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It follows from the assumption that you're not Bill Gates, don't have enough money to actually shift the marginal expected utilities of the charitable investment, and that charities themselves do not operate in an efficient market for expected utilons, so that the two top charities do not already have marginal expected utilities in perfect balance.

the assumption whose violation your argument relies on, is you not having enough money to shift the marginal expected utilities, when "you" are considered to be controlling the choices of all the donors who choose in a sufficiently similar way. I would agree that given the right assumptions about the initial marginal expected utilities and how more money would change the marginal utilities and marginal expected utilities, that this assumption might sometimes be violated doesn't look like an entirely frivolous objection to a naively construed strategy of "give everything to your top charity".

(BTW, It's not clear to me why mistrust in your ability to evaluate the utility of donations to different charities should end up balancing out to produce very close expected utilities. It would seem to have to involve something like Holden's normal distribution for charity effectiveness, or something else that would make it so that whenever large utilites are involved, the corresponding probabilities will necessarily be requisitely small.)

(edit: quickly fixed some errors)

for instance it may be easier to exploit to the extent sufficient to get into the top 5

This seems sort of important.

Sure, if I have two algorithms A1 and A2, and A1 spits out a single charity, and A2 spits out an unsorted list of 5 charities, and A1 is easy for people to exploit but A2 is much more difficult for people to exploit, it's entirely plausible that I'll do better using A2, even if that means spreading my resources among five charities.

OTOH, if A2 is just as easy for people to exploit as A1, it's not clear that this gets me any benefit at all.
And if A2 is easier to exploit, it leaves me actively worse off.

Granted, if, as in your turret example, A2 is simply (A1 plus some random noise), A2 cannot be easier to game than A1. And, sure, if (as in your turret example) all I care about is that I've hit the best charity with some of my money, random diversification of the sort you recommend works well.

I suspect that some people donating to charities have different goals.

As expected, you ignored the assumption that "charities themselves do not operate in an efficient market for expected utilons, so that the two top charities do not already have marginal expected utilities in perfect balance."

To clarify a few points that may have been lost behind abstractions:

Suppose there is a sub-population of donors, people who do not understand physics very well, and do not understand how one could just claim that a device won't work without thorough analysis of a blueprint. Those people may be inclined to donate to the research charity working on magnetic free energy devices, if such charity exists; a high payoff low probability scenario.

Suppose you have N such people willing to donate, on average, $M to cause or causes.

Two strategies are considered: donating to 1 subjectively best charity, or 5 subjectively top charities.

Under the strategy to donate to 1 'best' charity, the pay off for a magnetic perpetual motion device charity, if it is to be created, is 5 times larger than under the strategy to divide between top 5 . There is five times the reward for exploitation of this particular insecurity in the choice process; for sufficiently large M and N single-charity donating will cross the threshold whereby such charity will be economically viable, and some semi-cranks semi-frauds will jump on it.

But what's about the people donating to normal charities, like the water and mosquito nets and the like? The difference between top normal charities boil down to fairly inaccurate value judgements about which most people do not feel particularly certain.

Ultimately, the issue is that the correlation of your selection of charity with the charity's actual efficacy is affected by your choice. It is similar to the gun turret example.

There is two types of uncertainty here. The probabilistic uncertainty, from which expected utility can be straightforwardly evaluated, and the systematic bias which is unknown to the agent but may be known to other agents (e.g. inferred from observations).