My adventures in demonology

Wired has an article about the CSER Existential Risk Conference in December 2016, rather flatteringly comparing us to superheroes. Plus a list of more or less likely risks we discussed. Calling them the “10 biggest threats” is perhaps exaggerating a fair bit: nobody is seriously worried about simulation shutdowns. But some of the others are worth working a lot more on.

High-energy demons

I am cited as talking about existential risk from demon summoning. Since this is bound to be misunderstood, here is the full story:

As noted in the Wired list, we wrote a paper looking at the risk from the LHC, finding that there is a problem with analysing very unlikely (but high impact) risks: the probability of a mistake in the analysis overshadows the risk itself, making the analysis bad at bounding the risk. This can be handled by doing multiple independent risk bounds, which is a hassle, but it is the only (?) way to reliably conclude that things are safe.

I blogged a bit about the LHC issue before we wrote the paper, bringing up the problem of estimating probabilities for unprecedented experiments through the case of Taleb’s demon (which properly should be Taylor’s demon, but Stigler’s law of eponymy strikes again). That probably got me to have a demon association to the wider physics risk issues.

The issue of how to think about unprecedented risks without succumbing to precautionary paralysis is important: we cannot avoid doing new things, yet we should not be stupid about it. This is extra tricky when considering experiments that create things or conditions that are not found in nature.

Not so serious?

A closely related issue is when it is reasonable to regard a proposed risk as non-serious. Predictions of risk from strangelets, black holes, vacuum decay and other “theoretical noise” caused by theoretical physics theories at least is triggered by some serious physics thinking, even if it is far out. Physicists have generally tended to ignore such risks, but when forced by anxious acceleratorphobes the arguments had to be nontrivial: the initial dismissal was not really well founded. Yet it seems totally reasonable to dismiss some risks. If somebody worries that the alien spacegods will take exception to the accelerator we generally look for a psychiatrist rather than take them seriously. Some theories have so low prior probability that it seems rational to ignore them.

But what is the proper de minimis boundary here? One crude way of estimating it is to say that risks of destroying the world with lower probability than one in 10 billion can safely be ignored – they correspond to a risk of less than one person in expectation. But we would not accept that for an individual chemistry experiment: if the chance of being blown up if someone did it was “less than 100%” but still far above some tiny number, they would presumably want to avoid risking their neck. And in the physics risk case the same risk is borne by every living human. Worse, by Bostrom’s astronomical waste argument, existential risks risks more than 10⁴⁶ possible future lives. So maybe we should put the boundary at less than 10^-46: any risk more likely must be investigated in detail. That will be a lot of work. Still, there are risks far below this level: the probability that all humans were to die from natural causes within a year is around 10^-7.2e11, which is OK.

One can argue that the boundary does not really exist: Martin Peterson argues that setting it at some fixed low probability, that realisations of the risk cannot be ascertained, or that it is below natural risks do not truly work: the boundary will be vague.

Demons lurking in the priors

Be as it may with the boundary, the real problem is that estimating prior probabilities is not always easy. They can vault over the vague boundary.

Hence my demon summoning example (from a blog post near Halloween I cannot find right now): what about the risk of somebody summoning a demon army? It might cause the end of the world. The theory “Demons are real and threatening” is not a hugely likely theory: atheists and modern Christians may assign it zero probability. But that breaks Cromwell’s rule: once you assign 0% to a probability no amount of evidence – including a demon army parading in front of you – will make you change your mind (or you are not applying probability theory correctly). The proper response is to assume some tiny probability $\epsilon$ , conveniently below the boundary.

…except that there are a lot of old-fashioned believers who do think the theory “Demons are real and threatening” is a totally fine theory. Sure, most academic readers of this blog will not belong to this group and instead to the $\epsilon$ probability group. But knowing that there are people out there that think something different from your view should make you want to update your view in their direction a bit – after all, you could be wrong and they might know something you don’t. (Yes, they ought to move a bit in your direction too.) But now suppose you move 1% in the direction of the believers from your $\epsilon$ belief. You will now believe in the theory to $\epsilon + 1\% \approx 1\%$ . That is, now you have a fairly good reason not to disregard the demon theory automatically. At least you should spend effort on checking it out. And once you are done with that you better start with the next crazy New Age theory, and the next conspiracy theory…

Reverend Bayes doesn’t help the unbeliever (or believer)

One way out is to argue that the probability of believers being right is so low that it can be disregarded. If they have probability $\epsilon$ of being right, then the actual demon risk is of size $\epsilon$ and we can ignore it – updates due to the others do not move us. But that is a pretty bold statement about human beliefs about anything: humans can surely be wrong about things, but being that certain that a common belief is wrong seems to require better evidence.

