When causes multiply


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Preface: Searching for ‘the one true cause area’, or perhaps several of them, strikes me as a poor model of how cause prioritisation should be thought about. Much better is an emphasis on what the best allocation of resources to various cause areas looks like over time and what we need to do to achieve this allocation. In this post I’ll lay out one argument for this view.

When the EA community discusses cause prioritisation, we usually model different causes as additive. However, in the real world, the interactions between many causes aren’t additive, but interact in much more complicated ways with each other. 

In this post I’ll present how we can model causes whose impact multiplies. If causes simply add together, it makes sense to focus on the cause with the highest impact per dollar. However, if causes multiply, we should locally distribute resources between them according to the ratio of their output elasticities, i.e. how much an increase in investment in one cause affects the outcome as a whole. The output elasticity can be interpreted as a measure of how tractable a cause is. This means that local funding decisions (monetary ‘crowdedness’) should be proportional to how tractable the causes are if they’re multiplicative.

Sam Bankman-Fried has written about multiplicative causes with the same output elasticity before, in which case it is optimal to distribute resources between the multiplying causes equally. You might want to read his post before reading this one.

To illustrate this, think about economic progress vs. cultural progress. If we imagine an economically as well as culturally destitute world, we could pour all our resources into improving our world economically - and could achieve a 1984 or Brave New World dystopia. Or we could pour all our resources into improving it culturally. In that case we might have wonderful relationships with our fellow humans and beautiful art to enjoy, but would still starve and die of illnesses early. Most appealing is the world in which we put an equal amount of resources into economical and cultural progress and much more so than in the alternative worlds. In this world people will live a bit longer and don’t starve quite as much while also having acceptable relationships with their peers.

But this assumes economical vs. cultural progress are similarly tractable. What happens if the amount of resources we put into economical and technological progress multiplies, but putting extra resources in cultural progress doesn’t affect cultural progress as much as putting extra resources in economic progress affects economic progress?

To find an answer to this question, we can look at the Cobb Douglas production function and expand its use. Historically, it describes the inputs of capital and labour and how much output can be produced by those inputs.

Goods = A * Lalpha * Cbeta. In this historical version L is the labour input, while alpha is the output elasticity of labour, i.e. how many % more goods will be produced if the amount of labour is increased by 1%. C is the capital input, while beta is the output elasticity of capital. Goods are the output that is being produced. A is the ‘total factor productivity’ which captures the effects on output that aren’t explained by the input variables.

We can now ask the question how resources between labour and capital should be allocated to maximize the number of goods produced. The mathematically optimal allocation to maximize the output is determined by the ratio between the output elasticities of capital and labour, so alpha:beta. Note that in this case the output elasticities are constants.

If labour’s output elasticity was 1, but capital’s output elasticity was 0.1 (though note that those aren't the true historical ones), then to produce the most goods with a given set of resources it’s optimal to put ten times as many resources into labour than into capital.

If we now adapt the historical Cobb Douglas production function and look at our hypothetical society, we can answer our question:

Thriving of humanity = A * Resources for economic progressgamma * Resources for cultural progressdelta

A is the factor again that measures everything that results in the thriving of humanity that isn’t explained by putting in resources for economic and cultural progress.

If it is ten times easier to make progress on the thriving of humanity by investing resources in economic progress than by investing resources in cultural progress (i.e. gamma is ten times as big as delta), then as in our previous example the optimal allocation is to spend ten times as many resources on economic progress. 

Thus, the important question to ask for optimal resource allocation in multiplicative scenarios is what the ratio of the output elasticities is. However, output elasticities might change as the inputs change. Most often, the output elasticities won’t be constants. This means in many cases the production function will only tell us locally which cause is in most need of more resources to improve the overall outcome.

To calculate an output elasticity, we need to find out how much increasing the respective input by 1% is affecting the outcome as a percentage. In our example, we look at how many resources are being spent on cultural progress already i.e. how much talent or funding is currently being allocated to it. We then assess how much an increase of 1% is affecting the output. If the thriving of humanity improved by 10% due to the 1% increase of the resources for cultural progress, we have an output elasticity of 10%/1% = 10. If the thriving of humanity improved only by 0.1%, the output elasticity would be 0.1%/1% = 0.1.

What does all of this mean in practice for cause prioritisation? While many causes aren’t actually additive and modelling them as additive might give subpar results, modelling them simply as multiplicative isn’t close to perfect either. However, it might still be an improvement. 

Questions for which modelling the problem as multiplicative might be helpful are e.g. whether we should add new talent to the EA community or improve the talent we already have? Should the EA community focus to add its resources on the efforts to reduce GCRs or to add them to efforts to help humanity flourish? We could also think of the technical ideas to improve institutional decision making like improving forecasting abilities as multiplying with those institution’s willingness to implement those ideas.

When we think about global funding in the inputs for our production functions, we fundamentally care about what the EA community can do. So it’s important to compare like with like by thinking about the most effective uses of resources that will determine the output elasticities. Note also that while we’re looking at such large pools of funding, the EA community will hardly be able to affect the funding ratio substantially. Therefore, this type of exercise will often just show us which single cause should be prioritised by the EA community and thereby act additive after all. This is different if we look at questions with multiplicative factors in which the decisions by the EA community can affect the input ratios like whether we should add more talent to the EA community or focus on improving existing talent.

Which other cause prioritisation questions can you think of that are better modelled as multiplicative instead of additive? 

TL,DR: When we try to prioritise between different additive causes, it makes sense to focus on the one with the highest impact per dollar. But if we try to prioritise between different multiplicative causes, we should locally spread our resources between them according to their output elasticity ratios. That means the proportions of funding (‘crowdedness’) should locally be equal to the proportions of the output elasticities (a measure for the ‘tractability’ of the respective causes).

 

Thanks to Jacob Hilton who reviewed a draft of this post.