’s problem the agent receives more money in rounds in which it chooses a higher probability of one-boxing. Let’s call this version of LoE “standard LoE”. We will call other versions, in which choice is updated to bring some other variable (in this case the physical action) to assume values that are associated with high payoffs, “non-standard LoE”.

Although non-standard LoE yields CDT-ish behavior in Newcomb’s problem, it can easily be criticized on causalist grounds. Consider a non-Newcomblike variant of Newcomb’s problem in which there is no predictor but merely an entity that reads the agent’s mind and fills box B with a million dollars in causal dependence on the probability distribution chosen by the agent. The causal graph representing this decision problem is given below with the subject of choice being marked red. Unless they are equipped with an incomplete model of the world – one that doesn’t include the probability distribution step –, CDT and EDT agree that one should choose the probability distribution over actions that one-boxes with probability 1 in this variant of Newcomb’s problem. After all, choosing that probability distribution causes the game master to see that you will probably one-box and thus also causes him to put money under box B. But if you play this alternative version of Newcomb’s problem and use LoE on the level of one- versus two-boxing, then you would converge on two-boxing because, again, you will fare better in rounds in which you happen to two-box.

RandomizationBlogPost.jpg

Be it in Newcomb’s original problem or in this variant of Newcomb’s problem, non-standard LoE can lead to learning processes that don’t seem to match LoE’s “spirit”. When you apply standard LoE (and probably also in most cases of applying non-standard LoE), you develop a tendency to exhibit rewarded choices, and this will lead to more reward in the future. But if you adjust your choices with some intermediate variable in mind, you may get worse and worse. For instance, in either the regular or non-Newcomblike Newcomb’s problem, non-standard LoE adjusts the choice (the probability distribution over actions) so that the (physically implemented) action is more likely to be the one associated with higher reward (two-boxing), but the choice itself (high probability of two-boxing) will be one that is associated with low rewards. Thus, learning according to non-standard LoE can lead to decreasing rewards (in both Newcomblike and non-Newcomblike problems).

All in all, what I call non-standard LoE looks a bit like a hack rather than some systematic, sound version of CDT learning.

As a side note, the sensitivity to the details of how LoE is set up relative to randomization shows that the decision theory (CDT versus EDT versus something else) implied by some agent design can sometimes be very fragile. I originally thought that there would generally be some correspondence between agent designs and decision theories, such that changing the decision theory implemented by an agent usually requires large-scale changes to the agent’s architecture. But switching from standard LoE to non-standard LoE is an example where what seems like a relatively small change can significantly change the resulting behavior in Newcomb-like problems. Randomization in decision markets is another such example. (And the Gödel machine is yet another example, albeit one that seems less relevant in practice.)

Acknowledgements

I thank Lukas Gloor, Tobias Baumann and Max Daniel for advance comments.

Pearl on causality

Here’s a quote by Judea Pearl (from p. 419f. of the Epilogue of the second edition of Causality) that, in light of his other writing on the topic, I found surprising when I first read it:

Let us examine how the surgery interpretation resolves Russell’s enigma concerning the clash between the directionality of causal relations and the symmetry of physical equations. The equations of physics are indeed symmetrical, but when we compare the phrases “A causes B” versus “B causes A,” we are not talking about a single set of equations. Rather, we are comparing two world models, represented by two different sets of equations: one in which the equation for A is surgically removed; the other where the equation for B is removed. Russell would probably stop us at this point and ask: “How can you talk about two world models when in fact there is only one world model, given by all the equations of physics put together?” The answer is: yes. If you wish to include the entire universe in the model, causality disappears because interventions disappear – the manipulator and the manipulated lose their distinction. However, scientists rarely consider the entirety of the universe as an object of investigation. In most cases the scientist carves a piece from the universe and proclaims that piece in – namely, the focus of investigation. The rest of the universe is then considered out or background and is summarized by what we call boundary conditions. This choice of ins and outs creates asymmetry in the way we look at things, and it is this asymmetry that permits us to talk about “outside intervention” and hence about causality and cause-effect directionality.

Futarchy implements evidential decision theory

Futarchy is a meta-algorithm for making decisions using a given set of traders. For every possible action a, the beliefs of these traders are aggregated using a prediction market for that action, which, if a is actually taken, evaluates to an amount of money that is proportional to how much utility is received. If a is not taken, the market is not evaluated, all trades are reverted, and everyone keeps their original assets. The idea is that – after some learning and after bad traders lose most of their money to competent ones – the market price for a will come to represent the expected utility of taking that action. Futarchy then takes the action whose market price is highest.

