OP here :) Thanks for the interesting discussion that the two of you have had!

Lukas_Gloor, I think we agree on most points. Your example of estimating a low probability of medical emergency is great! And I reckon that you are communicating appropriately about it. You're probably telling your doctor something like "we came because we couldn't rule out complication X" and not "we came because X has a probability of 2%" ;-)

You also seem to be well aware of the uncertainty. Your situation does not feel like one where you went to the ER 50 times, were sent home 49 times, and have from this developed a good calibration. It looks more like a situation where you know about danger signs which could be caused by emergencies, and have some rules like "if we see A and B and not C, we need to go to the ER".^[1]

Your situation and my post both involve low probabilities in high-stakes situations. That said, the goal of my post is to remind people that this type of probability is often uncertain, and that they should communicate this with the appropriate humility.

1. That's how I would think about it, at least... it might well be that you're more rational than I, and use probabilities more explicitly. ↩︎

Richard Chappell writes something similar here, better than I could. Thanks Lizka for linking to that post!

Pascalian probabilities are instead (I propose) ones that lack robust epistemic support. They're more or less made up, and could easily be "off" by many, many orders of magnitude. Per Holden Karnofsky's argument in 'Why we can't take explicit expected value estimates literally', Bayesian adjustments would plausibly mandate massively discounting these non-robust initial estimates (roughly in proportion to their claims to massive impact), leading to low adjusted expected value after all.

Maybe I should have titled this post differently, for example "Beware of non-robust probability estimates multiplied by large numbers".

I agree that our different reactions come partly from having different intuitions about the boundaries of a thought experiment. Which factors should one include vs exclude when evaluating answers?

For me, I assumed that the question can't be just about expected values. This seemed too trivial. For simple questions like that, it would be clearer to ask the question directly (e.g., "Are you in favor of high-risk interventions with large expected rewards?") than to use a thought experiment. So I concluded that the thought experiment probably goes a bit further.

If it goes further, there are many factors that might come into play:

• How certain are we of the numbers?
• Are there any negative effects if the intervention fails? These could be direct negative outcomes, but also indirect ones like difficulty to raise funds in the future, reputation loss...
• Are we allocating a small part of a budget, or our total money? Is this a repeated decision or a one-off?

I had no good answers, and no good guesses about the question's intent. Maybe this is clearer for you, given that you mention "the way EA culture has handled thought experiments thus far" in a comment below. I, for one, decided to skip the question :/

This is a great point.

Clearly you are right. That said, the examples that you give are the kind of frequentist probabilities for which one can actually measure rates. This is quite different from the probability given in the survey, which presumably comes from an imperfect Bayesian model with imprecise inputs.

I also don't want to belabor the point... but I'm pretty sure my probability of being stuck by lightning today is far from 0.001%. Given where I live and today's weather, it could be a few orders of magnitude lower. If I use your unadjusted probability (10 micromorts) and am willing to spend $25 to avert a micromort, I would conclude that I should invest $250 in lightning protection today... that seems the kind of wrong conclusion that my post warns about.

I think humility is useful in cases like the present survey question, when a specific low probability, derived from an imperfect model, can change the entire conclusion. There are many computations where the outcome is fairly robust to small absolute estimation errors (e.g., intervention (1) in the question). On the other hand, for computations that depend on a low probability with high sensitivity, we should be extra careful about that probability.

Sorry for having been imprecise in my post -- I wrote the question from memory after having already submitted the survey. I'll change it to "avert".

There is some public information about this here: https://www.givewell.org/charities/amf#Registration

Details vary by country. It's often a process where enumerators go door-to-door and interview the head of household to determine how many people live in a household. There can be some incentives to over-report the number of people, to receive more bednets. However, there is a limit on the number of nets per household (usually 3 or 4), and some of the data is independently verified by a second team of enumerators.

For what it's worth, AMF has population data from distributing bednets to every household. As an organization that cares about being highly effective, AMF tries hard to get the number of nets right. The target is to have approximately one net per 1.8 people (a net covers two people usually, but then there are households with an odd number of people or with pregnant women).

AMF distributed nets in five Nigerian states in the last two years. You can see these distributions here: https://www.againstmalaria.com/Distributions.aspx?MapID=68

AMF reports the population for each state; to see them, click on the state name, then on "Pre-Distribution". These numbers are:

I've compared the numbers with those from UNFPA, from here: https://data.humdata.org/dataset/cod-ps-nga

It looks like AMF's numbers are quite a bit higher, except in Bauchi state. This makes me slightly less willing to believe that Nigeria's population numbers are inflated. But of course, AMF could have been a victim of bad initial population estimates, or could have had left-over nets that were then given to routine distribution or used in other locations. I don't have any information about that.

I've appreciated this response.

The biggest discrepancy seems to be around the number of nurses:

• Lee writes that 1,709 nurses emigrated from Nigeria to the UK in a year, and that the UK takes ~85% of the total.
• Nick cites a Guardian article claiming that 15,000 nurses emigrate per year, and says that less than 25% go to the UK

Any insight on these large differences?

There is now also a translation into Toki Pona.