The believer will doubtlessly claim seeing a lot of evidence for the divine, giving some big update $\Pr[belief|evidence]=\Pr[evidence|belief]\Pr[belief]/\Pr[evidence]$ , but the non-believer will notice that the evidence is also pretty compatible with non-belief: $\frac{\Pr[evidence|belief]}{\Pr[evidence|nonbelief]}\approx 1$ – most believers seem to have strong priors for their belief that they then strengthen by selective evidence or interpretation without taking into account the more relevant ratio $\Pr[belief|evidence] / \Pr[nonbelief|evidence]$ . And the believers counter that the same is true for the non-believers…

Insofar we are just messing around with our own evidence-free priors we should just assume that others might know something we don’t know (maybe even in a way that we do not even recognise epistemically) and update in their direction. Which again forces us to spend time investigating demon risk.

OK, let’s give in…

Another way of reasoning is to say that maybe we should investigate all risks somebody can make us guess a non-negligible prior for. It is just that we should allocate our efforts proportional to our current probability guesstimates. Start with the big risks, and work our way down towards the crazier ones. This is a bit like the post about the best problems to work on: setting priorities is important, and we want to go for the ones where we chew off most uninvestigated risk.

If we work our way down the list this way it seems that demon risk will be analysed relatively early, but also dismissed quickly: within the religious framework it is not a likely existential risk in most religions. In reality few if any religious people hold the view that demon summoning is an existential risk, since they tend to think that the end of the world is a religious drama and hence not intended to be triggered by humans – only divine powers or fate gets to start it, not curious demonologists.

That wasn’t too painful?

Have we defeated the demon summoning problem? Not quite. There is no reason for all those priors to sum to 1 – they are suggested by people with very different and even crazy views – and even if we normalise them we get a very long and heavy tail of weird small risks. We can easily use up any amount of effort on this, effort we might want to spend on doing other useful things like actually reducing real risks or doing fun particle physics.

There might be solutions to this issue by reasoning backwards: instead of looking at how X could cause Y that could cause Z that destroys the world we ask “If the world would be destroyed by Z, what would need to have happened to cause it?” Working backwards to Y, Y’, Y” and other possibilities covers a larger space than our initial chain from X. If we are successful we can now state what conditions are needed to get to dangerous Y-like states and how likely they are. This is a way of removing entire chunks of the risk landscape in efficient ways.

This is how I think we can actually handle these small, awkward and likely non-existent risks. We develop mental tools to efficiently get rid of lots of them in one fell sweep, leaving the stuff that needs to be investigated further. But doing this right… well, the devil lurks in the details. Especially the thicket of totally idiosyncratic risks that cannot be handled in a general way. Which is no reason not to push forward, armed with epsilons and Bayes’ rule.

Addendum (2017-02-14)

That the unbeliever may have to update a bit in the believer direction may look like a win for the believers. But they, if they are rational, should do a small update into the unbeliever direction. The most important consequence is that now they need to consider existential risks due to non-supernatural causes like nuclear war, AI or particle physics. They would assign them a lower credence than the unbeliever, but as per the usual arguments for the super-importance of existential risk this still means they may have to spend effort on thinking about and mitigating these risks that they otherwise would have dismissed as something God would have prevented. This may be far more annoying to them than unbelievers having to think a bit about demonology.

Emlyn O’Regan makes some great points over at Google+, which I think are worth analyzing:

“Should you somehow incorporate the fact that the world has avoided destruction until now into your probabilities?”
“Ideas without a tech angle might be shelved by saying there is no reason to expect them to happen soon.” (since they depend on world properties that have remained unchanged.)
” Ideas like demon summoning might be limited also by being shown to be likely to be the product of cognitive biases, rather than being coherent free-standing ideas about the universe.”

In the case of (1), observer selection effects can come into play. If there are no observers on a post demon-world (demons maybe don’t count) then we cannot expect to see instances of demon apocalypses in the past. This is why the cosmic ray argument for the safety of the LHC need to point to the survival of the Moon or other remote objects rather than the Earth to argue that being hit by cosmic rays over long periods prove that it is safe. Also, as noted by Emlyn, the Doomsday argument might imply that we should expect a relatively near-term end, given the length of our past: whether this matters or not depends a lot on how one handles observer selection theory.

