In this video I’ll say a little bit
about the general idea behind
Rich get richer phenomena and models thereof.
So the starting point is observation that
the popularity of many things is distributed
according to a power law or something
that’s power law like has a long tail.
For example book sales
There are very very many books
that sell very very few copies and
there are few books that are widely popular.
And if you plot a histogram of that
you would see a long tail.
The story is similar, say for scientific papers
how often they get cited.
Most scientific papers get cited very rarely,
once or twice if at all.
And then there’s some very very popular
scientific papers, influential scientific papers,
that get cited many many many times.
Again there’s a long tail
perhaps described by a power law.
Another example is the popularity of web sites
Some web sites have very very many links
pointing to them or have very very
many hits on the day,
whereas other web sites, many many more websites
are not popular at all.
And have just one or two links to them
if any links it at all.
So all of these phenomena can be
if one looks to data, looks like
they might be described by a power law.
So the question is why is that.
So one answer would be
well, because some webpages are better.
Some scientific papers are better.
Some books are better.
Some music, some songs are better and so on.
And that’s surely part of the story.
But it could also be that
there’s a different and alternative dynamics at play.
And that’s this rich get richer idea
So let me describe in general terms what that might be.
So here’s the idea
let’s say I am researching a topic
maybe power laws
and I’m trying to find references
about a certain aspect of power laws,
so I can learn more about them.
So one way I might do that
is that I might start with one paper and then
look in the references for that paper to see
who they cite as I try to learn
more about the certain topic
so if I do that
and then eventually maybe I write a paper
and I am going to cite some of the papers that I’ve found
and so in that dynamic
I’m much more likely to find papers
that I’ve already cited many times,
If I’m using citations as a way
to figure out what papers to find.
I could also do
I mean that’s not the only way I would find papers
But that would be a primary way
If I did a search on Google Scholar,
It often return hits, higher, rank more highly
If those paper have been cited more often.
So the idea is maybe originally
there is a handful of papers and
they’re all equally good
but then just by chance one or two of them
happened to get cited more often
well, then those papers are now have an advantage
that little initial advantage can grow and
those papers would get cited more often
and those papers and then more often still and so on.
Another example might be
maybe I’m looking for a book to read
something for the next airplane flight I have to take
I might ask people for recommendations
And I’m gonna get recommended books
that people have read.
So certain book is more likely to get recommended to me
the more often it’s been read
Therefore I’m more likely to read it
then somebody might ask me for recommendation
and I would recommend to them
the book that I just read.
Because other people have recommended it to me.
So the idea is that all of these systems
there is a little bit of instability.
An initial random bump in population
can grow very quickly
and lead to some superstar books
some hits some really popular papers.
And in this view those highly cited papers or
really popular books or web sites
aren’t necessarily the best.
Maybe they just got the lucky
and then route that advantage
to a really large citation count
or really high popularity.
Now of course both of these things could be
in play at the same time
Some books are better than others,
surely that’s true
But also I think it’s true that surely
there is some other random effects as well.
I’ll return to that later in this section
but for now what I want to do is
investigate a particular model
that leads to one of these
rich gets richer dynamics.
And it won’t go all the way
into the mathematical details
Because that’s a bit beyond what we can do
but let specify the model and
look at a few results
so do that the next video
and then I’ll step back and talk
more broadly about the sorts of phenomena
that these types of models can apply to
and look at some other applications
and implications of them.