This post is a part of Rethink Priorities’ Worldview Investigations Team’s __CURVE Sequence__: “Causes and Uncertainty: Rethinking Value in Expectation.” The aim of this sequence is twofold: first, to consider alternatives to expected value maximization for cause prioritization; second, to evaluate the claim that a commitment to expected value maximization robustly supports the conclusion that we ought to prioritize existential risk mitigation over all else. This post presents a software tool we're developing to better understand risk and effectiveness.

**Executive Summary**

The cross-cause cost-effectiveness model (CCM) is a software tool under development ** **by Rethink Priorities to produce cost-effectiveness evaluations in different cause areas.

**Video introduction: ****the CCM in the context of the curve sequence****, ****an overview of CCM functionality **

- The CCM enables evaluations of interventions in global health and development, animal welfare, and existential risk mitigation.
- The CCM also includes functionality for evaluating research projects aimed at improving existing interventions or discovering more effective alternatives.

The CCM follows a Monte Carlo approach to assessing probabilities.

- The CCM accepts user-supplied distributions as parameter values.
- Our primary goal with the CCM is to clarify how parameter choices translate into uncertainty about possible results.

The limitations of the CCM make it an inadequate tool for definitive comparisons.

- The model is optimized for certain easily quantifiable effective projects and cannot assess many relevant causes.
- Probability distributions are a questionable way of representing deep uncertainty.
- The model may not adequately handle possible interdependence between parameters.

Building and using the CCM has confirmed some of our expectations. It has also surprised us in other ways.

- Given parameter choices that are plausible to us, existential risk mitigation projects dominate others in expected value in the long term, but the results are too high variance to approximate through Monte Carlo simulations without drawing billions of samples.
- The expected value of existential risk mitigation in the long run is mostly determined by the tail-end possible values for a handful of deeply uncertain parameters.
- The most promising animal welfare interventions have a much higher expected value than the leading global health and development interventions with a somewhat higher level of uncertainty.
- Even with relatively straightforward short-term interventions and research projects, much of the expected value of projects results from the unlikely combination of tail-end parameter values.

We plan to host **an online walkthrough and Q&A of the model **with the Rethink Priorities Worldview Investigations Team on Giving Tuesday, November 28, 2023, at 9 am PT / noon ET / 5 pm BT / 6 pm CET. If you would like to attend this event, please __sign up__ here.

# Overview

Rethink Priorities’ cross-cause cost-effectiveness model (CCM) is a software tool we are developing for evaluating the relative effectiveness of projects across three general domains: global health and development, animal welfare, and the mitigation of existential risks. You can play with our initial version at ccm.rethinkpriorities.org and provide us feedback in this post or via this form.

The model produces effectiveness estimates, understood in terms of the effect on the sum of welfare across individuals, for interventions and research projects within these domains. Results are generated by computations on the values of user-supplied parameters. Because of the many controversies and uncertainties around these parameters, it follows a Monte Carlo approach to accommodating our uncertainty: users don’t supply precise values but instead specify distributions of possible values; then, each run of the model generates a large number of samples from these parameter distributions to use as inputs to compute many separate possible results. The aim is for the conclusions to reflect what we should believe about the spread of possible results given our uncertainty about the parameters.

# Purpose

The CCM calculates distributions of the relative effectiveness of different charitable interventions and research projects so that they can be compared. Because these distributions depend on so many uncertain parameter values, it is not intended to establish definitive conclusions about the relative effectiveness of different projects. It is difficult to incorporate the vast number of relevant considerations and the full breadth of our uncertainties within a single model.

Instead, the outputs of the CCM provide *evidence* about relative cost-effectiveness. Users must combine that evidence with both an understanding of the model’s limitations and other sources of evidence to come to their own opinions. The CCM can influence what we believe even if it shouldn’t decide it.

In addition to helping us to understand the implications of parameter values, the CCM is also intended to be used as a tool to better grasp the dynamics of uncertainty. It can be enlightening to see how much very remote possibilities dominate expected value calculations and how small changes to some parameters can make a big difference to the results. The best way to use the model is to interact with it: to see how various parameter distributions affect outputs.

# Key Features

We’re not the first to generate cost-effectiveness estimates for diverse projects or the first to make a model to do so. We see the value of the present model in terms of the following features:

### We model uncertainty with simulations

As we’ve said, we’re uncertain about many of the main parameters that go into producing results in the model. To reflect that uncertainty, we run our model with different values for those parameters.

In the current version of the model, we use 150,000 independent samples from each of the parameter distributions to generate results. These samples can be thought of as inputs to independent runs. The runs generate an array of outcomes that reflect our proper subjective probability distribution over results. Given adequate reflection of our uncertainties about the inputs to the model, these results should cover the range of possibilities we should rationally expect.

### We incorporate user-specified parameter distributions

To reflect uncertainty about parameters, the model generates multiple simulations using different combinations of values. The values for the parameters in each simulation are sampled from distributions over possible numbers. While we supply some default distributions based on what we believe to be reasonable, we also empower users to shape distributions to represent their own uncertainties. We include several types of distributions for users to select among; we also let them set the bounds and a confidence interval for their distribution of choice.