In the case of (2), there might be development in summoning methods. Maybe medieval methods could not work, but modern computer-aided chaos magick is up to it. Or there could be rare “the stars are right” situations that made past disasters impossible. Still, if you understand the risk domain you may be able to show that the risk is constant and hence must have been low (or that we are otherwise living in a very unlikely world). Traditions that do not believe in a growth of esoteric knowledge would presumably accept that past failures are evidence of future inability.

(3) is an error theory: believers in the risk are believers not because of proper evidence but from faulty reasoning of some kind, so they are not our epistemic peers and we do not need to update in their direction. If somebody is trying to blow up a building with a bomb we call the police, but if they try to do it by cursing we may just watch with amusement: past evidence of the efficacy of magic at causing big effects is nonexistent. So we have one set of evidence-supported theories (physics) and another set lacking evidence (magic), and we make the judgement that people believing in magic are just deluded and can be ignored.

(Real practitioners may argue that there sure is evidence for magic, it is just that magic is subtle and might act through convenient coincidences that look like they could have happened naturally but occur too often or too meaningfully to be just chance. However, the skeptic will want to actually see some statistics for this, and in any case demon apocalypses look like they are way out of the league for this kind of coincidental magic).

Emlyn suggests that maybe we could scoop all the non-physics like human ideas due to brain architecture into one bundle, and assign them one epsilon of probability as a group. But now we have the problem of assigning an idea to this group or not: if we are a bit uncertain about whether it should have $\epsilon$ probability or a big one, then it will get at least some fraction of the big probability and be outside the group. We can only do this if we are really certain that we can assign ideas accurately, and looking at how many people psychoanalyse, sociologise or historicise topics in engineering and physics to “debunk” them without looking at actual empirical content, we should be wary of our own ability to do it.

So, in short, (1) and (2) do not reduce our credence in the risk enough to make it irrelevant unless we get a lot of extra information. (3) is decent at making us sceptical, but our own fallibility at judging cognitive bias and mistakes (which follows from claiming others are making mistakes!) makes error theories weaker than they look. Still, the really consistent lack of evidence of anything resembling the risk being real and that claims internal to the systems of ideas that accept the possibility imply that there should be smaller, non-existential, instances that should be observable (e.g. individual Fausts getting caught on camera visibly succeeding in summoning demons), and hence we can discount these systems strongly in favor of more boring but safe physics or hard-to-disprove but safe coincidental magic.

How much should we spread out across future scenarios?

Robin Hanson mentions that some people take him to task for working on one scenario (WBE) that might not be the most likely future scenario (“standard AI”); he responds by noting that there are perhaps 100 times more people working on standard AI than WBE scenarios, yet the probability of AI is likely not a hundred times higher than WBE. He also notes that there is a tendency for thinkers to clump onto a few popular scenarios or issues. However:

In addition, due to diminishing returns, intellectual attention to future scenarios should probably be spread out more evenly than are probabilities. The first efforts to study each scenario can pick the low hanging fruit to make faster progress. In contrast, after many have worked on a scenario for a while there is less value to be gained from the next marginal effort on that scenario.

This is very similar to my own thinking about research effort. Should we focus on things that are likely to pan out, or explore a lot of possibilities just in case one of the less obvious cases happens? Given that early progress is quick and easy, we can often get a noticeable fraction of whatever utility the topic has by just a quick dip. The effective altruist heuristic of looking at neglected fields also is based on this intuition.

A model

But under what conditions does this actually work? Here is a simple model:

There are $N$ possible scenarios, one of which ( $j$ ) will come about. They have probability $P_i$ . We allocate a unit budget of effort to the scenarios: $\sum a_i = 1$ . For the scenario that comes about, we get utility $\sqrt{a_j}$ (diminishing returns).

Here is what happens if we allocate proportional to a power of the scenarios, $a_i \propto P_i^\alpha$ . $\alpha=0$ corresponds to even allocation, 1 proportional to the likelihood, >1 to favoring the most likely scenarios. In the following I will run Monte Carlo simulations where the probabilities are randomly generated each instantiation. The outer bluish envelope represents the 95% of the outcomes, the inner ranges from the lower to the upper quartile of the utility gained, and the red line is the expected utility.

Utility of allocating effort as a power of the probability of scenarios. Red line is expected utility, deeper blue envelope is lower and upper quartiles, lighter blue 95% interval.

