For those who are interested in the impact of design on substantial outcomes, here’s the number of subscribers in the 54 most popular subreddits on reddit.com:
It’s a nice, smooth transition reflecting the popularity of each subreddit.
The same goes for subreddits after the 54th one:
But let’s put them together:
A huge discontinuity appears between “TwoXChromosomes” and “woahdude”. Like 3.5 times. Normally, the data doesn’t behave this way.
But it does here. The reason is, the designers put exactly 53 elements in the two main menus (on the left and on the top):
(Check the numbers)
These elements, as adeadhead reminds in the comments, reflect the default choice of subscriptions added to a new user’s list. I can think of additional channels, like user attention and search engines, that create this big difference between included and excluded elements. However, the connection is causal and at the disposal of designers.
PS: You could notice the “atheism” subreddit that slightly spoils the discontinuity. The subreddit had been in the menus before (snapshot) but was removed after 2012. The subscribers remained, though few new ones signed in, because the subreddit wasn’t in the menus.
In business literature you can find claims about magic numbers in management. The number of ten is said to be where a firm starts, while anything below that is a team and needs a different approach. One hundred employees are the milestone where the CEO no longer knows her employees personally and corporate politics emerges. And so on.
Management depends on the size, of course. But the data points at no specific critical numbers. The histogram of firms by the number of employees:
(hat tip to Jeffrey Groen at the BLS for the data)
And the log scale:
If ten or any other number had any significance, we’d see abnormal behavior around it. Management experiences transitional difficulties and some firms disappear. It would look like discontinuities or multiple peaks, as with the middle income trap. But the distribution does not support this claim. Perhaps, specific numbers matters for certain subpopulations of firms, for instance, the IT industry. In that case, it’d be interesting to look at the data. But until that it would be overall great if authors were more responsible and back their statements with minimal evidences.
Many things in the world have a Zipfian distribution. Xavier Gabaix recently attempted to explain how this pattern may emerge for the case of cities. Lada Adamic covered how Zipf’s law goes online. The literature is vast because any field has its own examples.
But Zipf’s law is a market-type pattern: the outcome of many agents making decisions independently. When you have a planner, it may break.
Here’s an example:
(Data comes from generous Wikipedians.)
Zipf’s law implies that here you must see a nice linear relations along the ranks. Instead, you see three lines: top 3 (I), top 10 (II), and 30 songs (III). The slopes of the lines are different in an interesting way.
Line II and III have the same slope and discontinuity between 10 and 11. (Actually, the discontinuity is between 9 and 10, but the 10th song is Katy Perry’s 2013 release, while songs around it are older. Kind of an outlier.)
This discontinuity is the bonus for being in Top 10. If any magazine or website mentions YouTube most viewed videos, it’s usually something like top 3 or 10 or somethings like that. Other songs don’t get much attention, even if they’re equally good.
But there’s another effect: the bonus for taking the first place. This is what Line I and Line II are about. Psy goes through the roof of Zipf’s law just as Bieber did before him.
So, why it’s about planning? Well, without the media, there would be no tops. And tops are coordinating devices that say what we should watch, listen, and do first of all.
That is planning.