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I believe it because physicists-as-a-whole seem quite sure about it, and I've never seen (modern) physicists be wrong about something they're this sure about, and frankly I know fuck-all about physics beyond what I learned in high school. 98-ish % confidence that it's as correct as any model of the universe reasonably can be.
ACX also links to this paper analyzing federal cancer research, which claims it is so effective it only costs $326 in federal investment cost per life saved.
They claim $326 per life-year (specifically, DALY), not per life. Huge difference!
I agree with what you're saying; the reason I used trillions was exactly because it's an amount nobody has. Any being which can produce a trillion dollars on the spot is likely (more than 50%, is my guess) powerful enough to produce two trillion dollars, while the same cannot be said for billions.
As for expected utility vs expected payoff, I agree that under conditions of diminishing marginal utility the offer is almost never worth taking. I am perhaps a bit too used to the more absurd versions of Pascal's Mugging, where the mugger promises to grant you utility directly, or disutility in the form of a quadrillion years of torture.
Probably the intuition against accepting the money offer does indeed lie in diminishing marginal utility, but I find it interesting that I'm not tempted to take the offer even if it's stated in terms of things with constant marginal utility to me, like lives saved or years of torture prevented.
For smaller amounts of money (/utility), this works. But think of the scenario where the mugger promises you one trillion $ and you say no, based on the expected value. He then offers you two trillion $ (let's say your marginal utility of money is constant at this level, because you're an effective altruist and expect to save twice as many lives with twice the money). Do you really think that the mugger being willing to give you two trillion is less than half as likely as him being willing to give you one trilion? It seems to me that anyone willing and able to give a stranger one trillion for a bet is probably also able to give twice as much money.
I fully support this initiative, and am excited to see how it works out!
Do you have a theory of where think tanks with seemingly similar methods and goals, like the Brookings Institution and Niskanen Center, might be going wrong? Things Balsa could/would do differently to be more effective than them?