[Air-l] gini coefficients for measuring participation?

[Philip Howard]

One possibility that would not involve writing a program, would be to
calculate the distribution of messages in the same way that economists
calculate the distribution of wealth in a country.  They create an index of
population (0% of the people to 100% of the people) and an index of the
wealth (0% of the wealth to 100% of the wealth).  In a perfectly egalitarian
country 10% of the people have 10% of the wealth, 50% of the people have 50%
of the wealth, etc, and you can graph the slope 1=1.  In an inegalitarian
country 10% of the people have 40% of the wealth, 50% of the people have 80%
of the wealth and when you graph all of the points you get a curve of
inequality.  There is a basic calculus method for calculating the area of
the graph between the perfectly egalitarian distribution (1=1 slope) and the
ineglitarian distribution (wierd slope), and this is called the gini
coefficient.  Scandinavian countries ahve a small gini coefficient and
Brazil has a big gini coefficient.  So you might take a sample day or week,
count the messages, and then label each message by the author's name.  Say
you have 1000 messages but only 100 authors.  Graph this, 10% of the authors
write XX% of the messages, 20% of the authors write XXX% of the messages,
and so on up to 100% of the authors writing 100% of the messages.  The area
of the graph between the egalitarian distribution of messages and your
sample gives you a measure of content inequality - how much of the content
is generated by an elite group.  If the metric is low your group is pretty
egalitarian, if the metric is high you have a clique generating most of the
content.  The metric would be most meaningful if you could compare it to
another group's metric, so if you did this over several sample periods, you
could say whether the distribution of message posts was getting more or less
egalitarian / elitist as the list was evolving.

would make purdy graphs, and could be used for almost any sample of content
& authors where you can attribute 100% of the content to 100% of the
authors.
p.
Philip N. Howard
Assistant Professor
Department of Communication
University of Washington
http://faculty.washington.edu/pnhoward/