# High level overview on how to go about estimating "p(doom)" or the like

This is from a comment I left on a [recent blog post](https://garymarcus.substack.com/p/d28) from Gary Marcus, but I thought it might be of general interest here. Feedback and critiques definitely welcome!

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For what it's worth, here's a slightly longer overview on my own current preferred approach to estimating "p(doom)", "p(catastrophe)", or other extremely uncertain unprecedented events. I haven't yet quite worked out how to do this all properly though - as Gary mentioned, I'm still working on this as part of my PhD research and as part of the [MTAIR project](https://www.lesswrong.com/posts/sGkRDrpphsu6Jhega/a-model-based-approach-to-ai-existential-risk). The broad strokes are more or less standard [probabilistic risk assessment (PRA)](https://en.wikipedia.org/wiki/Probabilistic_risk_assessment), but some of the details are my own take or are debated.

**Step 1: Determine decision thresholds.** To restate the part Gary quoted from our email conversation: We only really care about "p(doom)" or the like as it relates to specific decisions. In particular, I think the reason most people in policy discussions care about something like p(doom) is because for many people higher default p(doom) means they're willing to make larger tradeoffs to reduce that risk. For example, if your p(doom) is very low then you might not want to restrict AI progress in any way just because of some remote possibility of catastrophe (although you might want to regulate AI for other reasons!). But if your p(doom) is higher then you start being willing to make harder and harder sacrifices to avoid really grave outcomes. And if your default p(doom) is extremely high then, yes, maybe you even start considering bombing data centers.

So the first step is to decide where the cutoff points are, at least roughly - what are the thresholds for p(doom) such that our decisions will change if it's above or below those points? For example, if our decisions would be the same (i.e., the tradeoffs we'd be willing to make wouldn't change) for any p(doom) between 0.1 and 0.9, then we don't need any more fine-grained resolution on p(doom) if we've decided it's at least within that range.

How exactly to decide where the proper thresholds are, of course, is a much more difficult question. This is where things like risk tolerance estimation, [decision making for non-ergodic processes](https://www.amazon.com/Ergodicity-Definition-Examples-Implications-Possible/dp/B09PHBV2HD), and [decision making under deep uncertainty (DMDU)](https://link.springer.com/book/10.1007/978-3-030-05252-2) come in. I'm still trying to work my way through the literature on this.

**Step 2: Determine plausible ranges for p(doom), or whatever probability you're trying to forecast.** Use available data, models, expert judgment elicitations, etc. to get an initial range for the quantity of interest, in this case p(doom). This can be a very rough estimate at first. There are differing opinions on the best ways to do this, but my own preference is to use a combination of the following:

*   Aggregate different expert judgements, quantitative models, etc. using some sort of weighted average approach. Part of my research is on how to do that weighting in a principled way, even if only on a subjective, superficial level (at least at first). Ideally we'd want to have principled ways of weighting different types of experts vs. quantitative models vs. prediction markets, presumably based on things like previous track records, potential biases, etc.
*   I currently lean towards trying to specify plausible probability ranges in the form of second-order probabilities when possible (e.g., what's your estimated probability distribution for p(doom), rather than just a point estimate). Other people think it's fine to just use a point estimate or maybe a confidence interval, and still others advocate for using various types of imprecise probabilities. It's still unclear to me what all the pros and cons of different approaches are here.
*   I usually advocate for [epistemic modesty](https://forum.effectivealtruism.org/posts/WKPd79PESRGZHQ5GY/in-defence-of-epistemic-modesty), at least for most policy decisions that will impact many people (like this one). Others seem to disagree with me on this, for reasons I don't quite understand, and instead they advocate for policy makers to think about the topic themselves and come to their own conclusions, even if they aren't themselves experts on the topic. (For more on this topic, see for example [*Why It's OK Not to Think for Yourself*](https://www.amazon.com/Why-Its-Not-Think-Yourself/dp/1032438266/) by Jon Matheson. For the opposite perspective, see Eliezer Yudkowsky's short book [*Inadequate Equilibria*](https://equilibriabook.com/).)

