One sort of budget is where you have a rigidly fixed amount of money to spend—your income is X per month, you need to spend something like X per month in order to have a decent life, you don’t have a lot of savings, so you will be spending about X per month and you just have to figure out what on. But even if you are comfortably out of paycheck-to-paycheck mode, you may still sometimes think in terms of budgets.
Suppose I’m buying a computer, a car, a camera, a bicycle, a painting to hang on the wall. There’s a big difference between how much I could spend without breaking the bank and how much I’m actually willing to spend. In principle the right way to make my choice is to figure out what utility I’ll get from each possibility, figure out what utility I’ll get from having any given amount more savings, and choose whatever maximizes the total. In practice that’s rather difficult. A common solution is to first pick some amount of money that seems reasonable: “I’ll allow myself to spend up to $600 on this”, “I expect to end up paying about $3000″, etc. And then to go shopping and be guided by that budget. You might end up substantially over or under that initial budget—maybe it turns out you underestimated what you have to spend to get a good enough car, maybe you hadn’t known that there’s an unknown artist who paints things exactly to your taste and sells them cheap, maybe you see a particular thing that you fall in love with. But the budget is still a useful tool for focusing your search.
What justifies all this is that there’s some sort of tradeoff between cost and value-to-you, and you can make a rough estimate of where on that curve without doing expected-utility calculations; e.g., to whatever extent your utility function is like others’, you’ll probably want to spend about the same amount on this thing as other people of roughly similar wealth and interests spend.
I think risk budgeting (and, in particular, COVID-19 risk budgeting) is just like this. It’s not that you have a rigidly fixed amount of risk you can take. (I mean, in some sense you surely do, because if you do things with a 10% chance of death every week then you won’t last long, just as even a multimillionaire with a large salary can’t literally spend unlimited amounts on everything, but you’re mostly operating with levels of risk that aren’t like that, just as the multimillionaire is mostly not going to run out of money even if they buy a fancier car.) But risk has a utility cost, just as stuff has a financial cost, and rather than trying to do expected utility calculations every time you do anything it may be easier to set a rough amount of risk you’re willing to incur in a given context.
Just as with financial budgeting, sometimes you’ll see something particularly attractive and say “screw the budget”. There’s a party you think you’ll really enjoy (translation: you expect the utility/risk tradeoff for this to be much more favourable than usual) so your usual budgeting heuristic needs to be adjusted. You should still look at the risks, but this is a one-off so you’re willing to take the trouble to think explicitly about the expected utilities and decide: yes, it’s fine.
That’s exactly like the situation where you’re shopping, you have a rough budget in mind, and you see something way over budget you really like, so you think “OK, is this really worth it for me?” and start doing calculations like “if I buy this and make up for it by not buying X, Y, and Z, is that a good tradeoff?” or “do I value this as much as X, Y, and Z which I spend similar amounts on?” or “if I buy this and don’t do anything to make up for it, it means I have to wait a week longer before I retire; is it worth a week of work?”.
(As with all budgeting, you should really be deciding policies rather than initial purchase choices; think not “how much do I want to go to this particular party?” but “if I decide to go to this particular party and am consistent, at what rate will I be going to such parties, and how much overall rate of risk does that expose me to, and how do I feel about that?”.)
This analogy with ordinary budgets feels solid enough to me that I think it’s sufficient to explain why risk budgeting (in general, or for COVID-19 in particular) is a thing; the specific phenomenon mentioned here—the fact that your own risks may spread to other people who don’t want to have to think about COVID-19 risks all the time—is one more reason, but I don’t think it’s the main one.
“Deciding how to accumulate COVID risk” closely resembles “deciding how to spend a small fraction of your money,” but not “deciding how to spend a large fraction of your money”: when money is tight, the territory contains a threshold that’s costly to go over, so your decision-making process should also contain a threshold that shouldn’t be gone over, i.e. a budget; but there is no such nonlinearity when accumulating (normal amounts of) COVID risk, or when spending a small fraction of your money.
In principle the right way to make my choice [of what to buy] is to figure out what utility I’ll get from each possibility, figure out what utility I’ll get from having any given amount more savings, and choose whatever maximizes the total… A common solution is to first pick some amount of money that seems reasonable… And then to go shopping and be guided by that budget.
Actually, I’m not sure I disagree with any of your explicit claims. The only claim I think we might disagree on is something like “budgeting is a good strategy even when costs/benefits add pretty much linearly,” as in the ‘spend a small fraction of your money’ or ‘accumulate COVID risk’ scenarios: I perceive you as agreeing with that statement, whereas I disagree with it (because it encourages you to think in terms of “whether I’ll exceed my budget” instead of the ground truth).
If you do endorse that bolded statement, I’m curious why. I read your comment as explaining why people do budget in low-stakes scenarios, but not why that’s optimal. (My best guess at your answer, reading between the lines, is “because it saves a lot of error-prone calculation,” which, hmm, doesn’t speak to me personally, but people differ, and maybe I overestimate my own ability to do good cost/benefit calculations.)
(Don’t get me wrong, I do sometimes do something that looks like budgeting, as you describe, when I’m spending small amounts of money; but I view it as a bad habit that I want to break myself of—with a proper eye towards TDT, though, of course.)
(I don’t know why I wrote “initial purchase choices” when I meant “individual purchase choices”, but obviously it was comprehensible anyway.)
As for whether budgeting is ever a good idea when the amounts are small enough for utility to be close to linear—I think it does two useful things: it saves cognitive effort, and it may help you resist spending more than, on careful and sober reflection, you would want to. How often those are worth the utility-loss from using a cheap approximation will vary.