For a more detailed description, see, e.g., Hanson’s (2007) original paper on the futarchy, which also discusses potential objections. For instance, what happens in markets for actions that are very unlikely to be chosen? Note, however, that for this blog post you’ll only need to understand the basic concept and none of the minutia of real-world implementation. The above description deliberately ignores and abstracts away from these. One example of such a discrepancy between standard descriptions of futarchy and my above account is that, in real-world governance, there is often a “default action” (such as, leave law and government as is). To keep the number of markets small, markets are set up to evaluate proposed changes relative to that default (such as the introduction of a new law) rather than simply for all possible actions. I should also note that I only know basic economics and am not an expert on the futarchy.

Traditionally, the futarchy has been thought of as a decision-making procedure for governance of human organizations. But in principle, AIs could be built on futarchies as well. Of course, many approaches to AI (such as most Deep Learning-based ones) already have all their knowledge concentrated into a single entity and thus don’t need any procedure (such as democracy’s voting or futarchy’s markets) to aggregate the beliefs of multiple entities. However, it has also been proposed that intelligence arises from the interaction and sometimes competition of a large number of simple subagents – see, for instance, Minsky’s book The Society of Mind, Dennett’s Consciousness Explained, and the modularity of mind hypothesis. Prediction markets and futarchies would be approaches to (or models of) combining the opinions of many of these agents, though I doubt that the human mind functions like either of the two. A theoretical example of the use of prediction markets in AI is MIRI’s logical induction paper. Furthermore, markets are generally similar to evolutionary algorithms.1

So, if we implement a futarchy-like system in an AI, what decision theory would that AI come to implement? It seems that the answer is EDT. Consider Newcomb’s problem as an example. Traders that predict one-boxing to yield a million and two-boxing to yield a thousand will earn money, since the agent will, in fact, receive a million if it one-boxes and a thousand if it two-boxes. More generally, the futarchy rewards traders based on how accurately they predict what is actually going to happen if the agent makes a particular choice. This leads the traders to estimate the value of an action as proportional to the expected utility conditional on that action since conditional probabilities are the correct way to make predictions.

There are some caveats, though. For instance, prediction markets only work if the question at hand can eventually be answered. Otherwise, the market cannot be evaluated. For instance, in Newcomb’s problem, one would usually assume that your winnings are eventually given and thus shown to you. But other versions of Newcomb’s problems are conceivable. For instance, if you are consequentialist, Omega could donate your winnings to your favorite charity in such a way that you will never be able to tell how much utility this has generated for you. Unless you simply make estimates – in which case the behavior of the markets depends primarily on what kind of expected value (regular or causal) you will use as an estimate –, you cannot set up a prediction market for this problem at all. An example of such a “hidden” Newcomb problem is cooperation via correlated decision making between distant agents.

Another unaddressed issue is whether the futarchy can deal correctly with other problems of space-time embedded intelligence, such as the BPB problem.

Notwithstanding the caveats, EDT seems to be an inherent the way the futarchy works. To get the futarchy to implement CDT, it would have to reward traders based on what the agent is causally responsible for or based on some untestable counterfactual (“what would have happened if I had two-boxed”). Whereas EDT arises naturally from the principles of the futarchy, other decision theories require modification and explicit specification.

I should mention that this post is not primarily intended as a futarchist argument for EDT. Most readers will already be familiar with the underlying pro-EDT argument, i.e., EDT making decisions based on what will actually happen if a particular decision is made. In fact, it may also be viewed as a causalist argument against the futarchy.2 Rather than either of these two, it is a small part of the answer to the “implementation problem of decision theory”, which is: if you want to create an AI that behaves in accordance to some particular decision theory, how should that AI be designed? Or, conversely, if you build an AI without explicitly implementing a specific decision theory, what kind of behavior (EDT or CDT or other) results from it?


1. There is some literature comparing the way markets function to evolution-like selection (see the first section of Blume and Easley 1992) – i.e., how irrational traders are weeded out and rational traders accrue more and more capital. I haven’t read much of that literature, but the main differences between the futarchy and evolutionary algorithms seem to be the following. First, the futarchy doesn’t specify how new traders are generated, because it classically relies on humans to do the betting (and the creation of new automated trading systems), whereas this is a central concern in evolutionary algorithms. Second, futarchies permanently leave the power in the hands of many algorithms, whereas evolutionary algorithms eventually settle for one. This also means that the individual traders in a futarchy can be permanently narrow and specialized. For instance, there could be traders who exploit a single pattern and rarely bet at all. I wonder whether it makes sense to combine evolutionary algorithms and prediction markets. 

2. Probably futarchist governments wouldn’t face sufficiently many Newcomb-like situations in which the payoff can be tested for the difference to be relevant (see chapter 4 of Arif Ahmed’s Evidence, Decision and Causality).

