VG

Vasco Grilo

5260 karmaJoined Jul 2020Working (0-5 years)Lisbon, Portugal
sites.google.com/view/vascogrilo?usp=sharing

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How others can help me

You can give me feedback here (anonymous or not). You are welcome to answer any of the following:

  • Do you have any thoughts on the value (or lack thereof) of my posts?
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Feel free to check my posts, and see if we can collaborate to contribute to a better world. I am open to part-time volunteering, and part-time or full-time paid work. In this case, I typically ask for 20 $/h, which is roughly equal to 2 times the global real GDP per capita.

Comments
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Topic contributions
25

Thanks for the comment, Stan!

Using PDF rather than CDF to compare the cost-effectiveness of preventing events of different magnitudes here seems off.

Technically speaking, the way I modelled the cost-effectiveness:

  • I am not comparing the cost-effectiveness of preventing events of different magnitudes.
  • Instead, I am comparing the cost-effectiveness of saving lives in periods of different population losses.

Using the CDF makes sense for the former, but the PDF is adequate for the latter.

You show that preventing (say) all potential wars next year with a death toll of 100 is 1000^1.6 = 63,000 times better in expectation than preventing all potential wars with a death toll of 100k.

I agree the above follows from using my tail index of 1.6. It is just worth noting that the wars have to involve exactly, not at least, 100 and 100 k deaths for the above to be correct.

More realistically, intervention A might decrease the probability of wars of magnitude 10-100 deaths and intervention B might decrease the probability of wars of magnitude 100,000 to 1,000,000 deaths. Suppose they decrease the probability of such wars over the next n years by the same amount. Which intervention is more valuable? We would use the same methodology as you did except we would use the CDF instead of the PDF. Intervention A would be only 1000^0.6 = 63 times as valuable.

This is not quite correct. The expected deaths from wars with  to  deaths is , where  are the minimum war deaths. So, for a tail index of , intervention A would be 251 (= (10^-0.6 - 100^-0.6)/((10^5)^-0.6 - (10^6)^-0.6)) times as cost-effective as B. As the upper bounds of the severity ranges of A and B get increasingly close to their lower bounds, the cost-effectiveness of A tends to 63 k times that of B. In any case, the qualitative conclusion is the same. Preventing smaller wars averts more deaths in expectation assuming war deaths follow a power law.

As an intuition pump we might look at the distribution of military deaths in the 20th century. Should the League of Nations/UN have spent more effort preventing small wars and less effort preventing large ones?

I do not know. Instead of relying on past deaths alone, I would rather use cost-effectiveness analyses to figure out what is more cost-effective, as the Centre for Exploratory Altruism Research (CEARCH) does. I just think it is misleading to directly compare the scale of different events without accounting for their likelihood, as in the example from Founders Pledge’s report Philanthropy to the Right of Boom I mention in the post.

When it comes to things that could be even deadlier than WWII, like nuclear war or a pandemic, it's obvious to me that the uncertainty about the death toll of such events increases at least linearly with the expected toll, and hence the "100-1000 vs 100k-1M" framing is superior to the PDF approach.

I am also quite uncertain about the death toll of catastrophic events! I used the PDF to remain consistent which Founders Pledge's example, which compared discrete death tolls (not ranges).

By "pre- and post-catastrophe population", I meant the population at the start and end of a period of 1 year, which I now also refer to as the initial and final population.

I guess you are thinking that the period of 1 year I mention above is one over which there is a catastrophe, i.e. a large reduction in population. However, I meant a random unconditioned year. I have now updated "period of 1 year" to "any period of 1 year (e.g. a calendar year)". Population has been growing, so my ratio between the initial and final population will have a high chance of being lower than 1.

Oh, I didn't mean for you to define the period explicitly as a fixed interval period. I assume this can vary by catastrophe. Like maybe population declines over 5 years with massive crop failures. Or, an engineered pathogen causes massive population decline in a few months.

Hi @MichaelStJules, I am tagging you because I have updated the following sentence. If there is a period longer than 1 year over which population decreases, the power laws describing the ratio between the initial and final population of each of the years following the 1st could have different tail indices, with lower tail indices for years in which there is a larger population loss. I do not think the duration of the period is too relevant for my overall point. For short and long catastrophes, I expect the PDF of the ratio between the initial and final population to decay faster than the benefits of saving a life, such that the expected value density of the cost-effectiveness decreases with the severity of the catastrophe (at least for my assumption that the cost to save a life does not depend on the severity of the catastrophe).

I just wasn't sure what exactly you meant. Another intepretation would be that P_f is the total post-catastrophe population, summing over all future generations, and I just wanted to check that you meant the population at a given time, not aggregating over time.

I see! Yes, both  and  are population sizes at a given point in time.

I think that the risk of human extinction over 1 year is almost all driven by some powerful new technology (with residues for the wilder astrophysical disasters, and the rise of some powerful ideology which somehow leads there). But this is an important class! In general dragon kings operate via something which is mechanically different than the more tame parts of the distribution, and "new technology" could totally facilitate that.

To clarify, my estimates are supposed to account for unknown unknowns. Otherwise, they would be any orders of magnitude lower.

Unfortunately, for the relevant part of the curve (catastrophes large enough to wipe out large fractions of the population) we have no data, so we'll be relying on theory.

I found the "Unfortunately" funny!

My understanding (based significantly just on the "mechanisms" section of that wikipedia page) is that dragon kings tend to arise in cases where there's a qualitatively different mechanism which causes the very large events but doesn't show up in the distribution of smaller events. In some cases we might not have such a mechanism, and in others we might.