### Our results capture outcome ineffectiveness

We are uncertain about the values of parameters that figure into our calculations of the expected value of our projects. We are also uncertain about how worldly events affect their outcomes. Campaigns can fail. Mitigation efforts can backfire. Research projects can be ignored. One might attempt to capture the effect of such random events by applying a discount to the result: if there is a 30% chance that a project will fail, we may simply reduce each sampled value by 30%. Instead, we attempt to capture this latter sort of uncertainty by randomly determining the outcomes of certain critical events in each simulation. If the critical events go well, the simulation receives the full calculated value of the intervention. If the critical events go otherwise, that simulation records no value or negative value.

Many projects stand to make a large positive difference to the world but only are effective under the right conditions. If there is some chance that our project will fail, we can expect the model’s output ranges to include many samples in which the intervention makes no difference.

Including the outcomes of worldly events helps us see how much of a risk there is that our efforts are wasted. This is important for accurately measuring risk under the alternative decision procedures explored elsewhere in this sequence.

### We enable users to specify the probability of extinction for different future eras

We put more work into our calculations around the value provided by existential risk mitigation compared with other cause areas. Effectiveness evaluations in this cause area are both sensitive to particularly complex considerations and relatively less well explored.

One critical feature to assessing the effect of existential risk mitigation is the number of our descendants. This depends in part on how long we last before extinction, which in turn depends on the future threats to our species. We make it possible for users to capture their own views about risk by specifying custom risk predictions that include yearly risk assessments for the relevant periods over the coming millennia.

# Structure

The tool contains two main modules.

First, the model contains a module for assessing the effectiveness of interventions directly aimed at making a difference. This tool utilizes sub-models for evaluating and comparing interventions addressing global health and development, animal welfare, and existential risk mitigation.

Second, the model contains a module for comparing the effectiveness of research projects intended to improve the effectiveness of money spent on direct interventions. This tool combines parameters concerning the probability of finding and implementing an improvement with the costs incurred by the search.

## Intervention module

The intervention assessment module provides evaluations of the effectiveness of interventions within three categories: global health and development, animal welfare, and existential risk mitigation. The effectiveness of interventions within each category is reported in DALYs-averted equivalent units per $1000 spent on the current margin.

Given the different requirements of interventions with distinct aims, the CCM relies on several sub-models to calculate intervention effectiveness of different kinds.

**Global Health and Development**

We include several benchmark estimates of cost-effectiveness for global health and development charities to assess the relative effectiveness of animal welfare and existential risk projects. We draw these estimates from other sources, such as GiveWell, that we expect to be as reliable as anything we could produce ourselves. However, these estimates don’t incorporate uncertainty. To try to account for this and to express our own uncertainties about these estimates, we use distributions centered on the estimates.

**Animal Welfare**

Our animal welfare model assesses the effects of different interventions on welfare among farmed animal populations. The parameters that go into these calculations include the size of the farmed population, the proportion that will be affected, the degree of improvement in welfare, and the costs of the project (among others.)

Since the common unit of value used to compare interventions is assessed in disability-adjusted human life years, we discount the well-being of non-human animals based on their probability of sentience and capacities for welfare. Our default values are based on the findings of the Moral Weight Project, though they can be changed to reflect a wide range of views about the moral considerations that bear on human/animal and animal/animal tradeoffs.

**Existential Risk Mitigation**

Our existential risk model estimates the effect that risk mitigation has on both preventing near-term catastrophes and extinction. In both cases, we calculate effectiveness in terms of the difference the intervention makes in years of human life lived.

We assume that existential risk mitigation work may lower (or accidentally raise) the chance of risk of catastrophic or existential events over a few decades, but has no perpetual impact on the level of risk. The primary value of an intervention is in helping us safely make it through this period. In many of the samples, the result of our model’s randomization means that we do not suffer an event in the coming decades regardless of the intervention. If that happens, or if we suffer an event despite the intervention, this means that the intervention provides no benefit for its cost. In some others, the intervention allows our species to survive for thousands of years, gradually colonizing the galaxy and beyond. In yet others, our efforts backfire and we bring about an extinction event that would not otherwise have occurred.

The significance of existential risk depends on future population sizes. In response to the extreme uncertainty of the future, we default to a cutoff point in a thousand years, where the population is limited by the Earth’s capacity. However, we make it possible to expand this time frame to any degree. We assume that, given enough time, humans will eventually expand beyond our solar system, and for simplicity accept a constant and equal rate of colonization in each direction. The future population of our successors will depend on the density of inhabitable systems, the population per system, and the speed at which we colonize them. Given the high growth rate of a volume with constant diameter expansion, we find that the speed of expansion and the time until extinction are the most important factors for deciding effectiveness. Interventions can have an extraordinarily high mean effectiveness even if, the vast majority of the time, they do nothing.

## Research projects module

The research projects sub-module provides evaluations of research projects aimed at improving the quality of global health and development and animal welfare intervention work. These research projects make a difference in the cost-effectiveness of money spent on a project if successful. However, they are often speculative and fail to find an improvement; or, they find an improvement that is not adopted. The sub-module lets users specify the effect of moving money from an intervention with a certain effectiveness to another hypothetical intervention of higher effectiveness, then, it creates an assessment of the value of the research due to promoting that change.

