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.