I’d make an analogy with ordinary budgets.
One sort of budget is where you have a rigidly fixed amount of money to spend—your income is X per month, you need to spend something like X per month in order to have a decent life, you don’t have a lot of savings, so you will be spending about X per month and you just have to figure out what on. But even if you are comfortably out of paycheck-to-paycheck mode, you may still sometimes think in terms of budgets.
Suppose I’m buying a computer, a car, a camera, a bicycle, a painting to hang on the wall. There’s a big difference between how much I could spend without breaking the bank and how much I’m actually willing to spend. In principle the right way to make my choice is to figure out what utility I’ll get from each possibility, figure out what utility I’ll get from having any given amount more savings, and choose whatever maximizes the total. In practice that’s rather difficult. A common solution is to first pick some amount of money that seems reasonable: “I’ll allow myself to spend up to $600 on this”, “I expect to end up paying about $3000″, etc. And then to go shopping and be guided by that budget. You might end up substantially over or under that initial budget—maybe it turns out you underestimated what you have to spend to get a good enough car, maybe you hadn’t known that there’s an unknown artist who paints things exactly to your taste and sells them cheap, maybe you see a particular thing that you fall in love with. But the budget is still a useful tool for focusing your search.
What justifies all this is that there’s some sort of tradeoff between cost and value-to-you, and you can make a rough estimate of where on that curve without doing expected-utility calculations; e.g., to whatever extent your utility function is like others’, you’ll probably want to spend about the same amount on this thing as other people of roughly similar wealth and interests spend.
I think risk budgeting (and, in particular, COVID-19 risk budgeting) is just like this. It’s not that you have a rigidly fixed amount of risk you can take. (I mean, in some sense you surely do, because if you do things with a 10% chance of death every week then you won’t last long, just as even a multimillionaire with a large salary can’t literally spend unlimited amounts on everything, but you’re mostly operating with levels of risk that aren’t like that, just as the multimillionaire is mostly not going to run out of money even if they buy a fancier car.) But risk has a utility cost, just as stuff has a financial cost, and rather than trying to do expected utility calculations every time you do anything it may be easier to set a rough amount of risk you’re willing to incur in a given context.
Just as with financial budgeting, sometimes you’ll see something particularly attractive and say “screw the budget”. There’s a party you think you’ll really enjoy (translation: you expect the utility/risk tradeoff for this to be much more favourable than usual) so your usual budgeting heuristic needs to be adjusted. You should still look at the risks, but this is a one-off so you’re willing to take the trouble to think explicitly about the expected utilities and decide: yes, it’s fine.
That’s exactly like the situation where you’re shopping, you have a rough budget in mind, and you see something way over budget you really like, so you think “OK, is this really worth it for me?” and start doing calculations like “if I buy this and make up for it by not buying X, Y, and Z, is that a good tradeoff?” or “do I value this as much as X, Y, and Z which I spend similar amounts on?” or “if I buy this and don’t do anything to make up for it, it means I have to wait a week longer before I retire; is it worth a week of work?”.
(As with all budgeting, you should really be deciding policies rather than initial purchase choices; think not “how much do I want to go to this particular party?” but “if I decide to go to this particular party and am consistent, at what rate will I be going to such parties, and how much overall rate of risk does that expose me to, and how do I feel about that?”.)
This analogy with ordinary budgets feels solid enough to me that I think it’s sufficient to explain why risk budgeting (in general, or for COVID-19 in particular) is a thing; the specific phenomenon mentioned here—the fact that your own risks may spread to other people who don’t want to have to think about COVID-19 risks all the time—is one more reason, but I don’t think it’s the main one.
Thanks for the thoughtful counterargument!
Things I think we agree on:
Yes, absolutely, strong agreement.
“Deciding how to accumulate COVID risk” closely resembles “deciding how to spend a small fraction of your money,” but not “deciding how to spend a large fraction of your money”: when money is tight, the territory contains a threshold that’s costly to go over, so your decision-making process should also contain a threshold that shouldn’t be gone over, i.e. a budget; but there is no such nonlinearity when accumulating (normal amounts of) COVID risk, or when spending a small fraction of your money.
Actually, I’m not sure I disagree with any of your explicit claims. The only claim I think we might disagree on is something like “budgeting is a good strategy even when costs/benefits add pretty much linearly,” as in the ‘spend a small fraction of your money’ or ‘accumulate COVID risk’ scenarios: I perceive you as agreeing with that statement, whereas I disagree with it (because it encourages you to think in terms of “whether I’ll exceed my budget” instead of the ground truth).
If you do endorse that bolded statement, I’m curious why. I read your comment as explaining why people do budget in low-stakes scenarios, but not why that’s optimal. (My best guess at your answer, reading between the lines, is “because it saves a lot of error-prone calculation,” which, hmm, doesn’t speak to me personally, but people differ, and maybe I overestimate my own ability to do good cost/benefit calculations.)
(Don’t get me wrong, I do sometimes do something that looks like budgeting, as you describe, when I’m spending small amounts of money; but I view it as a bad habit that I want to break myself of—with a proper eye towards TDT, though, of course.)
(I don’t know why I wrote “initial purchase choices” when I meant “individual purchase choices”, but obviously it was comprehensible anyway.)
As for whether budgeting is ever a good idea when the amounts are small enough for utility to be close to linear—I think it does two useful things: it saves cognitive effort, and it may help you resist spending more than, on careful and sober reflection, you would want to. How often those are worth the utility-loss from using a cheap approximation will vary.