A behaviorist approach to building phenomenological bridges

A few weeks ago, I wrote about the BPB problem and how it poses a problem for classical/non-logical decision theories. In my post, I briefly mentioned a behaviorist approach to BPB, only to immediately discard it:

One might think that one could map between physical processes and algorithms on a pragmatic or functional basis. That is, one could say that a physical process A implements a program p to the extent that the results of A correlate with the output of p. I think this idea goes into the right direction and we will later see an implementation of this pragmatic approach that does away with naturalized induction. However, it feels inappropriate as a solution to BPB. The main problem is that two processes can correlate in their output without having similar subjective experiences. For instance, it is easy to show that Merge sort and Insertion sort have the same output for any given input, even though they have very different “subjective experiences”.

Since writing the post I became more optimistic about this approach because the counterarguments I mentioned aren’t particularly persuasive. The core of the idea is the following: Let A and B be parameterless algorithms1. We’ll say that A and B are equivalent if we believe that A outputs x iff B outputs x. In the context of BPB, your current decision is an algorithm A and we’ll say B is an instance or implementation of A/you iff A and B are equivalent. In the following sections, I will discuss this approach in more detail.

You still need interpretations

The definition only solves one part of the BPB problem: specifying equivalence between algorithms. This would solve BPB if all agents were bots (rather than parts of a bot or collections of bots) in Soares and Fallenstein’s Botworld 1.0. But in a world without any Cartesian boundaries, one still has to map parts of the environment to parameterless algorithms. This could, for instance, be a function from histories of the world onto the output set of the algorithm. For example, if one’s set of possible world models is a set of cellular automata (CA) with various different initial conditions and one’s notion of an algorithm is something operating on natural numbers, then such an interpretation i would be a function from CA histories to the set of natural numbers. Relative to i, a CA with initial conditions contains an instance of algorithm A if A outputs x <=> i(H)=x, where H is a random variable representing the history created by that CA. So, intuitively, i is reading A’s output off from a description the world. For example, it may look at the physical signals sent by a robot’s microprocessor to a motor and convert these into the output alphabet of A. E.g., it may convert a signal that causes a robot’s wheels to spin to something like “forward”. Every interpretation i is a separate instance of A.

Joke interpretations

Since we still need interpretations, we still have the problem of “joke interpretations” (Drescher 2006, sect. 2.3; also see this Brian Tomasik essay and references therein). In particular, you could have an interpretation i that does most of the work, so that the equivalence of A and i(H) is the result of i rather than the CA doing something resembling A.

I don’t think it’s necessarily a problem that an EDT agent might optimize its action too much for the possibility of being a joke instantiation, because it gives all its copies in a world equal weight no matter which copy it believes to be. As an example, imagine that there is a possible world in which joke interpretations lead to you to identify with a rock. If the rock’s “behavior” does have a significant influence on the world and the output of your algorithm correlates strongly with it, then I see no problem with taking the rock into account. At least, that is what EDT would do anyway if it has a regular copy in that world.2 If the rock has little impact on the world, EDT wouldn’t care much about the possibility of being the rock. In fact, if the world also contains a strongly correlated non-instance3 of you that faces a real decision problem, then the rock joke interpretation would merely lead you to optimize for the action of that non-copy.

If you allow all joke interpretations, then you would view yourself in all worlds. Thus, the view may have similar implications as the l-zombie view where the joke interpretations serve as the l-zombies.4 Unless we’re trying to metaphysically justify the l-zombie view, this is not what we’re looking for. So, we may want to remove “joke interpretations” in some way. One idea could be to limit the interpretation’s computational power (Aaronson 2011, sect. 6). My understanding is that this is what people in CA theory use to define the notion of implementing an algorithm in a CA, see, e.g., Cook (2004, sect. 2). Another idea would be to include only interpretations that you yourself (or A itself) “can easily predict or understand”. Assuming that A doesn’t know its own output already, this means that i cannot do most of the work necessary to entangle A with i(H). For example, if i would just compute A without looking at H, then A couldn’t predict i very well if it cannot predict itself. If, on the other hand, i reads off the result of A from a computer screen in H, then A would be able to predict i’s behavior for every instance of H. Brian Tomasik lists a few more criteria to judge interpretations by.

Introspective discernibility

In my original rejection of the behaviorist approach, I made an argument about two sorting algorithms which always compute the same result but have different “subjective experiences”. I assumed that a similar problem could occur when comparing two equivalent decision-making procedures with different subjective experiences. But now I actually think that the behaviorist approach nicely aligns with what one might call introspective discernibility of experiences.