If a research project succeeds in finding an improvement in effectiveness, the value produced depends on how much money is influenced as a result. Research isn’t free, and so we count the costs of research in terms of the counterfactual use of that money on interventions themselves.

# Limitations

The intervention module has several significant limitations that reduce its usefulness for generating cross-cause comparisons of cost-effectiveness. All results need to be interpreted carefully and used judiciously.

### It is geared towards specific kinds of interventions

The sub-models for existential risk mitigation and animal welfare abstract some of the particularities of the interventions within their domain to allow them to represent different interventions following a similar logic. They are far from completely general. The animal welfare model is aimed at interventions reducing the suffering of animals. Interventions aimed at promoting vegetarianism, which have an indirect effect on animal suffering, are not represented. The existential risk mitigation model is aimed at interventions lowering the near-term risk of human extinction. Many other long-termist projects, such as projects aimed at improving institutional decision-making or moral circle expansion, are not represented.

Other interventions would require different parameter choices and different logic to process them. The sorts of interventions we chose to represent are reasonably general, believed to be highly effective in at least some cases, and of particular interest to Rethink Priorities. We have avoided attempting to model many idiosyncratic or difficult-to-assess interventions, but that leaves the model radically incomplete for general evaluative purposes.

### Distributions are a questionable way of handling deep uncertainty

We represent our uncertainty about parameters with distributions over possible values. This does a good job of accounting for some forms of uncertainty. To take advantage of this, users must take care to pay attention not just to mean values but also to the variety of results.

However, representing uncertainty with distributions requires knowing which distributions to choose. Often, when faced with questions about which we are truly ignorant, it is hard to know where to place boundaries or how to divide the bulk of the values. Representing uncertainties with distributions can give us a false sense of confidence that our ignorance has been properly incorporated when we have really replaced our uncertainties with a somewhat arbitrary distribution.

### The model doesn’t handle model uncertainty

Where feasible, the CCM aims to represent our uncertainty within the model so as to produce results that incorporate that uncertainty. However, not all forms of uncertainty can be represented within a model. While a significant amount of uncertainty may be in the values of parameters, we may also be uncertain about which parameters should be included in the model and how they should relate to each other. If we have chosen the wrong set of parameters, or left out some important parameters, the results will fail to reflect what we should believe. If we have left out considerations that could lower the value of some outcomes, the results will be overly optimistic. If we’re not confident that our choice of parameters is correct, then the model’s estimates will fall into a narrower band than they should.

### The model assumes parameter independence

We generate the value of parameters with independent samples from user-supplied distributions. The values chosen for each parameter have no effect on the values chosen for others. It is likely that some parameters should be dependent on each other, either because the underlying factors are interrelated or because our ignorance about them may be correlated. For example, the speed of human expansion throughout may be correlated with the probability of extinction by each year in the far future. Or, the number of shrimp farmed may be correlated with the proportion of shrimp we can expect to affect. Interdependence would suggest that the correct distribution of results will not have the shape that the model actually produces. We mitigate this in some cases by deriving some values from the parameters based on our understanding of their relationship, but we can’t fully capture all the probabilistic relationships between parameter values and we generally don’t try to.

# Lessons

Despite the CCM’s limitations, it offers several general lessons.

### The expected value of existential risk mitigation interventions depends on future population dynamics

For all we knew at the outset, many factors could have played a significant role in explaining the possible value of existential risk mitigation interventions. Given our interpretation of future value in terms of total welfare-weighted years lived, it turns out that the precise amount of value depends, more than anything, on two factors: the time until our successors go extinct and the speed of population expansion. Other factors, such as the value of individual lives, don’t make much of a difference.

The size of the effect is so tremendous that including a high expansion rate in the model as a possibility will lead existential risk to have extremely high expected cost-effectiveness, practically no matter how unlikely it is. Each of these two factors is radically uncertain. We don’t know what might cause human extinction assuming that we should survive for a thousand years. We have no idea how feasible it will be for us to colonize other systems. Thus, the high expected values produced by a model reflect the fact that we can’t rule out certain scenarios.

### The value of existential risk mitigation is extremely variable

Several factors combine to make existential risk mitigation work particularly high variance.

We measure mitigation effectiveness by the proportional reduction of yearly risk. In setting the defaults, we’ve also assumed that even if the per-century risk is high, the yearly risk is fairly low. It also seemed implausible to us that any single project, even a massive billion-dollar megaproject, would remove a significant portion of the risk of any given threat. Furthermore, for certain kinds of interventions, it seems like any project that might reduce risk might also raise it. For AI, we give this a nontrivial chance by default. Finally, in each simulation, the approximate value of extinction caused or prevented is highly dependent on the precise values of certain parameters.

The result of all this is that even with 150k simulations, the expected value calculations on any given run of the model (allowing a long future) will swing back and forth between positive and negative values. This is not to say that expected value is unknowable. Our model does even out once we’ve included billions of simulations. But the fact that it takes so many demonstrates that outcome results have extremely high variance and we have little ability to predict the actual value produced by any single intervention.

### Tail-end results can capture a huge amount of expected value

One surprising result of the model was how much of the expected value of even less speculative projects and interventions comes from rare combinations of tail-end samples of parameter values. We found that some of the results that could not fit into our charts because the values were too rare and extreme could nevertheless account for a large percentage of the expected value.

