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Power laws
Nov. 12th, 2014 11:33 amIt is starting to look as though one of the basic elements of functional internet literacy is awareness of power law distributions.
These show up frequently in social patterns involving either markets with immiscible goods or social networks of any significant size, and the Internet frequently involves the intersection of both. (The "Long Tail" of Chris Anderson's book title refers to the low end of a power law distribution, for example.)
People who point to a few highly successful self-published authors on Amazon as evidence that self-publishing is a gateway to success are ignoring the realities of a power-law distribution, much as people who pointed to weblogs as a way to get a voice out were a decade ago when blogging was new.
What caught my attention this morning regarding this was a segment on Metro Morning regarding a study involving teens and their use of social media. The study itself was done by a group at Centennial College and I have no doubt that certain aspects of it -- pointing out a relatively widespread willingness to ignore privacy concerns when posting to social networks, for example, or identifying hashtags related to self-promotion on twitter -- are at least grounded in real research. (On the other hand, their methodology page does not fill me with a great deal of confidence in their rigor, relating at least three "exploratory" (I assume = "focus") groups and "hundreds – possibly thousands - of hours combing social media sites, watching GIFs, decoding hashtags and generally documenting the trajectories of young people’s social identity exploration". I see no signs of mathematical rigor.)
But when I heard the author -- Debbie Gordon -- talk about some teens having hundreds of thousands or millions of followers, my immediate reaction was: "that has to be a power-law effect" -- popularity figures in a network environment are always power laws unless there's some significant constraint on them. Tails drop off rapidly in a power law distribution, and citing a few high figures does not provide a representative study.
(Even citing averages is misleading. I took the most-recently added ninety books on my LibraryThing account and then graphed them by number of members listing them. These formed a classic power curve, with a maximum value of 12,553, a minimum of 1, and an arithmetic mean of 822.833. However, 72 of the 90 books fell below the arithmetic mean, 54 were below half the mean (411), and the median was 199.5. 30 fell below 100.)
The numeric citations moved the interview from a "vaguely interesting" category into a "this is another one of those alarmist stories about how youth are going to hell in a handbasket that I've been hearing ever since I was young (when the stories bore no relation to anyone I knew)".
There have been a number of interesting discussions about how the young are adjusting to living in a panopticon society and how their values on privacy are not those of older generations. (Well, older living generations; the thegns of an Anglo-Saxon hall also had different privacy expectations, as did the inhabitants of a 16th century village.) This does not sound like a serious contribution to that discussion.
These show up frequently in social patterns involving either markets with immiscible goods or social networks of any significant size, and the Internet frequently involves the intersection of both. (The "Long Tail" of Chris Anderson's book title refers to the low end of a power law distribution, for example.)
People who point to a few highly successful self-published authors on Amazon as evidence that self-publishing is a gateway to success are ignoring the realities of a power-law distribution, much as people who pointed to weblogs as a way to get a voice out were a decade ago when blogging was new.
What caught my attention this morning regarding this was a segment on Metro Morning regarding a study involving teens and their use of social media. The study itself was done by a group at Centennial College and I have no doubt that certain aspects of it -- pointing out a relatively widespread willingness to ignore privacy concerns when posting to social networks, for example, or identifying hashtags related to self-promotion on twitter -- are at least grounded in real research. (On the other hand, their methodology page does not fill me with a great deal of confidence in their rigor, relating at least three "exploratory" (I assume = "focus") groups and "hundreds – possibly thousands - of hours combing social media sites, watching GIFs, decoding hashtags and generally documenting the trajectories of young people’s social identity exploration". I see no signs of mathematical rigor.)
But when I heard the author -- Debbie Gordon -- talk about some teens having hundreds of thousands or millions of followers, my immediate reaction was: "that has to be a power-law effect" -- popularity figures in a network environment are always power laws unless there's some significant constraint on them. Tails drop off rapidly in a power law distribution, and citing a few high figures does not provide a representative study.
(Even citing averages is misleading. I took the most-recently added ninety books on my LibraryThing account and then graphed them by number of members listing them. These formed a classic power curve, with a maximum value of 12,553, a minimum of 1, and an arithmetic mean of 822.833. However, 72 of the 90 books fell below the arithmetic mean, 54 were below half the mean (411), and the median was 199.5. 30 fell below 100.)
The numeric citations moved the interview from a "vaguely interesting" category into a "this is another one of those alarmist stories about how youth are going to hell in a handbasket that I've been hearing ever since I was young (when the stories bore no relation to anyone I knew)".
There have been a number of interesting discussions about how the young are adjusting to living in a panopticon society and how their values on privacy are not those of older generations. (Well, older living generations; the thegns of an Anglo-Saxon hall also had different privacy expectations, as did the inhabitants of a 16th century village.) This does not sound like a serious contribution to that discussion.
