Reply to All: Unsubscribe!
| Gabriel |
I subscribe to an academic listserv that’s usually very low traffic. Yesterday between 12:30 and 2:00 pm EDT there were a grand total of three messages discussing an issue within the list’s purview but not of interest to everyone on it. This was apparently too much for one reader of the list who at 2:54 pm EDT hit “reply to all” and wrote “Please remove me from this email list. Thanks.”
And that’s when all Hell broke loose.
What ensued over the next few hours was 47 messages (on a list that usually gets maybe 10 messages a month), most of which consisted of some minor variation of “unsubscribe.” A few messages were people explaining that this wouldn’t work and providing detailed instructions on how one actually could unsubscribe (a multi-step process). Two others were from foundation officers pleading with people to stay on the list so they could use it to disseminate RFPs (“take my grants, please!”). Finally at about 9:15 pm EDT the listserv admin wrote and said he was pulling the plug on the whole list for a cooling off period until things could get sorted out.
To most of the people on the list this must have been a very unpleasant experience, either because they were bothered by a flood of messages all saying “unsubscribe” or (as with the foundation officers) because they were people who valued the list and were dismayed to mass defections from it. I mostly found it intellectually fascinating since I was seeing an epidemic occur in real time and this is my favorite subject.
I went through each of the messages and recorded the time it was sent. Because the messages are bounced through a central server the timestamps are on the same clock. Here’s the time-series, counting from the first “unsubscribe” message:
0 12 19 26 29 30 30 30 30 33 33 33 41 43 49 51 55 58 58 59 60 65 67 68 68 76 79 81 83 85 86 87 98 107 116 122 125 131 137 169 287 311 317 345 355 383 390
Here’s the graph of the cumulative count.
The first 150 minutes or so of this is a classic s-curve, which tips at about the 30 minute mark, increases rapidly for about an hour, then starts to go asymptotic around 90 minutes.
OK, so there’s some kind of contagious process going on, but what kind? I’m thinking that it has to be mostly network externalities. That is, it’s unpleasant to get a bunch of emails that all say “unsubscribe” or “remove.” Some people may stoically delete them (or take a perverse pleasure in watching an epidemic unfold) whereas others may be very attached to the list and willing to put up with a lot of garbage to keep what they like. That is, there is a distribution of tolerance for annoying emails. For those people with a weak attachment to the list (many people apparently didn’t even remember subscribing) and little patience, they’re going to want to escape as soon as they get a few annoying emails, and they’re not going to think that carefully about the correct (and fairly elaborate) way to do it. So they hit reply to all. This of course makes it even more annoying and so people who are slightly less impatient will hit reply to all. My favorite example of the unthinking panic this can involve is one message, the body of which was “Unsubscribe me!” and the subject was “RE: abc-listserv: Please DO NOT email the whole list serve to be REMOVED from the mailing list.”
Another thing to note is that the tipping point occurs really early and outliers trickle in really late. If you ignore the late outliers coming in after 150 minutes, the curve is almost a perfect fit for the Gompertz function, described on pp 19-21 of the Mahajan and Peterson RSF green book as:
What the logarithms do is move the tipping point up a little earlier so that the diffusion is not symmetrical but the laggards trickle in over a long time. Note this is the opposite of the curve Ryan and Gross found for hybrid corn, where it took forever to reach the tipping point but once it did there were very few laggards. It’s nice to have a formula for it, but why does it follow this pattern? My guess is that it is not that some people read 30 annoying emails in the space of an hour, ignore them, and then an hour later two more emails are the straw that breaks the camel’s back. Rather I think that what’s going on is that some people are away from their email for a few hours, they get back, and what on Earth is this in my inbox? So there are really two random variables to consider, a distribution of thresholds of tolerance for annoying emails and a distribution of times for when people will go on the internet and become exposed to those emails. Diffusion models, especially as practiced by sociologists, tend to be much more attentive to the first kind of effect and much less to the second. However there are lots of situations where both may be going on and failing to account for the latter may give skewed views of the former.