Makes sense. We may even have both cases in the same tail distribution. The tail distribution of the annual war deaths as a fraction of the global population is characteristic of a power law from 0.001 % to 0.01 %, then it seems to have a dragon king from around 0.01 % to 0.1 %, and then it decreases much faster than predicted by a power law. Since the tail distribution can decay slower and faster than a power law, I feel like this is still a decent assumption.

It certainly seems plausible to me when considering catastrophes (and this is enough to drive significant concern, because if we can't rule it out it's prudent to be concerned, and risk having wasted some resources if we turn out to be in a world where the total risk is extremely small), via the kind of mechanisms I allude to in the first half of this comment.

I agree we cannot rule out dragon kings (flatter sections of the tail distribution), but this is not enough for saving lives in catastrophes to be more valuable than in normal times. At least for the annual war deaths as a fraction of the global population, the tail distribution still ends up decaying faster than a power law despite the presence of a dragon king, so the expected value density of the cost-effectiveness of saving lives is still lower for larger wars (at least given my assumption that the cost to save a life does not vary with the severity of the catastrophe). I concluded the same holds for the famine deaths caused by the climatic effects of nuclear war.

One could argue we should not only put decent weight on the existence of dragon kings, but also on the possibility that they will make the expected value density of saving lives higher than in normal times. However, this would be assuming the conclusion.

Thanks for the comment, David! I agree all those effects could be relevant. Accordingly, I assume that saving a life in catastrophes (periods over which there is a large reduction in population) is more valuable than saving a life in normal times (periods over which there is a minor increase in population). However, it looks like the probability of large population losses is sufficiently low to offset this, such that saving lives in normal time is more valuable in expectation.

Thanks for clarifying! I agree B) makes sense, and I am supposed to be doing B) in my post. I calculated the expected value density of the cost-effectiveness of saving a life from the product between:

  • A factor describing the value of saving a life ().
  • The PDF of the ratio between the initial and final population (), which is meant to reflect the probability of a catastrophe.

if you're primarily trying to model effects on extinction risk

I am not necessarily trying to do this. I intended to model the overall effect of saving lives, and I have the intuition that saving a life in a catastrophe (period over which there is a large reduction in population) conditional on it happening is more valuable than saving a life in normal times, so I assumed the value of saving a life increases with the severity of the catastrophe. One can assume preventing extinction is specially important by selecting a higher value for  ("the elasticity of the benefits [of saving a life] with respect to the ratio between the initial and final population").

Thanks for the critique, Owen! I strongly upvoted it.

I'm worried that modelling the tail risk here as a power law is doing a lot of work, since it's an assumption which makes the risk of very large events quite small (especially since you're taking a power law in the ratio

Assuming the PDF of the ratio between the initial and final population follows a loguniform distribution (instead of a power law), the expected value density of the cost-effectiveness of saving a life would be constant, i.e. it would not depend on the severity of the catastrophe. However, I think assuming a loguniform distribution for the ratio between the initial and final population majorly overestimates tail risk. For example, I think a population loss (over my period length of 1 year[1]) of 90 % to 99 % (ratio between the initial and final population of 10 to 100) is more likely than a population loss of 99.99 % to 99.999 % (ratio between the initial and final population of 10 k to 100 k), whereas a loguniform distribution would predict both of these to be equally likely.

aside from the threshold from requiring a certain number of humans to have a viable population

My reduction in population is supposed to refer to a period of 1 year, but the above only decreases population over longer horizons. 

the structure of the assumption essentially gives that extinction is impossible

I think human extinction over 1 year is extremely unlikely. I estimated 5.93*10^-12 for nuclear wars, 2.20*10^-14 for asteroids and comets, 3.38*10^-14 for supervolcanoes, a prior of 6.36*10^-14 for wars, and a prior of 4.35*10^-15 for terrorist attacks.

But we know from (the fancifully named) dragon king theory that the very largest events are often substantially larger than would be predicted by power law extrapolation.

Interesting! I did not know about that theory. On the other hand, there are counterexamples. David Roodman has argued the tail risk of solar storms decreases faster than predicted by a power law:

Complementary cumulative CDF of geomagnetic storm events as function of Dst, 1957-2014, power law and GP fits

I have also found the tail risk of wars decreases faster than predicted by a power law:

Do you have a sense of the extent to which the dragon king theory applies in the context of deaths in catastrophes?

  1. ^

    I have now clarified this in the post.

I'm confused by some of the set-up here. When considering catastrophes, your "cost to save a life" represents the cost to save that life conditional on the catastrophe being due to occur? (I'm not saying "conditional on occurring" because presumably you're allowed interventions which try to avert the catastrophe.)

My language was confusing. By "pre- and post-catastrophe population", I meant the population at the start and end of a period of 1 year, which I now also refer to as the initial and final population. I have now clarified this in the post.

I assume the cost to save a life in a given period is a function of the ratio between the initial and final population of the period.

Or is the point that you're only talking about saving lives via resilience mechanisms in catastrophes, rather than trying to make the catastrophes not happen or be small? But in that case the conclusions about existential risk mitigation would seem unwarranted.

I meant to refer to all mechanisms (e.g. prevention, response and resilience) which affect the variation in population over a period.

Thanks for all your comments, Owen!

That paper was explicitly considering strategies for reducing the risk of human extinction.

My expected value density of the cost-effectiveness of saving a life, which decreases as catastrophe severity increases, is supposed to account for longterm effects like decreasing the risk of human extinction.

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