I agree with your points about risk budgets not being logically necessary because risks are generally linear and independent. But I think about risk budgets as a supplement to the normal decision-making process, because people aren't good at making one-off decisions in the abstract.
If the party costs 1 hour of expected life, I'll go. If it's 2 hours, would I still go? 3 hours? It's hard to really wrestle with that decision and figure out where the tradeoffs aren't worth it. "1 hour" is already a more concrete framing than "2 micromorts", but you're still trading off a concrete outcome (going to a party) with something pretty abstract (1 hour expected value of life), so it's hard to make logically consistent decisions that don't vary with your mood, etc.
If, instead, you set an overall weekly risk budget, you can then trade off between specific concrete choices. "If I go to this party, I can't go to the grocery store. Which would I rather do?"
So it helps to make yourself more consistent and make your decisions more concrete. Help you "set policies" (and be consistent with them) vs. "making initial decisions" to gjm's point in the other comment.
Would be interested in your thoughts!
Hmm! I think the main crux of our disagreement is over "how abstract is '1 hour of life expectancy'?": you view it as pretty abstract, and I view it as pretty concrete.
The reason I view it as concrete is: I equate "1 hour of life expectancy" to "1 hour spent driving," since I mildly dislike driving. That makes it pretty concrete for me. So, if there's a party that I'm pretty excited about, how far would I be willing to drive in order to attend? 45 minutes each way, maybe? So "a party I'm pretty excited about" is worth about 3 micromorts to me.
Does this..
A friend is hosting a party tonight! It'll cost me 200 microCOVIDs, which, as a healthy thirty-something, I very cautiously estimate to cost about 2 micromorts,[1] which is roughly equivalent to 1 hour out of my remaining life expectancy. But I'm super excited for this party; I'd happily burn an hour of my life driving there and back. Should I go?
Unless something subtle is going on... obviously yes, right?
"What about your visit to that coffee shop earlier today? Don't you think that's decision-relevant?"
The coffee shop? I'm confused. Why would that be decision-relevant?
"Well, you accumulated about 150 microCOVIDs there."
Sure, but that's not really relevant to the decision theory of whether to attend the party, is it? The party is equally enjoyable either way, and the costs of multiple COVID exposures add pretty much linearly by the axiom of independence, so previously-incurred risks are irrelevant to my future decisions. (If the coffee shop had been a week ago, sure, I'd be inflicting some of those microCOVIDs on my fellow partygoers, which, sure, could be decision-relevant, I haven't done the math; but it seems very unlikely to me that I'll become a full-fledged germ factory between this morning and this evening, so I think that consideration is insignificant in this case.)
"But you try to maintain a 200-microCOVID-per-week risk budget, don't you?"
Sure, but... hmm.
"So there's something wrong with your assertion that previously-incurred risks are irrelevant to future decisions."
...or something is wrong with the idea of risk budgeting.
"...hmm."
...so, which is it?
Zero externalities
Maybe the answer will be clearer if we simplify the problem: let's get rid of externalities. Suppose I am the world's most boring superhero, Captain Can't-Transmit-COVID. I can still catch it just like anybody else, but the cost is borne by me alone, not my friends or housemates.
Now is my coffee-shop visit decision-relevant for whether I should attend the party?
I can't think of a single reason it would be.[2] This strongly suggests that "risk budgeting" has something to do with the risk of transmitting COVID to other people.
Externalities to an enthusiastic optimizer
Let's add an externality back in: suppose I can only transmit COVID to my partner. Perhaps risk budgets will fall naturally out of the arrangements we make.
Hmm. No risk budgets in sight.
Externalities requiring costly discussions
Suppose I can also transmit to my housemate?
That's starting to sound like a budget!
So, at least in this case, it seems like risk-budgeting is a technique that lets you reduce the amount of time you spend computing/communicating risks, at the cost of sometimes making suboptimal decisions (e.g. skipping an awesome party) because you're thinking in terms of "whether I'll exceed my budget" instead of the underlying costs/benefits.
Further consequences
So far, we've only explained why people who hate doing risk-discussions keep budgets; but I know several non-risk-discussion-hating people who keep budgets. Why would they do that? Hmm...
So now I have something resembling a budget, even though I, personally, have no particular distaste for risk-discussions.
Conclusions
For people whom risk-discussions cause significant pain, risk budgets serve as a tool for reducing the amount you have to talk with people about COVID: set a limit on how much risk you will ever take on, and let other people assume you're at that level. When you go over that limit, you tell your contacts about it, and endure the painful discussions.
For people who both associate closely with people whom risk-discussions cause significant pain, something that resembles a risk budget falls straightforwardly out of cold hard utility-maximization: if you go above a certain threshold, then you have to have notify a close-contact risk-discussion-hater; which causes them pain; which you probably either feel bad about or compensate them for; which reduces your utility.
For people who aren't close contacts with risk-discussion-haters, I don't think risk budgets make sense. Instead, you simply track your microCOVIDs and share your risk info with your contacts, so everybody can do normal cost/benefit analyses like they're hopefully used to, without "budgets" appearing anywhere in the calculus.[3] You probably do not have enough close contacts for the communication overhead to be significant.
100-to-1 is a guess at what my audience, i.e. you, thinks the microCOVID-to-micromort exchange rate is, judging by things like microcovid.org's recommended budget of 200/week. As best I can figure, though, for a healthy 30-year-old the actual exchange rate is about an order of magnitude higher, even including non-death outcomes like long COVID. I'm writing this footnote to assuage my guilt over contributing to a false appearance of consensus around "100 to 1" when I don't endorse it. ↩︎
Edit: okay, I thought of a reason: maybe I don't trust myself to make smart cost-benefit assessments on a case-by-case basis, and I think my brain will routinely exaggerate the benefits of risky activities, and my psychology is such that drawing a bright line and saying "this is my budget, I can't go over this" will at least bound how much risk my lying brain can trick me into. But I think that few of the people I see maintaining "risk budgets" would give this as the reason. ↩︎
Well, maybe your friends will have "under-300-microCOVID-people-only" parties, and those will add discontinuities to your utility function that look kind of like budgets, but I think the similarity is only superficial. ↩︎