**Step 3: Decide whether it's worth doing further analysis.** As above, if in Step 1 we've decided that our relevant decision thresholds are p(doom)=0.1 and p(doom)=0.9, and if Step 2 tells us that all plausible estimates for p(doom) are between those numbers, then we're done and no further analysis is required because further analysis wouldn't change our decisions in any way. Assuming it's not that simple though, we need to decide whether it's worth our time, effort, and money to do a deeper analysis of the issue. This is where [Value of Information (VoI)](https://en.wikipedia.org/wiki/Value_of_information) analysis techniques can be useful.

**Step 4 (assuming further analysis is warranted): Try to factor the problem.** Can we identify the key sub-questions that influence the top-level question of p(doom)? Can we get estimates for those sub-questions in a way that allows us to get better resolution on the key top-level question? This is more or less what Joe Carlsmith was trying to do in [his report](https://arxiv.org/abs/2206.13353), where he factored the problem into 6 sub-questions and tried to give estimates for those.

Once we have a decent factorization we can go looking for better data for each sub-question, or we can ask subject matter experts for their estimates of those sub-questions, or maybe we can try using prediction markets or the like.

The problem of course is that it's not always clear what's the best way to factor the problem, or how to put the sub-questions together in the right way so you get a useful overall estimate rather than something wildly off the mark, or how to make sure you didn't leave out anything really major, or how to account for "unknown unknowns", etc. Just getting to a good factorization of the problem can take a lot of time and effort and money, which is why we need Step 3.

One potential advantage of factorization is that it allows us to ask the sub-questions to different subject matter experts. For example, if we divide up the overall question of "what's your p(doom)?" into some factors that relate to machine learning and other factors that relate to economics, then we can go ask the ML experts about the ML questions and leave the economics questions for economists. (Or we can ask them both but maybe give more weight to the ML experts on the ML questions and more weight to the economists on the economics questions.) I haven't seen this done so much in practice though.

One idea I've been focusing on a lot for my research is to try to zoom in on "cruxes" between experts as a way of usefully factoring overall questions like p(doom). However, it turns out it's often very hard to figure out where experts actually disagree! One thing I really like is when experts say things like, "well if I agreed with you on A then I'd also agree with you on B," because then A is clearly a crux for that expert relative to question B. I actually really liked Gary's recent [Coleman Hughes podcast episode](https://scottaaronson.blog/?p=7431) with Scott Aaronson and Eliezer Yudkowsky, because I thought that they all did a great job on exactly this.

**Step 5: Iterate.** For each sub-question we can now ask whether further analysis on that question would change our overall decisions (we can use [sensitivity analysis](https://en.wikipedia.org/wiki/Sensitivity_analysis) techniques for this). If we decide further analysis would be helpful and worth the time and effort, then we can factor that sub-question into sub-sub-questions, and keep iterating until it's no longer worth it to do further analysis.

The first phase of our [MTAIR project](https://www.lesswrong.com/posts/sGkRDrpphsu6Jhega/a-model-based-approach-to-ai-existential-risk) (the [147 page report](https://arxiv.org/abs/2206.09360) Gary linked to) tried to do an exhaustive factorization of p(doom) at least on a qualitative level. It was *very* complicated and it wasn't even complete by the time we decided to at least publish what we had!

A lot of what [Epoch](https://epochai.org/) and similar organizations do can be seen as focusing in on particular sub-questions that they think are worth the extra analysis.  
  
For more on the Probabilistic Risk Assessment approach in general, I'd especially recommend Douglas Hubbard's classic [*How to Measure Anything*](https://www.amazon.com/How-Measure-Anything-Intangibles-Business/dp/1118539273), or any of his other books on the topic.