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I'm a managing partner at AltX, an EA-aligned quantitative crypto hedge fund. I previously earned to give as a Quant Trading Analyst at DRW. In my free time, I enjoy reading, discussing moral philosophy, and exploring Wikipedia rabbit holes.

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Hi! I’m assuming that by “this” you mean the post’s argument, “wild animals” you mean wild animal welfare research, and “stray domestic animals” you mean pet shelters. In that case, I think the post’s argument might apply to wild animal welfare research, depending upon one’s model of the effects of that research. However, I think this post’s argument is unlikely to apply to pet shelters.

Comparing area was intended :)

If it's unclear, I can add a note which says the circles should be compared by area.

Thanks for the compliment :)

When I write "skepticism of formal philosophy", I more precisely mean "skepticism that philosophical principles can capture all of what's intuitively important". Here's an example of skepticism of formal philosophy from Scott Alexander's review of What We Owe The Future:

I’m not sure I

wantto play the philosophy game. Maybe MacAskill can come up with some clever proof that the commitments I list above imply I have to have my eyes pecked out by angry seagulls or something. If that’s true, I will just not do that, and switch to some other set of axioms. If I can’t find any system of axioms that doesn’t do something terrible when extended to infinity, I will just refuse to extend things to infinity...I realize this is “anti-intellectual” and “defeating the entire point of philosophy”.

You make a good point regarding the relative niche-ness of animal welfare and AI x-risk. I agree that my post's analogy is crude and there are many reasons why people's dispositions might favor AI x-risk reduction over animal welfare.

Thanks Gage!

That's a good point I hadn't considered! I don't think that's OP's crux, but it is a coherent explanation of their neartermist cause prioritization.

This extra context makes the case much stronger.

Thanks for being charitable :)

On the percentile of a product of normal distributions, I wrote this Python script which shows that the 5th percentile of a product of normally distributed random variables will in general be a product of much higher percentiles (in this case, the 16th percentile):

import random

MU = 100

SIGMA = 10

N_SAMPLES = 10 ** 6

TARGET_QUANTILE = 0.05

INDIVIDUAL_QUANTILE = 83.55146375 # From Google Sheets NORMINV(0.05,100,10)samples = []

for _ in range(N_SAMPLES):

r1 = random.gauss(MU, SIGMA)

r2 = random.gauss(MU, SIGMA)

r3 = random.gauss(MU, SIGMA)

sample = r1 * r2 * r3

samples.append(sample)samples.sort()

# The sampled 5th percentile product

product_quantile = samples[int(N_SAMPLES * TARGET_QUANTILE)]

implied_individual_quantile = product_quantile ** (1/3)

implied_individual_quantile # ~90, which is the *16th* percentile by the empirical rule

I apologize for overstating the degree to which this reversion occurs in my original reply (which claimed an individual percentile of 20+ to get a product percentile of 5), but I hope this Python snippet shows that my point stands.

I did explicitly say that my calculation wasn't correct. And with the information on hand I can't see how I could've done better.

This is completely fair, and I'm sorry if my previous reply seemed accusatory or like it was piling on. If I were you, I'd probably caveat your analysis's conclusion to something more like "Under RP's 5th percentile weights, the cost-effectiveness of cage-free campaigns would probably be *lower* than that of the best global health interventions".

Hi Hamish! I appreciate your critique.

Others have enumerated many reservations with this critique, which I agree with. Here I'll give several more.

why isn't the "1000x" calculation actually spelled out?

As you've seen, given Rethink's moral weights, **many plausible choices for the remaining "made-up" numbers give a cost-effectiveness multiple on the order of 1000x**. Vasco Grilo conducted a similar analysis which found a multiple of 1.71k. I didn't commit to a specific analysis for a few reasons:

- I agree with your point that uncertainty is really high, and I don't want to give a precise multiple which may understate the uncertainty.
- Reasonable critiques can be made of pretty much any assumptions made which imply a specific multiple. Though these critiques are important for robust methodology, I wanted the post to focus specifically upon how difficult it seems to avoid the conclusion of prioritizing animal welfare in neartermism. I believe that given Rethink's moral weights, a cost-effectiveness multiple on the order of 1000x will be found by most plausible choices for the additional assumptions.

(Although I got the 5th and 95th percentiles of the output by simply multiplying the 5th and 95th percentiles of the inputs. This is not correct, but I'm not sure there's a better approach without more information about the input distributions.)

Sadly, I don't think that approach is correct. **The 5th percentile of a product of random variables is not the product of the 5th percentiles**---in fact, in general, it's going to be a product of much higher percentiles (20+).

To see this, imagine if a bridge is held up 3 spokes which are independently hammered in, and each spoke has a 5% chance of breaking each year. For the bridge to fall, all 3 spokes need to break. That's not the same as the bridge having a 5% chance of falling each year--the chance is actually far lower (0.01%). For the bridge to have a 5% chance of falling each year, each spoke would need to have a 37% chance of breaking each year.

As you stated, knowledge of distributions is required to rigorously compute percentiles of this product, but it seems likely that the 5th percentile case would still have the multiple several times that of GiveWell top charities.

let's not forget second order effects

This is a good point, but the second order effects of global health interventions on animals are likely much larger in magnitude. I think some second-order effects of many animal welfare interventions (moral circle expansion) are also positive, and I have no idea how it all shakes out.

Insightful and well-argued post!

I found it hard to update throughout this story because the presentation of evidence from both parties was (understandably) biased. As you pointed out, "Sharing Information About Nonlinear" presented sometimes true claims in a way which makes the reader unsympathetic to Nonlinear. Nonlinear's response presented compelling rebuttals in a way which was calculated to increase the reader's sympathy for Nonlinear. Both articles intentionally mix the evidence and the vibes in a way which makes it difficult to readers to separate the two. (I don't blame Nonlinear's response for this as much, since it was tit for tat.)

Thanks again for putting so much time and effort into this, and I'm excited to see what you write next.