This suggests that the boundaries we draw around our uncertainty can be very significant. If those boundaries are somewhat arbitrary, then the model is likely to be inaccurate. However, it also means that clarifying our uncertainty around extreme parameter values may be particularly important and neglected.

### Unrepresented correlations may be decisive

Finally, for simplicity, we have chosen to make parameters independent of each other. As noted above, this is potentially problematic: even if we represent the right parameters with the right distributions, we may overlook correlations between those distributions. The previous lessons also suggest that our uncertainty around correlations in high-variance events might upend the results.

If we had reason to think that there was a positive relationship between how likely existential risk mitigation projects were to backfire and how fast humanity might colonize space, the expected value of mitigation work might turn out to be massively negative. If there were some reason to expect a certain correlation between the moral weight of shrimp and the populations per inhabitable solar system, for instance, if a high moral weight led us to believe digital minds were possible, the relative value the model assigns to shrimp welfare and risks from runaway AI work might look quite different.

This is interesting in part because of how under-explored these correlations are. It is not entirely obvious to us that there are critical correlations that we haven’t modeled, but the fact that such correlations could reverse our relative assessments should leave us hesitant to casually accept the results of the model. Still, absent any particular proposed correlations, it may be the best we’ve got.

**Future Plans**

We have learned a lot from the process of planning and developing the CCM. It has forced us to clarify our assumptions and to quantify our uncertainty. Where it has produced surprising results, it has helped us to understand where they come from. In other places, it has helped to confirm our prior expectations.

We will continue to use and develop it at Rethink Priorities. The research projects module was built to help assess potential research projects at Rethink Priorities and we will use it for this purpose. We will test our parameter choices, refine its verdicts, and incorporate other considerations into the model. We also hope to be able to expand our interventions module to incorporate different kinds of interventions.

In the meantime, we hope that others will find it a valuable tool to explore their own assumptions.** If you have thoughts about what works well in our model or ideas about significant considerations that we’ve overlooked, we’d love to hear about it **via this form,** **in the comments below, or at dshiller@rethinkpriorities.org.

**Acknowledgements**

The CCM was designed and written by Bernardo Baron, Chase Carter, Agustín Covarrubias, Marcus Davis, Michael Dickens, Laura Duffy, Derek Shiller, and Peter Wildeford. The codebase makes extensive use of Peter Wildeford's squigglepy and incorporates componentry from quri's squiggle library.

This overview was written by Derek Shiller. Conceptual guidance on this project was provided by David Rhys Bernard**, **Hayley Clatterbuck, Laura Duffy, Bob Fischer, and Arvo Muñoz Morán. Thanks also to everyone who reported bugs or made suggestions for improvement. The post is a project of Rethink Priorities, a global priority think-and-do tank, aiming to do good at scale. We research and implement pressing opportunities to make the world better. We act upon these opportunities by developing and implementing strategies, projects, and solutions to key issues. We do this work in close partnership with foundations and impact-focused non-profits or other entities. If you're interested in Rethink Priorities' work, please consider subscribing to our __newsletter__. You can explore our completed public work __here__.

I really like the ambitious aims of this model, and I like the way you present it. I'm curating this post.

I would like to take the chance to remind readers about the walkthrough and Q&A on Giving Tuesday a ~week from now.

I agree with JWS. There isn't enough of this. If we're supposed to be a cause neutral community, then sometimes we need to actually attempt to scale this mountain. Thank for doing so!

If I understand correctly, all the variables are simulated freshly for each model. In particular, that applies to some underlying assumptions that are logically shared or correlated between models (say, sentience probabilities or x-risks).

I think this may cause some issues when comparing between different causes. At the very least, it seems likely to understate the certainty by which one intervention may be better than another. I think it may also affect the ordering, particularly if we take some kind of risk aversion or other non-linear utility into account.

To be clear, this would be a problem in any uncertainty-based CEA modeling, and clearly the situation in non-randomized models is usually much worse. It may also be very minor, not sure.

With "variables are simulated freshly for each model", do you mean that certain probability distributions are re-sampled when performing cause comparisons?

Yeah. If I understand correctly, everything is resampled rather than cached, so comparing results between two models is only done on aggregate rather than on a sample-by-sample basis

We used to have a caching layer meant to fix this, but the objective is for there not to be too much inter-run variability.

Excellent work. I've run out of good words to say about this Sequence. Hats off to the RP team.

Great start, I'm looking forward to seeing how this software develops!

I noticed that the model estimates of cost-effectiveness for GHD/animal welfare and x-risk interventions are not directly comparable. Whereas the x-risk interventions are modeled as a stream of benefits that could be realized over the next 1,000 years (barring extinction), the distribution of cost-effectiveness for a GHD or animal welfare is taken as given. Indeed:

So I'd be keen to see more granular modeling of the benefits of these interventions, especially over longer time scales. For example, cash transfers have not only immediate benefits to their recipients, but also a multiplier effect on the economy: according to this 80k episode, $1 in cash transfers produces $2.50 in additional economic output for the community. This could ultimately put the economy on a higher growth path. What effect would a $1000 donation to GiveDirectly or AMF have over the next 20-50 years?

