This has got to be one of the most common objections to EA-style cost-effectiveness analyses, and it is so deeply confused. Oddly, I can’t recall seeing anyone else explain why it’s so confused.
I suspect you could mathematically prove that, given certain assumptions, a cost-effectiveness analysis is the correct thing to do in theory. My intuition is that if you make some set of decisions, then this forces you to assign numeric cost-effectivenesses to the expected outcomes of those decisions, except you’re doing it implicitly instead of explicitly. I think the proof for this would look something like the proof of the VNM utility theorem.
I suspect you could mathematically prove that, given certain assumptions, a cost-effectiveness analysis is the correct thing to do in theory. My intuition is that if you make some set of decisions, then this forces you to assign numeric cost-effectivenesses to the expected outcomes of those decisions, except you’re doing it implicitly instead of explicitly. I think the proof for this would look something like the proof of the VNM utility theorem.