Let’s say I’m an agent that has, as a component, a sorting algorithm. Now, a world model may contain an agent that is just like me except that it uses a different sorting algorithm. Does that agent count as an instantiation of me? Well, that depends on whether I can introspectively discern which sorting algorithm I use. If I can, then I could let my output depend on the content of the sorting algorithm. And if I do that, then the equivalence between me and that other agent breaks. E.g., if I decide to output an explanation of my sorting algorithm, then my output would explain, say, bubble sort, whereas the other algorithm’s output would explain, say, merge sort. If, on the other hand, I don’t have introspective access to my sorting algorithm, then the code of the sorting algorithm cannot affect my output. Thus, the behaviorist view would interpret the other agent as an instantiation of me (as long as, of course, it, too, doesn’t have introspective access to its sorting algorithm). This conforms with the intuition that which kind of sorting algorithm I use is not part of my subjective experience. I find this natural relation to introspective discernibility very appealing.

That said, things are complicated by the equivalence relation being subjective. If you already know what A and B output, then they are equivalent if their output is the same — even if it is “coincidentally” so, i.e., if they perform completely unrelated computations. Of course, a decision algorithm will rarely know its own output in advance. So, this extreme case is probably rare. However, it is plausible that an algorithm’s knowledge about its own behavior excludes some conditional policies. For example, consider a case like Conitzer’s (2016, 2017), in which copies of an EU-maximizing agent face different but symmetric information. Depending on what the agent knows about its algorithm, it may view all the copies as equivalent or not. If it has relatively little self-knowledge, it could reason that if it lets its action depend on the information, the copies’ behavior would diverge. With more self-knowledge, on the other hand, it could reason that, because it is an EU maximizer and because the copies are in symmetric situations, its action will be the same no matter the information received.5

Consciousness

The BPB problem resembles the problem of consciousness: the question “does some physical system implement my algorithm?” is similar to the question “does some physical system have the conscious experience that I am having?”. For now, I don’t want to go too much into the relation between the two problems. But if we suppose that the two problems are connected, we can draw from the philosophy of mind to discuss our approach to BPB.

In particular, I expect that a common objection to the behaviorist approach will be that most instantiations in the behaviorist sense are behavioral p-zombies. That is, their output behavior is equivalent to the algorithm’s but they compute the output in a different way, and in particular in a way that doesn’t seem to give rise to conscious (or subjective) experiences. While the behaviorist view may lead us to identify with such a p-zombie, we can be certain, so the argument goes, that we are not given that we have conscious experiences.

Some particular examples include:

  • Lookup table-based agents
  • Messed up causal structures, e.g. Paul Durham’s experiments with his whole brain emulation in Greg Egan’s novel Permutation City.

I personally don’t find these arguments particularly convincing because I favor Dennett’s and Brian Tomasik’s eliminativist view on consciousness. That said, it’s not clear whether eliminativism would imply anything other than relativism/anti-realism for the BPB problem (if we view BPB and philosophy of mind as sufficiently strongly related).


1. I use the word “algorithm” in a very broad sense. I don’t mean to imply Turing computability. In fact, I think any explicit formal specification of the form “f()=…” should work for the purpose of the present definition. Perhaps, even implicit specifications of the output would work. 

2. Of course, I see how someone would find this counterintuitive. However, I suspect that this is primarily because the rock example triggers absurdity heuristics and because it is hard to imagine a situation in which you believe that your decision algorithm is strongly correlated with whether, say, some rock causes an avalanche. 

3. Although the behaviorist view defines the instance-of-me property via correlation, there can still be correlated physical subsystems that are not viewed as an instance of me. In particular, if you strongly limit the set of allowed interpretations (see the next paragraph), then the potential relationship between your own and the system’s action may be too complicated to be expressed as A outputs x <=> i(H)=x

4. I suspect that the two might differ in medical or “common cause” Newcomb-like problems like the coin flip creation problem

5. If this is undesirable, one may try to use logical counterfactuals to find out whether B also “would have” done the same as A if A had behaved differently. However, I’m very skeptical of logical counterfactuals in general. Cf. the “Counterfactual Robustness” section in Tomasik’s post. 

Multiverse-wide cooperation via correlated decision making – Summary

This is a short summary of some of the main points from my paper on multiverse-wide superrationality. For details, caveats and justifications, see the full paper. For shorter, accessible introductions, see here.

The target audience for this post consists of:

  • people who have already thought about the topic and thus don’t want to read through the long explanations given in the paper;
  • people who have already read (some of) the full paper and just want to refresh their memory;
  • people who don’t yet know whether they should read the full paper and thus want to know whether the content is interesting or relevant to them.
If you are not in any of these groups, this post may be confusing and not very helpful for understanding the main ideas.