Similarly, for an animal welfare intervention such as a corporate cage-free campaign, the long-term effects would depend on how long the cage-free policy is expected to last, how well it's enforced, etc. This would be undoubtedly complicated to model, but would help make these interventions easier to compare with traditionally "longtermist" interventions.

Thanks for this insightful comment. We've focused on capturing the sorts of value traditionally ascribed to each kind of intervention. For existential risk mitigation, this is additional life years lived. For animal welfare interventions, this is suffering averted. You're right that there are surely other effects of these interventions. Existential risk mitigation and ghd interventions will have an effect on animals, for instance. Animal welfare interventions might contribute to moral circle expansion. Including these side effects is not just difficult, it adds a significant amount of uncertainty. The side effects we choose to model may determine the ultimate value we get out. The way we choose to model these side effects will add a lot of noise that makes the upshots of the model much more sensitive to our particular choices. This doesn't mean that we think it's okay to ignore these possible effects. Instead, we conceive of the model as a starting point for further thought, not a conclusive verdict on relative value assessments.

To some extent, these sorts of considerations can be included via existing parameters. There is a parameter to determine how long the intervention's effects will last. I've been thinking of this as the length of time before the same policies would have been adopted, but you might think of this as the time at which companies renege on their commitments. We can also set a range of percentages of the population affected that represents the failure to follow through.

Thanks. D'you have all the CURVE posts published as some sort of ebook somewhere? That would be helpful

Hi Ramiro. No, we haven't collected the CURVE posts as an epub. At present, they're available on the Forum and in RP's Research Database. However, I'll mention your interest in this to the powers that be!

Hi there,

You model existential risk interventions as having a probability of being neutral, positive and negative. However, I think the effects of the intervention are continuous, and 0 effect is just a point, so I would say it has probability 0. I assume you do not consider 0 to be the default probability of the intervention having no effect because you are thinking about a negligible (positive/negative) effect. If one wanted to set the probability of the intervention having no effect to 0 while maintaining the original expected value, one could set:

Is there any reason for you having decided to go for non-null probabilities of the interventions having no effect?

Less importanty, I also think the negative part of the effects distribution may have a different shape than the positive part. So the model would ideally allow one to specify not only the probability of the intervention being negative, but also the effects distribution conditional on the effect being negative (in the same way one can for the positive part).

Meta point. I know you have a feedback form for this type of discussions, but I thought commenting here may be better to allow for public visibility/discussion. You may want to link to this post in the feedback form in case you would like people to consider sharing their feedback here (and authors of this post can unsubscribe from comments in case they do not want to be notified).

A zero effect reflects no difference in the value targeted by the intervention. For xrisk interventions, this means that no disaster was averted (even if the probability was changed). For animal welfare interventions, the welfare wasn’t changed by the intervention. Each intervention will have side effects that do matter, but those side effects will be hard to predict or occur on a much smaller scale. Non-profits pay salaries. Projects represent missed opportunity costs. Etc. Including them would add noise without meaningfully changing the results. We could use some scheme to flesh out these marginal effects, as you suggest, but it would take some care to figure out how to do so in a way that wasn’t arbitrary and potentially misleading. Do you see ways for this sort of change to be decision relevant?

It is also worth noting that assigning a large number of results to a single exact value makes certain computational shortcuts possible. More fine-grained assessments would only be feasible with fewer samples.

Fair point. I agree that having separate settings would be more realistic. I’m not sure whether it would make a significant difference to the results to have the ability to set different shapes of positive and negative distributions, given the way these effects are sampled for an all-or-nothing verdict on whether the intervention makes a difference. However, there are costs to greater configurability, and we opted for less configurability here. Though I could see a reasonable person having gone the other way.

Thanks for the clarifications!

Nevermind. I think the model as is makes sense because it is more general. One can always specify a smaller probability of the intervention having no effect, and then account for other factors in the distribution of the positive effect.

Right. If it is not super easy to add, then I guess it is not worth it.

Thanks for doing this!

Some questions and comments:

Hi Michael, here are some additional answers to your questions:

1. I roughly calibrated the reasonable risk aversion levels based on my own intuition and using a Twitter poll I did a few months ago: https://x.com/Laura_k_Duffy/status/1696180330997141710?s=20. A significant number (about a third of those who are risk averse) of people would only take the bet to save 1000 lives vs. 10 for certain if the chance of saving 1000 was over 5%. I judged this a reasonable cut-off for the moderate risk aversion level.

4. The reason the hen welfare interventions are much better than the shrimp stunning intervention is that shrimp harvest and slaughter don't last very long. So, the chronic welfare threats that ammonia concentrations battery cages impose on shrimp and hens, respectively, outweigh the shorter-duration welfare threats of harvest and slaughter.

The number of animals for black soldier flies is low, I agree. We are currently using estimates of current populations, and this estimate is probably much lower than population sizes in the future. We're only somewhat confident in the shrimp and hens estimates, and pretty uncertain about the others. Thus, I think one should feel very much at liberty to plug in different numbers for population sizes for animals like black soldier flies.

More broadly, I think this result is likely a limitation of models based on total population size, versus models that are based more on the number of animals affected per campaign. Ideally, as we gather more information about these types of interventions, we could assess the cost-effectiveness using better estimates of the number of animals affected per campaign.

Thanks for the thorough questions!

