Nick, Anders and Toby have been consulted by government agencies in the past, particularly Nick has done that several times (even by the Thailand's government apparently). If your concern is influence over government, FHI wins, given I don't think movement building would get us as far as having a Prime Minister meeting with FHI staff. It would have to be one serious movement to match just one or two meetings. It's likely that there aren't even enough eligible brains for a "AI-risks movement" of such scale.
However, it is not the case "influence over the government" should be the most important criteria. Mainly, because right now we wouldn't even know exactly what to tell them, and it might take decades until we do. Hence, the most important criteria is level of basic research. The mere fact your question hasn't any clear answers means we need more basic research, and thus that MIRI/ FHI have preference. I couldn't know whether FHI or MIRI would be better. As a wild guess, I would say FHI does more research but that it somehow feeds from MIRI non-academic flexibility and movement building. Likely, whichever had the preference over resources would lose this preference relatively fast as it outgrew the other.
On the other hand, I have heard MIRI/FHI/CEA staff claiming they are much more in need of qualified people than money. So, if CFAR is increasing qualification then they ought to have priority. But it's not clear if they are really doing that yet.
Note that Toby is a trustee of CEA and did most of his government consulting due to GWWC, not the FHI, so it's not clear that FHI wins out in terms of influence over government.
Moreover, if your concern is influence over government, CEA could still beat FHI (even if FHI is doing very high level advocacy) by acting as a multiplier on the FHI's efforts (and similar orgs): $1 donated to CEA could lead to more than $1 of financial or human capital delivered to the FHI or similar. I'm not claiming this is happening, but just pointing out that it's too simple to say FHI wins out just because they're doing some really good advocacy.
Disclaimer: I'm the Executive Director of 80,000 Hours, which is part of CEA.
In a discussion a couple months ago, Luke said, "I think it's hard to tell whether donations do more good at MIRI, FHI, CEA, or CFAR." So I want to have a thread to discuss that.
My own very rudimentary thoughts: I think the research MIRI does is probably valuable, but I don't think it's likely to lead to MIRI itself building FAI. I'm convinced AGI is much more likely to be built by a government or major corporation, which makes me more inclined to think movement-building activities are likely to be valuable, to increase the odds of the people at that government or corporation being conscious of AI safety issues, which MIRI isn't doing.
It seems like FHI is the obvious organization to donate to for that purpose, but Luke seems to think CEA (the Centre for Effective Altruism) and CFAR could also be good for that, and I'm not entirely clear on why. I sometimes get the impression that some of CFAR's work ends up being covert movement-building for AI-risk issues, but I'm not sure to what extent that's true. I know very little about CEA, and a brief check of their website leaves me a little unclear on why Luke recommends them, aside from the fact that they apparently work closely with FHI.
This has some immediate real-world relevance to me: I'm currently in the middle of a coding bootcamp and not making any money, but today my mom offered to make a donation to a charity of my choice for Christmas. So any input on what to tell her would be greatly appreciated, as would more information on CFAR and CEA, which I'm sorely lacking in.