[very quick technical-ish thoughts on a necessary condition] I would guess funding retrospectively today is only useful if you think you're going to increase funding in the future.
The purpose of funding is to enable people to complete projects -- more people are willing to do a project with more funding, and only really rare, super-duper value-aligned people will do a project with very little funding.
Retrospectively funding people that are already doing the project ignores they've already signaled they're the type that is happy to do the project for low funding. But, like you said, such funding also signals to future researchers on the margin that their expected funding is higher than whatever it is right now.
So, it's a way for orgs like OpenPhil to smooth researcher consumption over time if they expect they themselves will be getting richer in the future (and thus be able to increase funding for their projects). Retrospective funding should be set at the transfer required in expectation for the marginal researcher who brings in extra value equal to the cost of retrospective funding (MB = MC)? This argument is in expectation and is likely less effective for more risk-averse people -- if OpenPhil has the money now they should probably just increase upfront funding.
This also relies on other things, like OpenPhil being seen as trustworthy enough to keep up the scheme of retrospective funding, of the signal of retrospective funding being sufficiently public, etc.
(On the run now, but I see people linked some stuff in the comments i'll check out soon. If all of what I said is common knowledge already, sorry!!)
I was thinking about this problem a lot at the beginning of the summer, and I caught myself smiling a ton while reading this at the deja vu! I think this question of moral trade on political goods is fascinating, and I definitely agree with the premise: that spending in politics is much higher than is socially optimal because there is an ‘arms race’ element to political fundraising. Few thoughts:
I'm a 4th year Math/Econ undergrad at UChicago also super interested in mechanism design and was thinking about working out moral trade markets for my thesis. I sent you an email to collaborate if you're interested!
FEAT (Forecasting EA Tournament)
The Delphi Tournament
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