Hi Michael! Some answers:

There will be! We hope to release an update in the following days, implementing the ability to change the sample size, and allowing billions of samples. This was tricky because it required some optimizations on our end.

We were divided on selecting a reasonable default here, and I agree that a shorter default might be more reasonable for the latter case. This was more of a compromise solution, but I think we could pick either perspective and stick with it for the defaults.

That said, I want to emphasize that all default assumptions in CCM should be taken lightly, as we were focused on making a general tool, instead of refining (or agreeing upon) our own particular assumptions.

As with (3), I agree with your reasoning, and we'll probably be updating some of these template projects soon, but I would encourage you to tweak these assumptions to match yours.

I haven't engaged with this. But if I did, I think my big disagreement would be with how you deal with the value of the long-term future. My guess is your defaults dramatically underestimate the upside of technological maturity (near-lightspeed von neumann probes, hedonium, tearing apart stars, etc.) [edit: alternate frame: underestimate

accessible resourcesandefficiency of converting resources to value], and the model is set up in a way that makes it hard for users to fix this by substituting different parameters.Again, I think your default parameters make you dramatically underestimate the value of the future; relatedly, I think >10^20 times as much value comes from sources other than biological humans.

Insofar as RP uses this model, I think it will undervalue longterm-focused interventions.

Edit: I'd estimate the potential value of the long-term future more like How big is the cosmic endowment? And reason about cause prioritization like:

if you survive the time of perils, you win the equivalent of 10^70 happy human lives.I think you're right that we don't provide a really detailed model of the far future and we underestimate* expected value as a result. It's hard to know how to model the hypothetical technologies we've thought of, let alone the technologies that we haven't. These are the kinds of things you have to take into consideration when applying the model, and we don't endorse the outputs as definitive, even once you've tailored the parameters to your own views.

That said, I do think the model has a greater flexibility than you suggest. Some of these options are hidden by default, because they aren't relevant given the cutoff year of 3023 we default to. You can see them by extending that year far out. Our model uses parameters for expansion speed and population per star. It also lets you set the density of stars. If you think that we'll expand and near the speed of light and colonize every brown dwarf, you can set that. If you think each star will host a quintillion minds, you can set that too. We don't try to handle relative welfare levels for future beings; we just assume their welfare is the same as ours. This is probably pessimistic. We considered changing this, but it actually doesn't make a huge difference to the overall shape of the results, so we didn't consider it a priority. The same goes for clock speed differences. If you want to represent this within the model as written, you can just inflate the population per star. What the model can't do is capture non-cubic (and non-static) population growth rates. It also breaks down in the real far future, and we don't model the end of the universe.

Perhaps you object to parameter settings we chose as defaults. Whatever defaults we picked would be controversial. In response, let me just stress that they're not intended as our answers to these questions. They are just a flexible starting point for people to explore.

* My guess is that the EV of surviving to the far future is infinite, if it isn't undefined.

Thanks. I respect that the model is flexible and that it doesn't attempt to answer all questions. But at the end of the day, the model will be used to "help assess potential research projects at Rethink Priorities" and I fear it will undervalue longterm-focused stuff by a factor of >10^20.

I believe Marcus and Peter will release something before long discussing how they actually think about prioritization decisions.

AFAICT, the model also doesn't consider far future effects of animal welfare and GHD interventions. And against

relativeratios like >10^20 between x-risk and neartermist interventions, see:(I agree that the actual ratio isn't like 10^20. In my view this is mostly because of the long-term effects of neartermist stuff,* which the model doesn't consider, so my criticism

of the modelstands. Maybe I should have said "undervalue longterm-focused stuff by a factor of >10^20relative to the component of neartermist stuff that the model considers.")*Setting aside

causing others to change prioritization, which it feels wrong for this model to consider.Hi Zach,

Note such astronomical values require a very low longterm existential risk. For the current human population of ~ 10^10, and current life expectancy of ~ 100 years, one would need a longterm existential risk per century of 10^-60 (= 10^(70 - 10)) to get a net present value of 10^70 human lives. XPT's superforecasters and experts guessed a probability of human extinction by 2100 of 1 % and 6 %, so I do not think one can be confident that longterm existential risk per century will be 10^-60. One can counter this argument by suggesting the longterm future population will also be astronomicaly large, instead of 10^10 as I assumed. However, for that to be the case, one needs a long time without an existential catastrophe, which again requires an astronomically low longterm existential risk.

In addition, it is unclear to me how much cause prioritization depends on the size of the future. For example, if one thinks decelerating/accelerating economic growth affects AI extinction risk, many neatermist interventions would be able to meaningully decrease it by decelerating/accelerating economic growth. So the cost-effectiveness of such neartermist interventions and AI safety interventions would not differ by tens of orders of magnitude. Brian Tomasik makes related points in the article Michael linked below.

I have high credence in basically zero x-risk after [the time of perils / achieving technological maturity and then stabilizing / 2050]. Even if it was pretty low, "pretty low" * 10^70 ≈ 10^70. Most value comes from the worlds with

extremely low longterm rate of x-risk, even if you think they're unlikely.(I expect an effective population much much larger than 10^10 humans, but I'm not sure "population size" will be a useful concept (e.g. maybe we'll decide to wait billions of years before converting resources to value), but that's not the crux here.)