Main idea

  • Take values of agents with your decision algorithm into account to make it more likely that they do the same. I’ll use Hofstadter’s (1983) term superrationality to refer to this kind of cooperation.
  • Whereas acausal trade as it is usually understood seems to require mutual simulation and is thus hard to get right as a human, superrationality is easy to apply for humans (if they know how they can benefit agents that use the same decision algorithm).
  • Superrationality may not be relevant among agents on Earth, e.g. because on Earth we already have causal cooperation and few people use the same decision algorithm as we use. But if we think that we might live in a vast universe or multiverse (as seems to be a common view among physicists, see, e.g., Tegmark (2003)), then there are (potentially infinitely) many agents with whom we could cooperate in the above way.
  • This multiverse-wide superrationality (MSR) suggests that when deciding between policies in our part of the multiverse, we should essentially adopt a new utility function (or, more generally, a new set of preferences) which takes into account the preferences of all agents with our decision algorithm. I will call that our compromise utility function (CUF). Whatever CUF we adopt, the others will (be more likely to) adopt a structurally similar CUF. E.g., if our CUF gives more weight to our values, then the others’ CUF will also give more weight to their values. The gains from trade appear to be highest if everyone adopts the same CUF. If this is the case, multiverse-wide superrationality has strong implications for what decisions we should make.

The superrationality mechanism

  • Superrationality works without reciprocity. For example, imagine there is one agent for every integer and that for every i, agent i can benefit agent i+1 at low cost to herself. If all the agents use the same decision algorithm, then agent i should benefit agent i+1 to make it more likely that agent i-1 also cooperates in the same way. That is, agent i should give something to an agent that cannot in any way return the favor. This means that when cooperating superrationally, you don’t need to identify which agents can help you.
  • How should the new criterion for making decisions, our compromise utility function, look like?
    • Harsanyi’s (1955) aggregation theorem suggests that it should be a weighted sum of the utility functions of all the participating agents.
    • To maximize gains from trade, everyone should adopt the same weights.
    • Variance-voting (Cotton-Barratt 2013; MacAskill 2014, ch. 3) is a promising candidate.
    • If some of the values require coordination (e.g., if one of the agents wants there to be at least one proof of the Riemann conjecture in the multiverse), then things get more complicated.
  • “Updatelessness” has some implications. E.g., it means that one should, under certain conditions, accept a superrational compromise that is bad for oneself.

The values of the other agents

  • To maximize the compromise utility function, it is very useful (though not strictly necessary, see section “Interventions”) to know what other agents with similar decision algorithms care about.
  • The orthogonality thesis (Bostrom 2012) implies that the values of the other agents are probably different from ours, which means that taking them into account makes a difference.
  • Not all aspects of the values of agents with our decision algorithm are relevant:
    • Only the consequentialist parts of their values matter (though things like minimizing the number of rule violations committed by all agents is a perfectly fine consequentialist value system).
    • Only values that apply to our part of the multiverse are relevant. (Some agents may care exclusively or primarily about their part of the multiverse.)
    • At least humans care differently about far away than about near things. Because we are far away from most agents with our decision algorithm, we only need to think about what they care about in distant things.
    • Superrationalists may care more about their idealized values, so we may try to idealize their values. However, we should be very careful to idealize only in ways consistent with their meta-preferences. (Otherwise, your values may be mis-idealized.)
  • There are some ways to learn about what other superrational agents care about.
    • The empirical approach: We can survey the relevant aspects of human values. The values of humans who take superrationality seriously are particularly relevant.
      • An example of relevant research is Bain et al.’s (2013) study on what people care about in future societies. They found that people put most weight on how warm, caring and benevolent members of these societies are. If we believe that construal level theory (see Trope and Liberman (2010) for an excellent summary) is roughly correct, then such results should carry over to evaluations of other psychologically distant societies. Although these results have been replicated a few times (Bain et al. 2012; Park et al. 2015; Judge and Wilson 2015; Bain et al. 2016), they are tentative and merely exemplify relevant research in this domain.
      • Another interesting data point is the values of the EA/LW/SSC/rationalist community, to my knowledge the only group of people who plausibly act on superrationality.
    • The theoretical approach: We could think about the processes that affect the distribution of values in the multiverse.
      • Biological evolution
      • Cultural evolution (see, e.g., Henrich 2015)
      • Late great filters
        • For example, if a lot of civilizations self-destruct with weapons of mass destruction, then the compromise utility function may contain a lot more peaceful values than an analysis based on biological and cultural evolution suggests.
      • The transition to whole brain emulations (Hanson 2016)
      • The transition to de novo AI (Bostrom 2014)

