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Has anyone tried mathematically modeling opportunities for moral trade and applying the framework to real interventions? The forum posts mostly seem to talk about meat consumption and global health donations without using numbers. I haven’t read most of the linked material though, so there’s a good chance someone has already come up with parts of what I’ve written below – if that’s the case, please let me know where I can read it in the comments!


An assumption is that work that would otherwise be done by each agent has no value to the other.

Cost effectiveness = unit of value/cost

Percent of an intervention’s cost an agent should be willing to fund = percent effectiveness estimate (relative to current bar, which is the level of cost-effectiveness required for an intervention to be funded)

Leverage factor = 1/percent effectiveness estimate


I’ve recently been thinking about the problem of antibiotic resistance, which is partly caused by animal agriculture (bad for nonhuman animals) and prevents medicine from working (bad for humans and nonhuman animals). Depending on the effectiveness of a campaign that tackles both issues, you could get gains from collaboration.

Let’s say Open Philanthropy has two teams: animal welfare (AW) and global health and development (GH&D). AW thinks that the best intervention is a corporate campaign against Purdue to change to a slower-growing breed. AW also thinks that a corporate campaign against JBS would be 92% as impactful as the campaign against Purdue, but it won’t be quite as effective since their feed gives the chickens stronger bones, making the rapid growth rates less of a welfare issue.

GH&D thinks that the best intervention is GiveWell’s top recommendation. GH&D also thinks that the campaign against Purdue wouldn’t have any appreciable effect on human well-being, since they don’t use medically important antibiotics, and thus don’t contribute to antibiotic resistance that will be problematic for humans. However, since JBS uses many medically relevant antibiotics, they think a corporate chicken campaign against them could be 12% as effective as GiveWell’s recommendation. If the campaign works, the slower-growing breeds will require fewer antibiotics, thereby contributing less to the problem of antibiotic resistance.

The corporate campaign will cost $1,000,000 regardless of which company is targeted. Each team has a $1,000,000 budget. Without trade, GH&D will spend all their money on GiveWell recommendations, and AW will spend all their money on the Purdue campaign. Each considers the other’s impact to be 0 units, while theirs is 10 units.

GH&D should be willing to fund up to 12% of the JBS campaign (leverage factor = 8.33), assuming someone else, who would otherwise generate no value in their view, funds the rest. AW should be willing to fund up to 92% of the JBS campaign (leverage factor 1.09), assuming someone else, who would otherwise generate no value in their view, funds the rest.

With trade, GH&D will fund 8-12% of the campaign, and AW fund 88-92%. We’ve already discussed how to derive the maximum percentages. The minimum percentage is simply the smallest amount they could fund while leaving the other equally well off. GH&D must fund at least 8% because AW only benefits by funding 92% or less. Anywhere in these ranges, therefore, both are better off than they were before. Let’s say GH&D funds 10% and AW funds 90%.

The JBS campaign generates 9.2 units of value for AW and 1.2 units of value for GH&D. AW spends their remaining $100,000 on a fraction of the Purdue campaign, generating 1 unit of value. GH&D spends their remaining $900,000 on GiveWell recommended charities, generating 9 units of value. At the end of the day, both AW and GH&D end up with 10.2 units of value generated, which is greater than the original 10 they would have achieved without trade.

I suspect this sort of trade doesn’t happen often because it’s rare for a particular intervention to be sufficiently impactful under two worldviews to warrant collaborative funding. It’s also hard to prove that one would have donated less to the secondary intervention (i.e. that it was not already the top intervention). However, such a trade seems plausible with antibiotic resistance. Open Philanthropy conducted a shallow investigation in 2013 and spoke with some researchers. Interview notes say that “Reducing antimicrobial use in this industry is a significant challenge. Although there is some academic disagreement on this question, both Dr. Solomon and Dr. Patel believe that there is a significant risk that antibiotic resistance developed on farms could spread to humans.” This EA Forum post casts doubt on the idea that factory farming is a key contributor to the problem. This post is a good discussion of animal advocacy and antibiotic resistance, but the specific questions discussed are different from the contents of this post.


Regardless of the true effect in this case, the theory should be developed in case there’s another opportunity (or to incentivize and enable people to find opportunities). Another potential opportunity that seems worth investigating is trade between climate and animal advocacy groups. Animal agriculture has widely recognized environmental externalities, and Giving Green even lists the Good Food Institute as a top charity.

Since writing this text, I put together a moral trade surplus calculator with calculations for a chicken campaign and GFI. I’m also planning to incorporate the possibility that one agent assigns nonzero value to the other’s default work, which more closely reflects reality.

Thanks to Dave Banerjee for feedback on this post.

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Executive summary: The post proposes a mathematical framework for modeling opportunities for collaboration between groups with different priorities, and applies it to a hypothetical campaign targeting antibiotic use in animal agriculture.

Key points:

  1. A mathematical model is proposed for assessing when groups with different priorities (e.g. animal welfare and global health) could collaborate on an intervention and both be better off.
  2. The model calculates the percentage of funding each group should contribute based on the cost-effectiveness and value they assign to an intervention relative to their default option.
  3. An example applies the model to a hypothetical corporate campaign targeting antibiotic use in chicken production, which impacts both animal welfare and antibiotic resistance.
  4. The post suggests corporate campaigns reducing antibiotic use in animal agriculture as one area where such collaboration could occur. More analysis is needed to assess the actual opportunities.
  5. The theory could incentivize groups to search for and collaborate on interventions that provide mutual gains.
  6. Other possible areas for collaboration using this framework include animal agriculture's environmental impact.


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