Meta point. I would be curious to know why my comment was downvoted (2 karma in 4 votes without my own vote). For what is worth, I upvoted all your comments upstream my comment in this thread because I think they are valuable contributions to the discussion.

By "basically zero", you mean 0 in practice (e.g. for EV calculations)? I can see the above applying for some definitions of time of perils and technological maturity, but then I think they may be astronomically unlikely. I think it is often the case that people in EA circles are sensitive to the possibility of astronomical upside (e.g. 10^70 lives), but not to astronomically low chance of achieving that upside (e.g. 10^-60 chance of achieving 0 longterm existential risk). I explain this by a natural human tendency not to attribute super low probabilities for events whose mechanics we do not understand well (e.g. surviving the time of perils), such that e.g. people would attribute similar probabilities to a cosmic endowment of 10^50 and 10^70 lives. However, these may have super different probabilities for some distributions. For example, for a Pareto distribution (a power-law), the probability density of a given value is proportional to "value"^-(alpha + 1). So, for a tail index of alpha = 1, a value of 10^70 is 10^-40 (= 10^(-2*(70 - 50))) as likely as a value of 10^50. So intuitions that the probability of 10^50 value is similar to that of 10^70 value would be completely off.

One can counter my particular example above by arguing that a power law is a priori implausible, and that we should use a more uninformative prior like a loguniform distribution. However, I feel like the choice of the prior would be somewhat arbitrary. For example, the upper bound of the prior loguniform distribution would be hard to define, and would be the major driver of the overall expected value. I think we should proceed with caution if prioritisation is hinging on decently arbitrary choices informed by almost no empirical evidence.

By the way, are you saying above that you expect 0 existential risk if we successfully pass 2050?

To be honest, I do not think the crux is the expected value of the future either. If one has the (longtermist) view that most of the expected value of interventions is in the far future, then one should assess neartermist interventions by how much they e.g. change extinction risk. I assume you would not claim that donating to the Long-Term Future Fund (LTFF), as I have been doing, decreases extinction risk 10^70 times as cost-effectively as donating to GiveWell's top charities? Personally, I do not even know whether GiveWell's top charities increase or decrease extinction risk, but I think the ratio between the absolute value of the cost-effectiveness of LTFF and such charities is much smaller than 10^70. I would maybe say 90 % chance of it being smaller than 10^10, although this is hard to quantify.

Hi Vasco,

What do you think about these considerations for expecting the time of perils to be very short in the grand scheme of things? It just doesn't seem like the probability of possible future scenarios decays nearly fast enough to offset their greater value in expectation.

Hi Pablo,

Those considerations make sense to me, but without further analysis it is not obvious to me whether they imply e.g. an annual existential risk in 2300 of 0.1 % or 10^-10, or e.g. a longterm existential risk of 10^-20 or 10^-60. I still tend to agree the expected value of the future is astronomical (e.g. at least 10^15 lives), but then the question is how easily one can increase it.

If one grants that the time of perils will last at most only a few centuries, after which the per-century x-risk will be low enough to vindicate the hypothesis that the bulk of expected value lies in the long-term (even if one is uncertain about exactly how low it will drop), then deprioritizing longtermist interventions on tractability grounds seems hard to justify, because the concentration of total x-risk in the near-term means it's comparatively much easier to reduce.

I am not sure proximity in time is the best proxy for tractability. The ratio between the final and current global GDP seems better, as it accounts for both the time horizon, and rate of change/growth over it. Intuitively, for a fixed time horizon, the higher the rate of change/growth, the harder it is to predict the outcomes of our actions, i.e. tractability will tend to be lower. The higher tractability linked to a short time of perils may be roughly offset by the faster rate of change over it. Maybe Aschenbrenner's paper on existential risk and growth can inform this?

Note I am quite sympathetic to influencing the longterm future. As I said, I have been donating to the LTFF. However, I would disagree that donating to the LTFF is astronomically (e.g. 10 OOMs) better than to the Animal Welfare Fund.

Thanks for this!

In a separate comment I describe lots of minor quibbles and possible errors.

(1) Unfortunately, we didn't record any predictions beforehand. It would be interesting to compare. That said, the process of constructing the model is instructive in thinking about how to frame the main cruxes, and I'm not sure what questions we would have thought were most important in advance.

(2) Monte Carlo methods have the advantage of flexibility. A direct analytic approach will work until it doesn't, and then it won't work at all. Running a lot of simulations is slower and has more variance, but it doesn't constrain the kind of models you can develop. Models change over time, and we didn't want to limit ourselves at the outset.

As for whether such an approach would work with the model we ended up with: perhaps, but I think it would have been very complicated. There are some aspects of the model that seem to me like they would be difficult to assess analytically -- such as the breakdown of time until extinction across risk eras with and without the intervention, or the distinction between catastrophic and extinction-level risks.

We are currently working on incorporating some more direct approaches into our model where possible in order to make it more efficient.

Great you are looking at more direct implementations for increased efficiency, I think my intuition is it would be less hard than you make out, but of course I haven't seen the codebase so your intuition is more reliable. For the different eras, this would make it a bit harder, but the pmf is piecewise continuous over time, so I think it should still be fine. Keen to see future versions of this! :)

This is fantastic

Bentham would be proud

Several (hopefully) minor issues:

If you really want both maybe have a button users can toggle? Otherwise just sticking with one seems best.