This is the $N=2$ case: we have two possible scenarios with probability $p$ and $1-p$ (where $p$ is uniformly distributed in [0,1]). Just allocating evenly gives us $1/\sqrt{2}$ utility on average, but if we put in more effort on the more likely case we will get up to 0.8 utility. As we focus more and more on the likely case there is a corresponding increase in variance, since we may guess wrong and lose out. But 75% of the time we will do better than if we just allocated evenly. Still, allocating nearly everything to the most likely case means that one does lose out on a bit of hedging, so the expected utility declines slowly for large $\alpha$ .

The $N=100$ case (where the probabilities are allocated based on a flat Dirichlet distribution) behaves similarly, but the expected utility is smaller since it is less likely that we will hit the right scenario.

What is going on?

This doesn’t seem to fit Robin’s or my intuitions at all! The best we can say about uniform allocation is that it doesn’t produce much regret: whatever happens, we will have made some allocation to the possibility. For large N this actually works out better than the directed allocation for a sizable fraction of realizations, but on average we get less utility than betting on the likely choices.

The problem with the model is of course that we actually know the probabilities before making the allocation. In reality, we do not know the likelihood of AI, WBE or alien invasions. We have some information, and we do have priors (like Robin’s view that $P_{AI} < 100 P_{WBE}$ ), but we are not able to allocate perfectly. A more plausible model would give us probability estimates instead of the actual probabilities.

We know nothing

Let us start by looking at the worst possible case: we do not know what the true probabilities are at all. We can draw estimates from the same distribution – it is just that they are uncorrelated with the true situation, so they are just noise.

Utility of allocating effort as a power of the probability of scenarios, but the probabilities are just random guesses. Red line is expected utility, deeper blue envelope is lower and upper quartiles, lighter blue 95% interval. 100 possible scenarios, with uniform probability on the simplex.

In this case uniform distribution of effort is optimal. Not only does it avoid regret, it has a higher expected utility than trying to focus on a few scenarios ( $\alpha>0$ ). The larger N is, the less likely it is that we focus on the right scenario since we know nothing. The rationality of ignoring irrelevant information is pretty obvious.

Note that if we have to allocate a minimum effort to each investigated scenario we will be forced to effectively increase our $\alpha$ above 0. The above result gives the somewhat optimistic conclusion that the loss of utility compared to an even spread is rather mild: in the uniform case we have a pretty low amount of effort allocated to the winning scenario, so the low chance of being right in the nonuniform case is being balanced by having a slightly higher effort allocation on the selected scenarios. For high $\alpha$ there is a tail of rare big “wins” when we hit the right scenario that drags the expected utility upwards, even though in most realizations we bet on the wrong case. This is very much the hedgehog predictor story: ocasionally they have analysed the scenario that comes about in great detail and get intensely lauded, despite looking at the wrong things most of the time.

We know a bit

We can imagine that knowing more should allow us to gradually interpolate between the different results: the more you know, the more you should focus on the likely scenarios.

Optimal alpha as a function of how much information we have about the true probabilities. N=2. — Optimal alpha as a function of how much information we have about the true probabilities (noise due to Monte Carlo and discrete steps of alpha). N=2 (N=100 looks similar).

If we take the mean of the true probabilities with some randomly drawn probabilities (the “half random” case) the curve looks quite similar to the case where we actually know the probabilities: we get a maximum for $\alpha\approx 2$ . In fact, we can mix in just a bit ( $\beta$ ) of the true probability and get a fairly good guess where to allocate effort (i.e. we allocate effort as $a_i \propto (\beta P_i + (1-\beta)Q_i)^\alpha$ where $Q_i$ is uncorrelated noise probabilities). The optimal alpha grows roughly linearly with $\beta$ , $\alpha_{opt} \approx 4\beta$ in this case.

We learn

Adding a bit of realism, we can consider a learning process: after allocating some effort $\gamma$ to the different scenarios we get better information about the probabilities, and can now reallocate. A simple model may be that the standard deviation of noise behaves as $1/\sqrt{\tilde{a}_i}$ where $\tilde{a}_i$ is the effort placed in exploring the probability of scenario $i$ . So if we begin by allocating uniformly we will have noise at reallocation of the order of $1/\sqrt{\gamma/N}$ . We can set $\beta(\gamma)=\sqrt{\gamma/N}/C$ , where $C$ is some constant denoting how tough it is to get information. Putting this together with the above result we get $\alpha_{opt}(\gamma)=\sqrt{2\gamma/NC^2}$ . After this exploration, now we use the remaining $1-\gamma$ effort to work on the actual scenarios.