Interventions

  • There are some general ways in which we can effectively increase our compromise utility function without knowing its exact content.
    • Many meta-activities don’t require any such knowledge as long as we think that it can be acquired in the future. E.g., we could convince other people of MSR, do research on MSR, etc.
    • Sometimes, very very small bits of knowledge suffice to identify promising interventions. For example, if we believe that the consequentialist parts of human values are a better approximation of the consequentialist parts of other agents’ values than non-consequentialist human values, then we should make people more consequentialist (without necessarily promoting any particular consequentialist morality).
    • Another relevant point is that no matter how well we know the content of the compromise function, the argument in favor of maximizing it in our part of the universe is still just as valid. Thus, even if we know very little about its content, we should still do our best at maximizing it. (That said, we will often be better at maximizing the values of humans, in great part because we know and understand these values better.)
  • Meta-activities
    • Further research
    • Promoting multiverse-wide superrationality
  • Probably ensuring that superintelligent AIs have a decision theory that reasons correctly about superrationality is ultimately the most important intervention (although promoting multiverse-wide superrationality among humans can be instrumental for doing so).
  • There are some interventions in the moral advocacy space which align people’s preferences more with those of other superrational agents about our universe.
    • Promoting consequentialism
      • This is also good because consequentialism enables cooperation with the agents in other parts of the multiverse.
    • Promoting pluralism (e.g., convincing utilitarians to also take things other than welfare into account)
    • Promoting concern for benevolence and warmth (or whatever other value is much stronger represented in high versus low construal preferences)
    • Facilitating moral progress (i.e., presenting people with the arguments for both sides). Probably valuing preference idealization is more common than disvaluing it.
    • Promoting multiverse-wide preference utilitarianism
  • Promoting causal cooperation

A survey of polls on Newcomb’s problem

One classic story about Newcomb’s problem is that, at least initially, people one-box and two-box in roughly equal numbers (and that everyone is confident in their position). To find out whether this is true or what exact percentage of people would one-box I conducted a meta-survey of existing polls of people’s opinion on Newcomb’s problem.

The surveys I found are listed in the following table:

I deliberately included even surveys with tiny sample sizes to test whether the results from the larger sample size surveys are robust or whether they depend on the specifics of how they obtained the data. For example, the description of Newcomb’s problem in the Guardian survey contained a paragraph on why one should one-box (written by Arif Ahmed, author of Evidence, Decision and Causality) and a paragraph on why one should two-box (by David Edmonds). Perhaps the persuasiveness of these arguments influenced the result of the survey?

Looking at all the polls together, it seems that the picture is at least somewhat consistent. The two largest surveys of non-professionals both give one-boxing almost the same small edge. The other results diverge more, but some can be easily explained. For example, decision theory is a commonly discussed topic on LessWrong with some of the opinion leaders of the community (including founder Eliezer Yudkowsky) endorsing one-boxing. It is therefore not surprising that opinions on LessWrong have converged more than elsewhere. Considering the low sample sizes, the other smaller surveys of non-professionals also seem reasonably consistent with the impression that one-boxing is only slightly more common than two-boxing.

The surveys also show that, as has often been remarked on, there exists a significant difference between opinion among the general population / “amateur philosophers” and professional philosophers / decision theorists (though the consensus among decision theorists is not nearly as strong as on LessWrong).

Complications in evaluating neglectedness

Neglectedness (or crowdedness) is a heuristic that effective altruists use to assess how much impact they could have in a specific cause area. It is usually combined with scale (a.k.a. importance) and tractability (a.k.a. solvability), which together are meant to approximate expected value. (In fact, under certain idealized definitions of the three factors, multiplying them is equivalent to expected value. However, this removes the heuristic nature of these factors and probably does not describe how people typically apply them.) For introductions and thoughts on the framework as well as neglectedness in particular see:

One reason why the neglectedness heuristic and the framework in general are so popular is that they are much easier to apply than explicit cost-effectiveness or expected value calculations. In this post, I will argue that evaluating neglectedness (which may usually be seen as the most heuristic and easiest to evaluate part of the framework) is actually quite complicated. This is in part to make people more aware of issues that are sometimes not and often only implicitly taken into account. In some cases, it may also be an argument against using the heuristic at all. Presumably, most of the following considerations won’t surprise many practitioners. Nonetheless, it appears useful to write them down, which, to my knowledge, hasn’t been done before.

Neglectedness and diminishing returns

There are a few different definitions of neglectedness. For example, consider the following three:

  1. “If we add more resources to the cause, we can expect more promising interventions to be carried out.” (source)
  2. You care about a cause much more than the rest of society. (source)
  3. “How many people, or dollars, are currently being dedicated to solving the problem?” (source)

The first one is quite close to expected value-type calculations and so it is quite clear why it is important. The second and third are more concrete and easier to measure but ultimately only relevant because they are proxies of the first. If society is already investing a lot into a cause, then the most promising interventions in that cause area are already taken up and only less effective ones remain.

Because the second and, even more so, the third are easier to measure, I expect that, in practice, most people use these two when they evaluate neglectedness. Incidentally, these definitions also fit the terms “neglectedness” and “crowdedness” much better. I will argue that neglectedness in the second and third sense has to be translated into neglectedness into the first sense and that this translation is difficult. Specifically, I will argue that the diminishing returns curves on which the connection between already invested resources and the value of the marginal dollar is based on can assume different scales and shapes that have to be taken into account.