OK, but what if life is worse than 0, surely we need a way to represent this as well? My vague memory from the moral weights series was that you assumed valence is symmetric about 0, so perhaps the more sensible unit would be the negative of the value of a fully content life.

alThanks for your engagement and these insightful questions.

That sounds like a bug. Thanks for reporting!

(The URL packs in all the settings, so you can send it to someone else -- though I'm not sure this is working on the main page. To do this, it needs to be quite long.)

You're right, it does. Generally, the aim here is just conceptual clarity. It can be harder to assess the combination of two probability assignments than those assignments individually.

Yeah. It has been a point of confusion within the team too. The reason for cost per DALY is that is a metric that is often used by people making allocation decisions. However, it isn't a great representation for Monte Carlo simulations where a lot of outcomes involve no effect, because the cost per DALY is effectively infinite. This has some odd implications. For our purposes, DALYs per $1000 is a better representation. To try to accommodate both considerations, we include both values in different places.

The issue here is that interventions can affect different levels of suffering. For instance, a corporate campaign might include multiple asks that affect animals in different ways. We could have made the model more complicated by incorporating its effect on each different level. Instead, we simplified by 'summarizing' the impact with one level. We calibrated with research on the impact of similar afflictions in humans. You can represent a negative value just by choosing a higher number of hours than actually suffered. Think of it in terms of the amount of normal life that that suffering would balance out. If it is really bad, one hour of suffering might be as bad as weeks of normal life would be good.

There is a balance between accuracy and model configurability. In some places, we want to include numbers that are based on other research that we thought was likely to be accurate, but where we couldn't directly translate into the parameters of the model. I would like to convert those assessments into the terms of the model, maybe backtracking to see what parameters get a similar answer, but this wasn't a priority.

Our estimates include both calculations of catastrophic events and extinction. For the small-scale biorisk, the chance of a catastrophic event is relatively high, but the chance of extinction is low. I think you're seeing the results of catastrophic events and no extinction events. When I up the probability of extinction to be higher, and include the far future, I see very large numbers. (E.g. https://bit.ly/ccm-bio-high-risk).

Thanks, that all makes sense, yes I think that is it with the biorisk intervention, that I was only ever seeing a catastrophic event prevented and not an extinction event. For the cost/DALY or DALY/cost, I think making this conversion manually is trivial, so it would makes most sense to me to just report the DALYs/cost and let someone take the inverse themselves if they want the other unit.

Hi Oscar,

Note E(1/X) differs from 1/E(X), so one cannot get the mean cost per DALY from the inverse of the mean DALYs per cost. However, I guess the model only asks for values of the cost per DALY to define distributions? If so, since such values do not refer to expectations, I agree converting from $/DALY to DALY/$ can be done by just taking the inverse.

Ah good point that we cannot in general swap the order of the expectation operator and an inverse. For scenarios where the cost is fixed, taking the inverse would be fine, but if both the cost and the impact are variable, then yes it becomes harder, and less meaningful I think if the amount of impact could be 0.

Hi, apologies if this is based on a silly misreading of outputs, but I was just trying out the CCM and choosing 'Direct Cash Transfers' gives:

How can the median ($1.54) be over 2 OOMs below the lower bar for 90% of simulations ($406.38)?

Similarly, the 'GiveWell Bar' yields:

Am I right to interpret this as saying that the median is outside the range of 90% of simulations?

Based on the numbers, I'm guessing that this is a bug in which we're showing the median DALYs averted per $1000 but describing it as the median cost per DALY. We're planning to get rid of the cost per DALY averted and just stick with DALYs per $1000 to avoid future confusions.

Thanks for clarifying!

Nice work! Are there plans to share the source code of the model?

Yes! We plan to release the source code soon.

Hi there,

Do you have distributions in the denominator which can take the value of 0? In my Monte Carlo simulations, this has been the only cause of sign uncertainty in the expected cost-effectiveness. However, your model is more complex than the ones I have worked with, and should involve wider distributions, such that maybe you get instability even without distributions in the denominator which can take the value of 0.

The issue is that our parameters can lead to different rates of cubic population growth. A 1% difference in the rate of cubic growth can lead to huge differences over 50,000 years. Ultimately, this means that if the right parameter values dictating population are sampled in a situation in which the effect of the intervention is backfires, the intervention might have an average negative value across all the samples. With high enough variance, the average sign will be determined by the sign of the most extreme value. If xrisk mitigation work backfires in 1/4 of cases, we might expect 1/4 of collections of samples to have a negative mean.

Thanks for clarifying, Derek!

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.

That makes sense to me, Dan!

Thank you so much for doing this! I guess I will end up using the model for my own cause prioritisation and analyses.

I agree with your conclusion that it is unclear which interventions are more cost-effective among ones decreasing extinction risk and improving animal welfare. However, you also say that:

I am a little surprised that you found surprising that the most promising animal welfare interventions have a much higher expected value that the leading global health and development interventions. As I commented:

Elaborating on the above, I commented:

You're right! That wasn't particularly surprising in light of our moral weights. Thanks for clarifying: I did a poor job of separating the confirmations from the surprising results.