I think the biggest issue with the bubble rule is that the math doesn’t work out. The secondary attack rate between house members is ~30% and probably much lower between other contacts. At that low of a rate, these games with the graph structure buy very little and may be harmful because they increase the fraction of contact occurring between similar people (which is bad because the social cost of a pair of people interacting is roughly the product of their infection risks).
I’m somewhat confused what you mean by “the math doesn’t work out.” Compared to what?
If you’re well coordinated, it seems like the secondary household infection rate isn’t too relevant, because you don’t interact with anyone else and you don’t get sick.
If you’re not well coordinated, in the absence of this rule you’re probably off doing crazier things.
Are you assuming something like “you’re medium coordinated, which is enough to jump through the basic hoops for 12-person-bubble but not enough to avoid one person getting sick and then getting the bubble sick?” Seems plausible, but what number would you have picked? (bearing in mind that if you choose too low a number, after 6 months people are like ‘screw it’ and doing whatever)
As a background assumption, I’m focused on the societal costs of getting infected, rather than the personal costs, since in most places the latter seem negligible unless you have pre-existing health conditions. I think this is also the right lens through which to evaluate Alameda’s policy, although I’ll discuss the personal calculation at the end.
From a social perspective, I think it’s quite clear that the average person is far from being effectively isolated, since R is around 0.9 and you can only get to around half of that via only household infection. So a 12 person bubble isn’t really a bubble… It’s 12 people who each bring in non trivial risk from the outside world. On the other hand they’re also not that likely to infect each other.
From a personal perspective, I think the real thing to care about is whether the other people are about as careful as you. By symmetry there’s no reason to think that another house that practices a similar level of precaution is more likely to get an outside infection than your house is. But by the same logic there’s nothing special about a 12 person bubble: you should be trying to interact with people with the same or better risk profile as you (from a personal perspective; from a societal perspective you should interact with riskier people, at least if you’re low risk, because bubbles full of risky people are the worst possible configuration and you want to help break those up).
As a background assumption, I’m focused on the societal costs of getting infected, rather than the personal costs, since in most places the latter seem negligible unless you have pre-existing health conditions.
But, of course, any 12-person bubble that contains someone with a pre-existing health condition can’t rest on 11 of the people thinking “oh, but I’m healthy!”.
From a social perspective, I think it’s quite clear that the average person is far from being effectively isolated, since R is around 0.9 and you can only get to around half of that via only household infection.
I think ‘the average person’ is the wrong thing to think about here. When the infection is rare, R will be driven by the actions of the riskiest people, since they’re the ones who predominantly have it, spread it, and catch it. If 50% of the population has an actual risk of 0, and there aren’t any graph connections between them and the other 50% of the population, then the whole population R will be driven by the connected half (and will only have slowed by by whatever connections got severed to the hermit half).
On the one hand, this is a message for hope (“you can probably relax to ‘normal human’ standards and only have an R of 1”), but also ‘normal human’ standards might be incompatible in other ways (someone who lives with 0 or 1 other person has much less to fear from a household secondary attack rate of 0.3 than someone who lives in a house of 12 people).
From a personal perspective, I think the real thing to care about is whether the other people are about as careful as you. … But by the same logic there’s nothing special about a 12 person bubble
Sure, 12 is a magic number, and actually weighing the tradeoffs should lead to different thresholds in different situations. But the overall thing you’re trying to balance is “risk cost” against “socialization gains”, and even if costs are linear, sublinear benefits scuttle these sorts of symmetry analyses.
I think the bit of this that I’m having the hardest time wrapping my head around is something like “if you accept people that are as careful as you, then you are less careful than you used to be.” Like, suppose you have a 12-person bubble, all of whom don’t interact with the outside world. Then if you say “we are open to all bubbles with at most 12 people, all of whom don’t interact with the outside world”, you now potentially have a bubble whose size is measured in the hundreds, which is a pretty different situation than the one you started in.
