This sounds like one of those puzzles of infinities. If you take the limits in one way then it seems like one infinity is bigger than another, but if you take the limits a different way then the other infinity seems bigger.

A toy version: say that things begin with 1 bubble universe at time 0 and proceed in time steps, and at time step k, 10^k new bubble universes begin. Each bubble universe lasts for 2 time steps and then disappears. This continues indefinitely.

Option A: each bubble universe has a value of 1 in the first time step of its existence and a value of 5 in its second time step. (Then it disappears, or forever after has value 0.)

Option B: each bubble universe has a value of 3 in the first time step of its existence and a value of 1 in its second time step. (Then it disappears, or forever after has value 0.)

This has the same basic structure as the setup in the post, though with much smaller numbers.

We could try summing across all bubble universes at each time step, and then taking the limit as the total number of time steps increases without bound. Option B is 3x as good in the zeroth time step (value of 3 vs. 1), 2.125x as good through the next time step (value of 34 vs. 16), about 2.072x as good through the next time step (value of 344 vs. 166), and in the limit as the number of time steps increases without bound it is 2.0666... times as good (31/15). That is how this post sets up its comparison of infinities (with larger numbers so the ratio would be much more lopsided).

Instead, we could try summing within each bubble universe across all of its time steps, and then sum across all complete bubble universes. Each bubble universe has a total value of 6 in Option A vs. 4 in Option B, so Option A is 1.5x as good for each of them. Option A is 1.5x as good for the first bubble universe that appears (6 vs. 4), and for the first 11 bubble universes it is 1.5x as good (66 vs. 44), and for the first 111 bubble universes it is 1.5x as good (666 vs. 444), and if you take the limit as the number of bubble universes increases without bound it is 1.5x as good. This matches the standard longtermist argument (which has larger numbers so the ratio would be more lopsided).

I disagree. One way of looking at it:

Imagine many, many civilizations that are roughly as technologically advanced as present-day human civilization.

Claim 1: Some of them will wind up having astronomical value (at least according to their own values)

Claim 2: Of those civilizations that do wind up having astronomical value, some will have gone through near misses, or high-risk periods, when they could have gone extinct if things had worked out slightly differently

Claim 3: Of those civilizations that do go extinct, some would have had wound up having astronomical value if they had survived that one extinction event. These are civilizations much like the ones in claim 2, but who got hit instead of getting a near miss.

Claim 4: Given claims 1-3, and that the "some" civilizations described in claims 1-3 are not vanishingly rare (enough to balance out the very high value), the expected value of averting a random extinction event for a technologically advanced civilization is astronomically high.

Then to apply this to humanity, we need something like:

Claim 5: We don't have sufficient information to exclude present-day humanity from being one of the civilizations from claim 1 which winds up having astronomical value (or at least humanity conditional on successfully navigating the transition to superintelligent AI and surviving the next century in control of its own destiny)

I've raised related points here, and also here with followup, about how exponential decay with a fixed decay rate is not a good model to use for estimating long-term survival probability.

Does your model without log(GNI per capita) basically just include a proxy for log(GNI per capita), by including other predictor variables that, in combination, are highly predictive of log(GNI per capita)?

With a pool of 1058 potential predictor variables, many of which have some relationship to economic development or material standards of living, it wouldn't be surprising if you could build a model to predict log(GNI per capita) with a very good fit. If that is possible with this pool of variables, and if log(GNI per capita) is linearly predictive of life satisfaction, then if you build a model predicting life satisfaction which can't include log(GNI per capita), it can instead account for that variance by including the variables that predict log(GNI per capita).

And if you transform log(GNI per capita) into a form whose relationship with life satisfaction is sufficiently non-linear, and build a model which can only account for the linear portion of the relationship between that transformed variable and life satisfaction, then within that linear model those proxy variables might do a much better job than transformed log(GNI per capita) of accounting for the variance in life satisfaction.

It looks like the 3 articles are in the appendix of the dissertation, on pages 65 (fear, Study A), 72 (hope, Study B), and 73 (mixed, Study C).

The effect of health insurance on health, such as the old RAND study, the Oregon Medicaid expansion, the India study from a couple years ago, or whatever else is out there.

Robin Hanson likes to cite these studies as showing that more medicine doesn't improve health, but I'm skeptical of the inference from 'not statistically significant' to 'no effect' (I'm in the comments there as "Unnamed"). I would like to see them re-analyzed based on effect size (e.g. a probability distribution or confidence interval for DALY per $).

