Ariel Simnegar 🔸 comments on Open Phil Should Allocate Most Neartermist Funding to Animal Welfare

[Ariel Simnegar 🔸]

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”.