A standard diminishing return curve may look roughly like this:

IMG_20170621_133952

The x-axis represents the amount of resources invested into some intervention or cause area, the y-axis represents the returns of that investment. The derivative of the returns (i.e., the marginal returns) decreases, potentially in inverse proportion to the cumulative investment.

Even if returns diminish in a way similar to that shape, there is still the question of the scale of that graph (not to be confused with the scale/importance of the cause area), i.e. whether values on the x-axis are in the thousands, millions or billions. In general, returns probably diminish slower in cause areas that are in some sense large and uniform. Take the global fight against malaria. Intervening in some areas is more effective than in others. For example, it is more effective in areas where malaria is more common, or where it is easier to, say, provide mosquito nets, etc. However, given how widespread malaria is (about 300 million cases in 2015), I would expect that there is a relatively large number of areas almost tied for the most effective places to fight malaria. Consequently, I would guess that once the most effective intervention is to distribute provide mosquito nets, even hundreds of millions do not diminish returns all that much.

Other interventions have much less room for funding and thus returns diminish much more quickly. For example, the returns of helping some specific person will usually diminish way before investing, say, a billion dollars.

If you judge neglectedness only based on the raw amount of resources invested into solving a problem (as suggested by 80,000 hours), then this may make small cause areas look a lot more promising than they actually are. Depending on the exact definitions, this remains the case if you combine neglectedness with scale and tractability. For example, consider the following two interventions:

  1. The global fight against malaria.
  2. The fight against malaria in some randomly selected subset of 1/100th of the global area or population.

The two should usually be roughly equally promising. (Perhaps 1 is a bit more promising because every intervention contained in 2 is also in 1. On the other hand, that would make “solve everything” hard to beat as an intervention. Of course, 2 can also be more or less promising if an unusual 1/100th is chosen.) But because the raw amount of resources invested into 1 is presumably 100 times as big as the amount of resources invested into 2, 2 would, on a naive view, be regarded as much more neglected than 1. The product of scale and tractability is the same in 1 and 2. (1 is a 100 times bigger problem, but solving it in its entirety is also roughly 100 times more difficult, though I presume that some definitions of the framework judge this differently. In general, it seems fine to move considerations out of neglectedness into tractability and scope as long as they are not double-counted or forgotten.) Thus, the overall product of the three is greater for 2, which appears to be wrong. If on the other hand, neglectedness denotes the extent to which returns have diminished (the first of the three definitions given at the beginning of this section), then the neglectedness of 1 and 2 will usually be roughly the same.

Besides the scale of the return curve, the shape can also vary. In fact, I think many interventions initially face increasing returns from learning/research, creating economies of scale, specialization within the cause area, etc. For example, in most cause areas, the first $10,000 are probably invested into prioritization, organizing, or (potentially symbolic) interventions that later turn out to be suboptimal. So, in practice return curves may actually look more like the following:

IMG_20170621_134248

This adds another piece of information (besides scale) that needs to be taken into account to translate the amount of invested resources into how much returns have diminished: how and when do returns start to diminish?

There are many other return curve shapes that may be less common but mess up the neglectedness framework more. For example, some projects produce some large amount of value if they succeed but produce close to no value if they fail. Thus, the (actual not expected) return curve for such projects may look like this:

IMG_20170621_134241

Examples may include developing vaccines, colonizing Mars or finding cause X.

If such a cause area is already relatively crowded according to the third (and second) sense, that may make them less “crowded” in the first sense. For example, if nobody had invested money into finding a vaccine against malaria (and you don’t expect others to invest money into it into the future either, see below) then this cause area is maximally neglected in the second and third sense. However, given how expensive clinical trials are, the marginal returns of donating a few thousand dollars into it are essentially zero. If on the other hand, others have already contributed enough money to get a research project off the ground at all, then the marginal returns are higher, because there is at least some chance that your money will enable a trial in which a vaccine is found. (Remember that we don’t know the exact shape of the return curve, so we don’t know when the successful trial is funded.)

I would like to emphasize that the point of this section is not so much that people apply neglectedness incorrectly by merely looking at the amount of resources invested into a cause and not thinking about implications in terms of diminishing returns at all. Instead, I suspect that most people implicitly translate into diminishing returns and take the kind of the project into account. However, it may be beneficial if people were more aware of this issue and how it makes evaluating neglectedness more difficult.

