(2023-10-18) Davies Areas Under A Curve And Other Useless Things

Dan Davies: areas under a curve, and other useless things. The Lorenz curve is a way of plotting an income distribution... so that a perfectly equal society would plot as a straight line at 45 degrees.

The area between the actual Lorenz curve and the theoretical 45 degree line is how you measure the Gini Coefficient.

But, of course, different shapes can have the same area.

These charts have the same Gini coefficient, because I drew them that way. Which one describes a more equal society? Hard to say.

Gini is a scale-free measure in a context where scale sometimes matters

it’s reasonable to say in this sort of context that “single-valued measures like the Gini coefficient don’t really tell you the full story – you have to look at the full Lorenz curve”.

Or at least, it seems reasonable to say this. Then a few evenings later, when you are staring at a trellis plot of a dozen of the bloody things, you start to realise that, in the words of Spinal Tap, it’s possible to have “too much bloody perspective”.

This is why people invent single-valued scale-free metrics; because actually, comparing multiple values simultaneously is difficult

Something like this happens a lot in financial risk management contexts, where risk managers are always presenting big charts and warning that you have to look at the whole estimated probability distribution, and then getting disappointed when the executives fixate on averages and single-number measures. A lot of the causes of the 2008 financial crisis (credit crisis 2008) can be traced back to the concept of “value at risk”, a standardised metric created at JP Morgan.

To be clear, this is bad and it sucks and executives shouldn’t do it. But it’s also inevitable.

A common theme of this ‘stack is that the business of management is, literally, making things manageable. It’s the activity of taking all the information that the world generates every day, and deciding what you’re going to throw away.

The trick is not to try and find the perfect summary metric... It’s to have the capacity to take a step back; to mostly think about the single numbers, but to be aware that you’re throwing information away and that you need to rummage through the discard bin every now and then.