I'm not sure this is true, sceptical inquiry can have a high expected value when it helps you work out what is a better use of limited resources. [...]

Note that Holden qualified his statement with "(too often)".

I think that in a case with an action that has low probability of producing a large gain, any investigation that will confirm whether this is true or not is worth attempting unless either [...] It seems to me that in both of these cases it would be pretty obviously stupid to have a sceptical enquiry.

Concerning your second point: suppose that spending a million dollars on intervention A ostensibly has an expected value X which is many orders of magnitude greater than that of any intervention (and suppose for simplicity negligible diminishing marginal utility per dollar). Suppose that it would cost $100,000 to investigate whether the ostensibly high expected value is well-grounded.

Then investigating the cost-effectiveness of intervention A comes at an ostensible opportunity cost of X/10. But it's ostensibly the case that the remaining $900,000 could in no case be spent with cost-effectiveness within an order of magnitude then spending the money on intervention A. So in the setting that I've just described, the opportunity cost of investigating is ostensibly too high to justify an investigation.

Note that a similar situation could prevail even if investigating the intervention cost only $100 or $10 provided that the ostensible expected value X is sufficiently high relative to other known options.

The point that I'm driving at here is that there's not a binary "can afford" or "can't afford" distinction concerning the possibility of funding A: it can easily happen that spending any resources whatsoever investigating A is ostensibly too costly to be worthwhile. This conclusion is counter-intuitive; seemingly very similar to Pascal Mugging.

The fact that naive EEV leads to this conclusion is evidence against the value of naive EEV. Of course, one can attempt to use a more sophisticated version of EEV; see the second and third paragraphs of Carl Shulman's comment here.

Why do you believe this. Do you have any evidence or even arguments? It seems pretty unintuitive to me that the sum of a bunch of actions, each of which increases total welfare, could somehow be a decrease in total welfare.

See my fourth point in the section titled "In favor of a local approach to philanthropy" here.

When you say taken to the extreme, I suspect you are imagining our hypothetical EEV agents ignoring various side-effects of their actions, in which case the problem is with them failing to take all factors into account, rather than with them using EEV.

It's not humanly possible to take all factors into account; our brains aren't designed to do so. Given how the human brain is structured, using implicit knowledge which is inexplicable can yield better decision making for humans than using explicit knowledge. This is the point of the section of Holden's post titled "Generalizing the Bayesian approach."

Not true. If all donors followed EEV, charities would indeed have an incentive to conceal information about things they are doing badly, and donors would in turn, and in accordance with EEV, start to treat failure to disclose information as evidence that the information was unflattering. This would in turn incentivise charities to disclose information about things they are doing slightly badly, which would in turn cause donors to view secrecy in an even worse light, and so on. I we eventually reach an equilibrium where charities disclose all information.

I think you're right about this.

Of course, this assumes that all charities and all donors are completely rational, which is a total fantasy, but I think the same can be said of your own argument, and even if we do end up stuck part-way to equilibrium with charities keeping some information secret, as donors we can just take that information into account and correctly treat it as Bayesian evidence of a problem.

My intuition is that in the real world the incentive effects of using EEV would in fact be bad despite the point that you raise; but refining and articulating my intuition here would take some time and in any case is oblique to the primary matters under consideration.