Future resources

When estimating the neglectedness of a cause, we need to take into account, not only people who are currently working on the problem (as a literal reading of 80,000 hours’ definition suggests), but also people who have worked on it in the past and future. If a lot of people have worked on a problem in the past, then this indicates that the low-hanging fruit has already been picked. Thus, even if nobody is working in the area anymore, marginal returns have probably diminished a lot. I can’t think of a good example where this is a decisive consideration because if an area has been given up on (such that there is a big difference between past and current attention), it will usually score low in tractability, anyway. Perhaps one example is the search for new ways to organize society, government and economy. Many resources are still invested into thinking about this topic, so even if we just consider resources invested today, it would not do well in terms of neglectedness. However, if we consider that people have thought about and “experimented” in this area for thousands of years, it appears to be even more crowded.

We also have to take future people and resources into account when evaluating neglectedness. Of course, future people cannot “take away” the most promising intervention in the way that current and past people can. However, their existence causes the top interventions to be performed anyway. For example, let’s say that there are 1000 equally costly possible interventions in an area, generating 1000, 999, 998, …, 1 “utils” (or lives saved, years of suffering averted, etc.), respectively. Each intervention can only be performed once. The best 100 interventions have already been taken away by past people. Thus, if you have money for one intervention, you can now only generate 900 utils. But if you know that future people will engage in 300 further interventions in that area, then whether you intervene or not actually only makes a difference of 600 utils. All interventions besides the one generating 600 utils would have been executed anyway. (In Why Charities Don’t Differ Astronomically in Cost-Effectiveness, Brian Tomasik makes a similar point.)

The number of future people who would counterfactually engage in some cause area is an important consideration in many cause areas considered by effective altruists. In general, if a cause area is neglected by current and past people, the possibility of future people engaging in an intervention creates a lot of variance in neglectedness evaluations. If recently 10 people started working on an area, then it is very uncertain how much attention it will have in the future. And if it will receive a lot more attention regardless of our effort, then the neglectedness score may change by a factor of 100. The future resources that will go into long-established (and thus already less neglected) cause areas, on the other hand, are easier to predict and can’t make as much of a difference.

One example where future people and resources are an important consideration is AI safety. People often state that AI safety is a highly neglected cause area, presumably under the assumption that this should be completely obvious given how few people currently work in the area. At least, it is rare that the possibility of future people going into AI safety is considered explicitly. Langan-Dathi even writes that “due to [AI safety] being a recent development it is also highly neglected.” I, on the other hand, would argue that being a recent development only makes a cause look highly neglected if one doesn’t consider future people. (Again, Brian makes almost the same point regarding AI safety.)

Overall, I think many questions in AI safety should nonetheless be regarded as relatively neglected because I think there is a good chance that future people won’t recognize them as important fast enough. That said, I think some AI safety problems will become relevant in regular AI capability research or near time applications (such as self-driving cars). For example, I expect that some of Amodei et al.’s (2016) “Concrete Problems in AI Safety” will be (or would have been) picked up, anyway. Research in these areas of AI safety is thus potentially less intrinsically valuable, although it may still have a lot of instrumental benefits that make them worthwhile to pursue.

My impression is that neglecting future people in evaluating neglectedness is more common than forgetting to translate from invested resources into diminishing marginal returns. Nonetheless, in the context of this post the point of this section is that considering future resources makes neglectedness more difficult to evaluate. Obviously, it is hard to foresee how many resources will be invested into a project in the future. Because the most promising areas will not have received a lot of attention, yet, the question of their neglectedness will be dominated by how much resources they will receive in the future. Thus, in the most important cases, neglectedness is hard to estimate.

What should count as “the same cause area”?

At least the operationalization of neglectedness involves estimating the amount of (past, current and future) resources invested into a cause area. But which resources count as going into the same cause area? For example, if the cause area is malaria, should you count people who work in global poverty as working in the same cause area?

Because the number of people working in an area is only relevant as a proxy for how much marginal returns have diminished, the answer seems to be: Count people (and resources) to the extent that their activities diminish the marginal returns in the cause area in question. Thus, resources invested into alleviating global poverty have to be taken into account, because if people’s income increases, this will allow them to take measures against malaria as well.

As another example, consider the cause area of advocating some moral view X (say effective altruism). If only a few people currently promote that view, then one may naively view advocating X as neglected. However, if neglectedness is intended to be a proxy for diminishing returns, then it seems that we also have to take into account moral advocates of other views. Because most people regularly engage in some form of moral advocacy (e.g., when they talk about morality with their friends and children), many people already hold moral views that our advocacy has to compete with. Thus, we may want to take these other moral advocates into account for evaluating neglectedness. That said, if we apply neglectedness together with tractability and scope, it seems reasonable to include such considerations in either tractability or neglectedness. (As Rob Wiblin remarks, the three factors blur heavily into each other. In particular, neglectedness can make an intervention more tractable. As Wiblin notes, we should take care not to double-count arguments. We also shouldn’t forget to count arguments at all, though.)

Acknowledgements

I am indebted to Tobias Baumann for valuable comments.