If everyone spends there 1 random hour, how many people do we need so that each hour with probability 90% (or at least 80%) at least 2 people are there?
First, let’s assume that everyone logs on and off at the hour, then there are 24 windows a day. Let’s also assume that everyone chooses to work each hour with probability 1⁄24, rather than working one hour a day for certain. We then have a binomial distribution with parameters num and 1⁄24, and can increment the number of people until we get less than 20% of the probability in 0 and 1, and it turns out we cross that barrier at 71 people.
This is an underestimate because we assumed that the start/end times are synchronized.
We can also enforce the “always work exactly one hour a day” rule by seeing this as a combinatorial problem, where we have num people and 23 clock bells which are permuted randomly, and we want to know the percentage of clock bells that have at most one person in between them.
To estimate how much of an underestimate that was, I wrote a very short program to simulate this scenario. From my model, we cross over to 80% at about 85 people. Incorporating a random spread in how long people are logged in, from 0.5 to 1.5 hours, doesn’t change anything.
I am not sure how many people you could get to sign up, but the fewer you get, the more hours they’d have to commit. From my model, if you can only get 60 people, they’ll need to work on average 1.5 hours; for 45 people, you’d need them to commit to 2 hours.
The numbers don’t look too good. Even 60 people, with an average commitment of 1.5 hours, seems like a challenge. Maybe the LW community could meet it?
In practice, it’s not going to need 85 people (and it’s not going to work for everyone unscheduled), though, because the assumptions are implausible. According to the last survey, ~60% of users are in the US or Canada (and probably another 5% in South America?), and then >22% are in Europe. I would also guess that most people will probably also want to work in the evenings (say an 8h span between 6pm and 2am). This will probably concentrate the desired times a lot, so the popular times can be 80% populated with only something like 45 people (this is me guessing). Conversely, the unpopular times are going to be really dead.
On that note, it would probably make sense to create some sort of schedule. E.g. “We encourage you to come between 4pm and 8am PST.” Or to coordinate smaller specific time slots (e.g. “come at 2pm PST for one hour”) with a higher chance of having them filled.
If you constrain it to an 8 hour spread, it does indeed help things—you’d only need around 34 people agreeing to commit to 1 hour, so even more optimistic than your guess. And if we do get people to coordinate smaller specific time slots, perhaps convincing 25% to take a 1.5 hour slot and the rest to commit a minimum of 1 hour, this moves things closer to only needing a group of 30. Not too bad.
I’ve been very pleasantly surprised to see that the room has had people in it 24⁄7 since I first checked on it afternoon yesterday (current time for me is 5pm)! Usually about 5-6, I think the lowest I’ve seen is 3, although someone reported that in the quiet hours it got down to 2.
We’ll see if we’re able to keep it up, promising so far!
I like this idea, thought about checking it out, realized I don’t really know how to expect and that it might not be optimal for my personality type...then slapped myself for obvious dithering.
I’ll commit to dropping in tomorrow when I get home from work (~5:30EST) for at least an hour, to see if this suits me. After that, we’ll see.
Results report: I did get some done. More than I can usually do on demand, though it’s hard to say whether the benefit came from the technique or just from the novelty. Either way, I’ll continue doing it until it stops working, at least four times a week, in the ~6:00-7:00EST time slot.
First, let’s assume that everyone logs on and off at the hour, then there are 24 windows a day. Let’s also assume that everyone chooses to work each hour with probability 1⁄24, rather than working one hour a day for certain. We then have a binomial distribution with parameters num and 1⁄24, and can increment the number of people until we get less than 20% of the probability in 0 and 1, and it turns out we cross that barrier at 71 people.
This is an underestimate because we assumed that the start/end times are synchronized.
We can also enforce the “always work exactly one hour a day” rule by seeing this as a combinatorial problem, where we have num people and 23 clock bells which are permuted randomly, and we want to know the percentage of clock bells that have at most one person in between them.
To estimate how much of an underestimate that was, I wrote a very short program to simulate this scenario. From my model, we cross over to 80% at about 85 people. Incorporating a random spread in how long people are logged in, from 0.5 to 1.5 hours, doesn’t change anything.
I am not sure how many people you could get to sign up, but the fewer you get, the more hours they’d have to commit. From my model, if you can only get 60 people, they’ll need to work on average 1.5 hours; for 45 people, you’d need them to commit to 2 hours.
The numbers don’t look too good. Even 60 people, with an average commitment of 1.5 hours, seems like a challenge. Maybe the LW community could meet it?
In practice, it’s not going to need 85 people (and it’s not going to work for everyone unscheduled), though, because the assumptions are implausible. According to the last survey, ~60% of users are in the US or Canada (and probably another 5% in South America?), and then >22% are in Europe. I would also guess that most people will probably also want to work in the evenings (say an 8h span between 6pm and 2am). This will probably concentrate the desired times a lot, so the popular times can be 80% populated with only something like 45 people (this is me guessing). Conversely, the unpopular times are going to be really dead.
On that note, it would probably make sense to create some sort of schedule. E.g. “We encourage you to come between 4pm and 8am PST.” Or to coordinate smaller specific time slots (e.g. “come at 2pm PST for one hour”) with a higher chance of having them filled.
If you constrain it to an 8 hour spread, it does indeed help things—you’d only need around 34 people agreeing to commit to 1 hour, so even more optimistic than your guess. And if we do get people to coordinate smaller specific time slots, perhaps convincing 25% to take a 1.5 hour slot and the rest to commit a minimum of 1 hour, this moves things closer to only needing a group of 30. Not too bad.
I’ve been very pleasantly surprised to see that the room has had people in it 24⁄7 since I first checked on it afternoon yesterday (current time for me is 5pm)! Usually about 5-6, I think the lowest I’ve seen is 3, although someone reported that in the quiet hours it got down to 2.
We’ll see if we’re able to keep it up, promising so far!
I like this idea, thought about checking it out, realized I don’t really know how to expect and that it might not be optimal for my personality type...then slapped myself for obvious dithering.
I’ll commit to dropping in tomorrow when I get home from work (~5:30EST) for at least an hour, to see if this suits me. After that, we’ll see.
Results report: I did get some done. More than I can usually do on demand, though it’s hard to say whether the benefit came from the technique or just from the novelty. Either way, I’ll continue doing it until it stops working, at least four times a week, in the ~6:00-7:00EST time slot.