# Diversifying money on different charities

post by Paul_Lang · 2019-05-08T08:56:24.956Z · score: 3 (2 votes) · EA · GW · 6 commentsThis is a question post.

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Assuming that I precisely know which charity does how much good, I thought for a long time that it is most efficient to spend all my charity budget on this single charity. However, last week I thought that utility can be expressed as a function of how much money every charity has. So rather then spending everything on one charity, I should allocate my money based on the gradient of the utility function in it's current state (provided the utility function is smooth around this state). I would appreciate some (hopefully mathematically not challenging) comment.

Thanks.

## Answers

Yes, charities are typically presumed to have diminishing marginal utility from money, so at some point you should stop funding one and start funding the next. However in practice charities have large budgets that don't respond much to individual donors, so the right answer can stay the same from your first dollar to your last. Therefore I don't think most of us have to worry about this. What kind of donations are you thinking of? If it's in the low five figures or less, then I would not think about it. Larger budgets can be a different story. Also depends on the size of charity, of course.

This answer holds for almost all situations a small donor might encounter.

The most common exception I can think of: A charity is running a special campaign where dollars are more valuable until a certain point (for example, they are eligible to get their next $5000 in donations matched dollar-for-dollar, but no further matching past that, so your 5001st dollar suddenly has half the impact of the first dollar, and you might start giving elsewhere at that point).

There are other situations I've encountered with the same kind of artificial limit. Facebook, for example, only allowed each donor to give $20,000 for their last Giving Tuesday match. This means that someone planning to give more might find that their best marginal use of money is to transfer money to other people so they can donate to the Giving Tuesday match themselves (though I'd consider this to be an ethical gray area, as it clearly goes against Facebook's intentions for that restriction).

Thank you both for your answer. I am really just thinking of marginal utility, as I am just a student with limited budget. I just do not think that the vector the maximizes marginal utility points in the direction of the most efficient charity (which I thought is true a few weeks ago). Now I think it should point in the direction of the gradient of U(x1, ..., xn), the utility as function of the budget of charities x1 to xn. That is, it points in the direction of many charities, and I should split my spendings accordingly between the charities to maximise the benefit (assuming negligible overhead costs of splitting).

Why do you think this? Are you trying to account for uncertainty about what the most efficient charity is? Otherwise, I don't understand this particular argument for "multiple charities" over "one charity".

No, I am not trying to account for uncertainty.

But look for instance at this or this picture and assume it shows utility z as function of the budget of two charities x and y. For almost every point (x, y), the steepest slope is in neither in direction (0, 1) nor in direction (1, 0) but in a combination of both direction. In other words, to optimize utility, I should give part of my money to charity x, part to charity y.

OK, I realised the flaw in my argumentation. If I have 1000 GBP to give away, I could either 'walk' 1000 GBP in direction of charity x or 1000 GBP in direction of charity y but only sqrt(x^2 + y^2) in a combination of x and y, e.g. the maximal gradient. The optimal allocation (x, y) of money is what maximises the scalar product of gradient (dU/dx, dU/dy) * (x, y) under the restriction that x + y = 1000. If dU/dx = dU/dy a 50/50 allocation as good as an allocation of all money to the most effective charity. Otherwise giving all money to the most effective charity maximises utility. Sorry for the confusion and thanks for the discussion.

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