I'd guess that this is because an x-risk intervention might have on the order of a 1/100,000 chance of averting extinction. So if you run 150k simulations, you might get 0 or 1 or 2 or 3 simulations in which the intervention does anything. Then there's another part of the model for estimating the value of averting extinction, but you're only taking 0 or 1 or 2 or 3 draws that matter from that part of the model because in the vast majority of the 150k simulations that part of the model is just multiplied by zero.

And if the intervention sometimes increases extinction risk instead of reducing it, then the few draws where the intervention matters will include some where its effect is very negative rather than very positive.

One way around this is to factor the model, and do 150k Monte Carlo simulations for the 'value of avoiding extinction' part of the model only. The part of the model that deals with how the intervention affects the probability of extinction could be solved analytically, or solved with a separate set of simulations, and then combined analytically with the simulated distribution of value of avoiding extinction. Or perhaps there's some other way of factoring the model, e.g. factoring out the cases where the intervention has no effect and then running simulations on the effect of the intervention conditional on it having an effect.

I believe the paper you're referring to is "Water Treatment And Child Mortality: A Meta-Analysis And Cost-effectiveness Analysis" by Kremer, Luby, Maertens, Tan, & Więcek (2023).

The abstract of this version of the paper (which I found online) says:

We estimated a mean cross-study reduction in the odds of all-cause under-5 mortality of about 30% (Peto odds ratio, OR, 0.72; 95% CI 0.55 to 0.92; Bayes OR 0.70; 95% CrI 0.49 to 0.93). The results were qualitatively similar under alternative modeling and data inclusion choices. Taking into account heterogeneity across studies, the expected reduction in a new implementation is 25%.

That's a point estimate of a 25-30% reduction in mortality (across 3 methods of estimating that number), with a confidence/credible interval that has a lower bound of a 7-8% reduction in mortality. So, it's a fairly noisy estimate, due to some combination of the noisiness of individual studies and the heterogeneity across different studies.

That interval for the reduction in mortality just barely overlaps with your number that "Sub-saharan Africa diarrhoea causes 5-10% of child mortality." (The overlap might be larger if that rate was higher than 5-10% in the years & locations where the studies were conducted.)

So it could be that the clean water interventions prevent most children's deaths from diarrhoea and few other deaths, if the mortality reduction is near the bottom of the range that Kremer & colleagues estimate. Or they might prevent a decent chunk of other deaths, but not nearly as many as your Part 4 chart & list suggest, if the true mortality reduction is something like 15%.

There is generally also a possibility of a meta-analysis giving inflated results, due to factors like publication bias affecting which studies they include or other methodological issues in the original studies, which could mean that the true effect is smaller than the lower bound of their interval. I don't know how likely that is in this case.

Here's a more detailed look at their meta-analysis results:

More from Existential Risk Observatory (@XRobservatory) on Twitter:

It was a landmark speech by @RishiSunak: the first real recognition of existential risk by a world leader. But even better are the press questions at the end:

@itvnews: "If the risks are as big as you say, shouldn't we at the very least slow down AI development, at least long enough to understand and control the risks."

@SkyNews: "Is it fair to say we know enough already to call for a moratorium on artificial general intelligence? Would you back a moratorium on AGI?" 

Sky again: "Given the harms and the risk you pointed out in this report, and some of those are profound, surely there must be some red lines we can draw at this point. Which ones are yours?"

@TheSun: "You say we shouldn't be losing sleep over this stuff. If not, why not?"

@theipaper: "You haven't really talked about whether your government is actually going to regulate. Will there be an AI Bill or similar on the The King's Speech?" 

iNews again: "On the details of that regulation: does the government remain commited to this idea of responsible scaling, whereby you sort of test models after they're being developed, or is it time to start thinking about how you intervene to stop the most dangerous models being developed at all?" 

Who would have thought one year ago? The public debate about AI xrisk so far outdoes everyone's expectations. Next step: convincing answers.

https://www.youtube.com/watch?v=hSup6mgNhzQ

One way to build risk decay into a model is to assume that the risk is unknown within some range, and to update on survival.

A very simple version of this is to assume an unknown constant per-century extinction risk, and to start with a uniform distribution on the size of that risk. Then the probability of going extinct in the first century is 1/2 (by symmetry), and the probability of going extinct in the second century conditional on surviving the first is smaller than that (since the higher-risk worlds have disproportionately already gone extinct) - with these assumptions it is exactly 1/3. In fact these very simple assumptions match Laplace's law of succession, and so the probability of going extinct in the nth century conditional on surviving the first n-1 is 1/(n+1), and the unconditional probability of surviving at least n centuries is also 1/(n+1).

More realistic versions could put more thought into the prior, instead of just picking something that's mathematically convenient.