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Kaj_Sotala comments on Probabilities Small Enough To Ignore: An attack on Pascal's Mugging - Less Wrong Discussion

20 Post author: Kaj_Sotala 16 September 2015 10:45AM

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Comment author: Kaj_Sotala 19 September 2015 05:23:17PM *  1 point [-]

There seems to be no obvious reason to assume that the probability falls exactly in proportion to the number of lives saved.

If GiveWell told me they thought that real-life intervention A could save one life with probability PA and real-life intervention B could save a hundred lives with probability PB, I'm pretty sure that dividing PB by 100 would be the wrong move to make.

Comment author: V_V 19 September 2015 09:51:06PM *  -1 points [-]

There seems to be no obvious reason to assume that the probability falls exactly in proportion to the number of lives saved.

It is an assumption to make asymptotically (that is, for the tails of the distribution), which is reasonable due to all the nice properties of exponential family distributions.

If GiveWell told me they thought that real-life intervention A could save one life with probability PA and real-life intervention B could save a hundred lives with probability PB, I'm pretty sure that dividing PB by 100 would be the wrong move to make.

I'm not implying that.

EDIT:

As a simple example, if you model the number of lives saved by each intervention as a normal distribution, you are immune to Pascal's Muggings. In fact, if your utility is linear in the number of lives saved, you'll just need to compare the means of these distributions and take the maximum. Black swan events at the tails don't affect your decision process.

Using normal distributions may be perhaps appropriate when evaluating GiveWell interventions, but for a general purpose decision process you will have, for each action, a probability distribution over possible future world state trajectories, which when combined with an utility function, will yield a generally complicated and multimodal distribution over utility. But as long as the shape of the distribution at the tails is normal-like, you wouldn't be affected by Pascal's Muggings.

Comment author: Kaj_Sotala 20 September 2015 11:38:36AM 0 points [-]

But it looks like the shape of the distributions isn't normal-like? In fact, that's one of the standard EA arguments for why it's important to spend energy on finding the most effective thing you can do: if possible intervention outcomes really were approximately normally distributed, then your exact choice of an intervention wouldn't matter all that much. But actually the distribution of outcomes looks very skewed; to quote The moral imperative towards cost-effectiveness:

DCP2 includes cost-effectiveness estimates for 108 health interventions, which are presented in the chart below, arranged from least effective to most effective [...] This larger sample of interventions is even more disparate in terms of costeffectiveness. The least effective intervention analysed is still the treatment for Kaposi’s sarcoma, but there are also interventions up to ten times more cost-effective than education for high risk groups. In total, the interventions are spread over more than four orders of magnitude, ranging from 0.02 to 300 DALYs per $1,000, with a median of 5. Thus, moving money from the least effective intervention to the most effective would produce about 15,000 times the benefit, and even moving it from the median intervention to the most effective would produce about 60 times the benefit.

It can also be seen that due to the skewed distribution, the most effective interventions produce a disproportionate amount of the benefits. According to the DCP2 data, if we funded all of these interventions equally, 80% of the benefits would be produced by the top 20% of the interventions. [...]

Moreover, there have been health interventions that are even more effective than any of those studied in the DCP2. [...] For instance in the case of smallpox, the total cost of eradication was about $400 million. Since more than 100 million lives have been saved so far, this has come to less than $4 per life saved — significantly superior to all interventions in the DCP2.

Comment author: V_V 20 September 2015 12:46:36PM *  -1 points [-]

I think you misunderstood what I said or I didn't explain myself well: I'm not assuming that the DALY distribution obtained if you choose interventions at random is normal. I'm assuming that for each intervention, the DALY distribution it produces is normal, with an intervention-dependent mean and variance.

I think that for the kind of interventions that GiveWell considers, this is a reasonable assumption: if the number of DALYs produced by each intervention is the result of a sum of many roughly independent variables (e.g. DALYs gained by helping Alice, DALYs gained by helping Bob, etc.) the total should be approximately normally distributed, due to the central limit theorem.

For other types of interventions, e.g. whether to fund a research project, you may want to use a more general family of distributions that allows non-zero skewness (e.g. skew-normal distributions), but as long as the distribution is light-tailed and you don't use extreme values for the parameters, you would not run into Pascal's Mugging issues.

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