# Lab Lunch - Michael Fourman

Quantifying inequality in the distribution of a binary advantage.

A binary advantage is something, such as a tertiary education, or a home broadband connection, or immunity to some disease.

The ?haves?, have the advantage while the ?have-nots? do not. In the broadband case, the haves are online; the

have-nots are offline.

We are interested in the contribution the distribution of this advantage makes to existing inequality. In this talk I will present two

measures. The first measures the divide from the perspective of those who are offline. We call this the depth of the digital divide:

the degree to which the digital divide serves to exacerbate existing inequality for those who are offline.

The second measures the divide from the perspective of society. We call this breadth of the divide: the degree to which the digital

divide serves to make society more divided.

The Gini coefficient has been widely used since 1908 to quantify inequality in the distributions of income and wealth.

Variations have been applied to quantify inequality in other areas, including the distribution of domestic broadband connections

and home computers, and inequalities in health advantages such as immunisation, and disadvantages, such as neonatal death.

In 2005 Wagstaff, working in the context of health inequality, observed that such applications of the Gini to the distribution of a

binary advantage are problematic. Wagstaff proposed a renormalisation of the Gini coefficient for such applications.

A couple of years ago, I made the same observation (independently, but too late), and used the same renormalisation in the context

of broadband. Wagstaff?s proposal has been the subject of prolonged debate in the Journal of Health Inequality.

In this talk, I will show that our depth measure corresponds to Wagstaff?s renormalisation of the Gini for a binary advantage, and that

our breadth measure corresponds to a different renormalisation, which I have not (yet?) found in the literature.

I will illustrate the talk using postcode data for the last few years to quantify the changing breadth and depth of the digital divide in different

local authorities (in Scotland) and district (in England).

See http://idea.ed.ac.uk/digiscot/scotland/ for some initial results.