I don’t think bubble size is the right thing to measure; instead you should measure the amount of contract you have with people, weighted by time, distance, indoor/outdoor, mask-wearing, and how likely the other person is to be infected (I.e. how careful they are).
An important part of my mental model is that infection risk is roughly linear in contact time.
I think the biggest issue with the bubble rule is that the math doesn’t work out. The secondary attack rate between house members is ~30% and probably much lower between other contacts. At that low of a rate, these games with the graph structure buy very little and may be harmful because they increase the fraction of contact occurring between similar people (which is bad because the social cost of a pair of people interacting is roughly the product of their infection risks).
I’m somewhat confused what you mean by “the math doesn’t work out.” Compared to what?
If you’re well coordinated, it seems like the secondary household infection rate isn’t too relevant, because you don’t interact with anyone else and you don’t get sick.
If you’re not well coordinated, in the absence of this rule you’re probably off doing crazier things.
Are you assuming something like “you’re medium coordinated, which is enough to jump through the basic hoops for 12-person-bubble but not enough to avoid one person getting sick and then getting the bubble sick?” Seems plausible, but what number would you have picked? (bearing in mind that if you choose too low a number, after 6 months people are like ‘screw it’ and doing whatever)
As a background assumption, I’m focused on the societal costs of getting infected, rather than the personal costs, since in most places the latter seem negligible unless you have pre-existing health conditions. I think this is also the right lens through which to evaluate Alameda’s policy, although I’ll discuss the personal calculation at the end.
From a social perspective, I think it’s quite clear that the average person is far from being effectively isolated, since R is around 0.9 and you can only get to around half of that via only household infection. So a 12 person bubble isn’t really a bubble… It’s 12 people who each bring in non trivial risk from the outside world. On the other hand they’re also not that likely to infect each other.
From a personal perspective, I think the real thing to care about is whether the other people are about as careful as you. By symmetry there’s no reason to think that another house that practices a similar level of precaution is more likely to get an outside infection than your house is. But by the same logic there’s nothing special about a 12 person bubble: you should be trying to interact with people with the same or better risk profile as you (from a personal perspective; from a societal perspective you should interact with riskier people, at least if you’re low risk, because bubbles full of risky people are the worst possible configuration and you want to help break those up).
But, of course, any 12-person bubble that contains someone with a pre-existing health condition can’t rest on 11 of the people thinking “oh, but I’m healthy!”.
I think ‘the average person’ is the wrong thing to think about here. When the infection is rare, R will be driven by the actions of the riskiest people, since they’re the ones who predominantly have it, spread it, and catch it. If 50% of the population has an actual risk of 0, and there aren’t any graph connections between them and the other 50% of the population, then the whole population R will be driven by the connected half (and will only have slowed by by whatever connections got severed to the hermit half).
On the one hand, this is a message for hope (“you can probably relax to ‘normal human’ standards and only have an R of 1”), but also ‘normal human’ standards might be incompatible in other ways (someone who lives with 0 or 1 other person has much less to fear from a household secondary attack rate of 0.3 than someone who lives in a house of 12 people).
Sure, 12 is a magic number, and actually weighing the tradeoffs should lead to different thresholds in different situations. But the overall thing you’re trying to balance is “risk cost” against “socialization gains”, and even if costs are linear, sublinear benefits scuttle these sorts of symmetry analyses.
I think the bit of this that I’m having the hardest time wrapping my head around is something like “if you accept people that are as careful as you, then you are less careful than you used to be.” Like, suppose you have a 12-person bubble, all of whom don’t interact with the outside world. Then if you say “we are open to all bubbles with at most 12 people, all of whom don’t interact with the outside world”, you now potentially have a bubble whose size is measured in the hundreds, which is a pretty different situation than the one you started in.
I don’t think bubble size is the right thing to measure; instead you should measure the amount of contract you have with people, weighted by time, distance, indoor/outdoor, mask-wearing, and how likely the other person is to be infected (I.e. how careful they are).
An important part of my mental model is that infection risk is roughly linear in contact time.