[This post is the first in a series I’d call “Things that I probably will not develop in a proper paper, but I find interesting enough to write here”]
One way to quantify change in cultural dynamics is to measure the turnover rate of a particular domain. The turnover (z) is the number of new items that enter, after a certain amount of time t, in an ordered list of size N. What does this mean? A straightforward example of turnover is the new entries in a Top-list Chart. This week, for example, 4 new singles entered in the BBC UK Top-40 Single Chart (see here – of course the actual number of new entries will change from week to week). So, for the week starting 8 March 2015, z=4 (the number of new items that enter…), t=1 week (…after a certain amount of time…), N=40 (…in an ordered list of size N). Notice that, with this information, one can calculate the turnover for all N from 1 to 40 (for example, this week, the 4 new entries are at the 1st, 7th, 13th, and 18th place, so, for, say N=10, z would be equal to 2).
These top lists are today ubiquitous, so that is relatively easy to calculate turnover for many cultural domains (here, for example, the bestseller hardcover fiction books from the New York Times. While there is not an explicit way to filter the new entries, one can easily check from the number of “weeks on list” information the books that are in the list for the first time, and then get z). In fact, with slightly more effort, one can calculate the turnover of plenty of cultural domains, provided that is possible to extract the frequencies of traits through time.
Last year, together with Alex Bentley, I published a paper where we showed that the turnover profile (i.e. how z varies for different N) of a cultural domain is informative about the selective forces acting on that cultural domain (I talk about it in this post). The turnover profile is an aggregate measure that considers an average of the turnover rate through time. So, for example, the turnover profile of the BBC UK Top-40 Singles for 2014 would be, for each N (from 1 to 40), how many new singles, on average, each week of 2014, entered in the correspondent top-N.
Another way to look at the same information is to consider the time dimension of the turnover rate, without aggregating. One could check, for example, if, during 2014, there were “turbulent” periods for the UK Top-40, with many new entries, and “stable” periods with few changes. Different cultural domains (say books versus songs) could be characterised by different regimes. Finally, long-term turnover rates can suggest some more general changes in popular cultural dynamics.
On the last point, I calculated the turnover rate through time for two datasets. The first one (see figure below), is the Billboard Top-100 weekly Singles chart from 1946 to 2007 (data from Alex Bentley). Our N is now equal to 100, and the y-axis gives information on z through time. The weekly turnover is averaged for each year.
The second one is the Top-10 yearly fiction books in United States from 1900 to 2000 (data from various sources, from a project of John M. Unsworth). In this case I plotted the authors turnover, averaged for each decade. For example, for the 1940 decade, z=7 means that each year, on average, 7 new authors entered in the top-10 in respect to the previous year.
A striking feature of the two series is the decrease, starting around the 60s, of the turnover rate. This means that, in the last part of the century, the same best-selling authors and musicians tended to be more successful, comparatively, than what was happening in the first period of the data, where change in the top-N was faster. For example, in the 90s, the three most successful authors (Danielle Steel, Stephen King, and John Grisham) occupied 39 of the 100 possible positions in the top-10!
If this decrease is common in other popular cultural domains (which I suspect, but I do not know), it is interesting to wonder what kind of mechanisms could have produced it. One of my favourite hypotheses is that is exactly the fact that public top-lists started to be widespread (it is not unreasonable to think that today the phenomenon is even more prominent, almost farcical, with online diffusion of top-n of virtually everything). Below, as an example, a plot from the Google Books Ngram that shows that references to the same term “Top 10” were basically absent in popular culture (to be precise: in the English language books present in the Google sample) until the 60s. 
Top lists provide a way to know what others, unrelated, individuals prefer and to avoid to choose by yourself. Why go to the bookstore and choose by myself a book, that could turn out to be bad, when I can just check the “what’s hot” section, and rely on the judgement of (millions of) other people? Of course, one could consider both the decrease of turnover and the increase of top lists popularity as the effect of some other more general mechanism (call it “consumerism”, “globalisation”, or whatever) but this does not change the fact that top lists are perfect artefacts to support a conformist bias (in cultural evolutionary terms: a disproportionate preference for common traits).
Another hypothesis is that Danielle Steel books are actually better (i.e. more effective spreaders) than Mary Johnston books (the author of To Have and To Hold, the American bestseller of 1900, according to my data). While this may sound a little crazy, one can imagine that, as the number of books and the number of readers increased, probably exponentially, during the century, higher competition generated better and better (in the sense above) books, so that it is now more difficult to write something more effective than what is already in the top list, in respect to what was happening at the beginning of the century. I was reminded of this idea when some friends recently described to me how their daughter was caught in an “epidemic” of Harry Potter in a primary school class in Edinburgh, where in around a month all pupils (the majority of whom did not know about it before) read the first book of the series. This does not mean that we reached the highest peak of literature, or of “effectiveness”, with J. K. Rowling or Danielle Steel, but that, perhaps, to go back to an higher turnover, new authors would need to explore the “design space” of narrative in other directions.
Alberto Acerbi (old website) 