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, 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.
...so, which is it?
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. 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.
Me: So. My best estimate for partner-to-vaccinated-partner transmission, given how often we see each other, is 30% over two weeks, so for every 10 microCOVIDs I accrue, 3 spill over onto you.
My partner, the enthusiastic optimizer: Indeed. Using the 100-to-1-to-0.5 exchange rate between microCOVIDs, micromorts, and life-hours, this means that you cost me about one hour of my life for every 600 microCOVIDs you accumulate. However, a good Coasean would point out that this externality is the result of a joint decision -- your decision to take risks, plus my decision to date you during your infectious period -- so I'm willing to split that cost 50/50. Post-dinner cleanup usually takes half an hour; how about, for every 600 microCOVIDs you accrue 2-12 days before a date, you handle cleanup on a night when it would normally fall on me?
Me: And vice-versa? Every 600 microCOVIDs that you accumulate, you--
Them: Of course.
Me: Sounds fair!
Them: Oh, and-- each of us has other connections, housemates and such, who might not want to interact with us when we're high-risk. The math isn't clear to me off the bat, but we might ballpark that as doubling the cost of each of our microCOVIDs. Change from 600 microCOVIDs per dishes to 300?
Hmm. No risk budgets in sight.
Externalities requiring costly discussions
Suppose I can also transmit to my housemate?
Me: So. My best estimate for housemate-to-vaccinated-housemate transmission is 30% over two weeks, so for every 10 microCOVIDs I accrue, 3 spill over onto you.
My housemate, the sick and tired of everything about COVID: ...okay.
Me: Alex and I worked out this system where, for every 300 microCOVIDs each of us accumulates in the infectiousness window before a date, we owe the other a get-out-of-doing-the-dishes token, to compensate them for the risk we're imposing--
Me: --and your facial expression right now confirms my expectation that you would hate this. Can you elaborate on why?
Them: Just... constantly thinking about COVID, weighing every social interaction, opening microcovid.org every time I go outside, keeping track of how many microCOVIDs I'm getting from you so that I can report that number to the two other people I regularly interact with... it would ruin my days. I just really, really want to not think about it anymore.
Me: Okay, sure, I can sympathize with that. I... I'm afraid that the "don't think about it at all" strategy has really high costs for me, since I'll need to make pessimistic assumptions about your COVID risk in order to uphold my agreements with Alex and other folks...
Them: I know, I know. Ugh. How about... I'll just... I won't keep precise counts of my microCOVIDs, but I'll keep enough of an eye on things to know the rough order of magnitude of my risk, and... I don't want to have to keep you constantly updated, but how about, you can safely use 200 microCOVIDs as your pessimistic person-risk for me, and if I need to do anything that puts me over that threshold, I'll let you know.
Me: Let's see, if I assume you always have 200, then I'll have 60 from you on each my dates with Alex, so this arrangement will cost me an average of 6 minutes of dishes-doing per date... yeah, all right, I think I can make this work.
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.
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...
My housemate, later: Hey, I was thinking about what you said, about your arrangement with Alex and "every 300 microCOVIDs" -- it sounds like you're keeping the option open to sometimes take on pretty large amounts of risk.
Me: Yeah, probably not often, but it's a possibility.
Them: And... you taking 300 microCOVIDs would give me about 100, a significant chunk of my budget, possibly forcing me to have risk-management conversations I find painful with the other people I've told they can safely bound my risk at 200.
Me: Hmm. Yeah, that sounds accurate. So, if I ever plan to go above... 200, say, which is about 60 for you... then perhaps I should let you know -- which imposes a cost on you, for the emotional toll of both that conversation and the downstream conversations you might have to have with those other people.
Me: So, figuring that those conversations will be about... two hours of unpleasantness, all told?... a cost which I'm willing to split with you 50/50... if I ever go above 200, then I need to save you one hour of time. Payable by doing chores?
Them: Yeah, that sounds good.
So now I have something resembling a budget, even though I, personally, have no particular distaste for risk-discussions.
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. 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. ↩︎