This is a very interesting paper. Here is a short thread explaining the idea. Right now, people must be confined in a lot of places to stop the virus from spreading, because we don't have enough tests to test everyone and let people who aren't infected go back to work. 1/n
Eventually, we need to increase our testing capacity, but in the meantime, @CGollier suggests that, instead of trying to test everyone individually, we pool their biological samples and test people by group. 2/n
I don't know anything about this technique, so I have no idea if it affects the sensitivity or specificity of the test, but as we'll see the paper makes unrealistic assumptions about those anyway. It's just about exploring the idea. 3/n
If the test is negative, you know that no one in the group is infected, so everyone in it can go back to work. This assumes that tests have perfect sensitivity, i. e. there are no false negatives, which is false. Things are more complicated with a more realistic assumption. 4/n
But the paper doesn't try to relax this assumption, which I think is fine to present the basic idea, as things become a lot more complicated when you do. If we're going to seriously consider this proposal, however, we'll have to do that. 5/n
Anyway, on this admittedly unrealistic assumption, if the test is negative, you know that no one in the group is infected and everyone can go back to work. Since we can only do a limited number of tests by day, this could allow more people to go back to work quickly. 6/n
So the question @CGollier asks is: what is the optimal size n of the groups, i. e. the size that will maximize the expected number N of people back to work with a single test. By making a few other simplifying assumptions, it's trivial too calculate. 7/n 
As you can see, the optimal size of groups depends on the prevalence of infection (i. e. the proportion of people who are infected in the population), it's increasingly smaller as the prevalence increases. 8/n
This makes perfect sense: the higher the prevalence, the more likely it is that, as you increase the size of the group, at least one person in it is infected, in which case everyone in it must remain confined because we have no way of knowing who that is. 9/n
Next, @CGollier tries to give a rough estimate of the social value of doing a pooled test, using GDP per capita as the cost of confinement for one person. Unsurprisingly the value depends on the prevalence of infection. 10/n
He says using GDP per capita as the social cost of confinement for one person gives only a lower bound of the social value of exiting confinement, because this is the average and it will be higher if we test first people with the highest economic output. 11/n
I don't think it's that obvious, however, because people's productivity, even that of people who have skills that are crucial to restarting the economy, depends on the presence of other people. 12/n
So if only a small proportion of people are back to work, productivity may be crippled and the amount of wealth created even by the ordinarily most productive people could be much lower than usual. 13/n
To use a silly example to illustrate, if you're the guy who attaches the doors of a car on the frame but the guy who makes the doors is still confined, it won't do the economy much good if you're ordinarily very productive. 14/n
But we can be smart about this and it's just a minor squabble. I think @CGollier's idea is pretty neat and that we should explore it ASAP as a way of limiting the economic damage caused by the epidemic while keeping people safe. 15/15