Expected utility as a function of amount of probability-estimating effort (gamma) for C=1 (hard to update probabilities), C=0.1 and C=0.01 (easy to update). N=100.

This is surprisingly inefficient. The reason is that the expected utility declines as $\sqrt{1-\gamma}$ and the gain is just the utility difference between the uniform case $\alpha=0$ and optimal $\alpha_{opt}$ , which we know is pretty small. If C is small (i.e. a small amount of effort is enough to figure out the scenario probabilities) there is an optimal nonzero $\gamma$ . This optimum $\gamma$ decreases as C becomes smaller. If C is large, then the best approach is just to spread efforts evenly.

Conclusions

So, how should we focus? These results suggest that the key issue is knowing how little we know compared to what can be known, and how much effort it would take to know significantly more.

If there is little more that can be discovered about what scenarios are likely, because our state of knowledge is pretty good, the world is very random, or improving knowledge about what will happen will be costly, then we should roll with it and distribute effort either among likely scenarios (when we know them) or spread efforts widely (when we are in ignorance).

If we can acquire significant information about the probabilities of scenarios, then we should do it – but not overdo it. If it is very easy to get information we need to just expend some modest effort and then use the rest to flesh out our scenarios. If it is doable but costly, then we may spend a fair bit of our budget on it. But if it is hard, it is better to go directly on the object level scenario analysis as above. We should not expect the improvement to be enormous.

Here I have used a square root diminishing return model. That drives some of the flatness of the optima: had I used a logarithm function things would have been even flatter, while if the returns diminish more mildly the gains of optimal effort allocation would have been more noticeable. Clearly, understanding the diminishing returns, number of alternatives, and cost of learning probabilities better matters for setting your strategy.

In the case of future studies we know the number of scenarios are very large. We know that the returns to forecasting efforts are strongly diminishing for most kinds of forecasts. We know that extra efforts in reducing uncertainty about scenario probabilities in e.g. climate models also have strongly diminishing returns. Together this suggests that Robin is right, and it is rational to stop clustering too hard on favorite scenarios. Insofar we learn something useful from considering scenarios we should explore as many as feasible.

Maps of mindspace

The ever awesome Scott Alexander made a map of the rationalist blogosphere (webosphere? infosphere?) that I just saw (hat tip to Waldemar Ingdahl). Besides having plenty of delightful xkcd-style in-jokes, it is also useful by showing me parts of my intellectual neighbourhood I did not know well and might want to follow (want to follow, but probably can’t follow because of time constraints).

He starts out with pointing at some other concept maps like that, both the classic xkcd one and Julia Galef’s map of Bay Area memespace, which was a pleasant surprise to me. The latter explains the causal/influence links between communities in a very clear way.

One can of course quibble endlessly on what is left in or out (I loved the comments about the apparent lack of dragons on the rationalist map), but the two maps also show two different approaches to relatedness. In the rationalist map distance is based on some form of high-dimensional similarity, crunching it down to 2D using an informal version of a Kohonen map. Bodies of water can be used to “cheat” and add discontinuities/tears. In the memespace map the world is a network of causal/influence links, and the overall similarities between linked groups can be slight even when they share core memes. Here the cheating consists of leaving out broad links (Burning Man is mentioned; it would connect many nodes weakly to each other). In both cases what is left out is important, just as the choice of resolution. Good maps show the information the creator wants to show, and communicates it well.

It is tempting to write endless posts about good mindspace maps and how they work, what they can and cannot show, and various design choices. There are quite a few out there. Some are network layouts made automatically, typically from co-citations. Others are designed by hand. Some are artworks in themselves. I don’t have the time today. But starting the day with two delightful ones that trigger much new thoughts and planning is a good way of starting the day.

Cryonics: too rational, hence fair game?

On Practical Ethics I blog about cryonics acceptance: Freezing critique: privileged views and cryonics. My argument is that cryonics tries to be a rational scientific approach, which means it is fair game for criticism. Meanwhile many traditional and anti-cryonic views are either directly religious or linked to religious views, which means people refrain from criticising them back. Since views that are criticised are seen as more questionable than non-criticised (if equally strange) views, this makes cryonics look less worth respecting.

Andart II

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