C[omp]ute

From: andrew cooke <andrew@...>

Date: Tue, 31 Jul 2012 22:43:39 -0400

This article -
http://www.theatlantic.com/technology/archive/2012/07/statistical-probability-that-mitt-romneys-new-twitter-followers-are-just-normal-users-0/260539/
- is mildly interesting.

I wouldn't have bothered posting a link except that I don't understand how
they can be so confident about the results.  In particular, look compare the
two graphs and tell me which curve looks odd:

http://cdn.theatlantic.com/static/mt/assets/science/indegree_615.jpg
http://cdn.theatlantic.com/static/mt/assets/science/obamaindegree_615.jpg

The odd man out is the yellow/gold curve for Romney.  The other three look
vaguely similar.  Yet that is the control group!  So what this seems to show
is that Romney, Obama, and other people as popular as Obama have a certain
shape; and that other people as popular as Romney have a different shape.

And when you put it like that, a mechanism seems pretty obvious:

Obama is very well known.  People in his control group are also well known.
Well known people have a certain shape (peaked to the left).

People like Romney are not well known and have a different shape (peaked
centrally).

One explanation for this is that bots follow the most well known people (but
that's not important for what I am arguing here).

So there are two sets of people, with different curves: well known and
not-so-well-known.

And then we have Romney.  Who has recently become very well known.  He has had
a lot of press coverage.  And so might be attracting followers distributed
like Obama, but who is still early enough in the game to have a total number
of votes comparable to less popular people.

I thought this was obvious, but am having a hard time making clear what I
mean...

Basically, Romney is being mis-identified as belonging to the less-popular
group because he has few followers.  But in fact he is an early stage version
of the popular group.  From that perspective he should have a similar profile
to Obama, but with a reduced scale (similar distribution but fewer total
followers).


One more time:

There's no ab-initio reason for shape to follow total number, which is what
the analysis assumes.  Perhaps Romney is simple a scaled down Obama (scaled
down because he only recently became very famous), rather than comparable to
less popular people that happen to have the same number of followers (people
who have a different kind of follower profile, with a different shape curve,
and which only happen to have a similar number of followers to Romney by
chance).

I hope that was clear to someone!

Andrew