Superstar lawyers?

The UK Supreme Court was established in 2009. Since that time, 1149 lawyers have argued cases before the court appearing for either the appellant or respondent.

Most of those lawyers have only ever appeared once before the court. A small number of lawyers have appeared before the court a great many times. If you follow the Supreme Court, the names of these lawyers won’t come as a surprise. They’re mostly public lawyers — the Treasury Counsel James Eadie (25 appearances) and Jonathan Swift (11 appearances) come first and fifth respectively, separated by Richard Drabble (15), Hugh Southey (14), and Dinah Rose (11).

This pattern — of a small number of barristers racking up a large number of appearances — is indicative of a power law (or something which looks very much like a power law over a short range).

You can see this in the chart below. I've plotted the number of appearances on the horizontal axis, against the number of barristers who have registered that many appearances. Note that I've log-transformed both of the axes, so that the distance from one appearance to two appearances is only a little bit shorter than the distance from two to five appearances.

The best fitting line through these points is a straight, downward sloping line. Because the axes are log transformed, this actually means that the number of barristers with at least x appearances drops off rapidly as x increases.

This pattern is more than a statistical curio, because there are a number of mechanisms which are known to generate power laws. Two are particularly well-known:

Superstar economics: in a famous paper from 1981, Sherwin Rosen introduced the idea of superstar economics — a model of markets where small differences in the quality of the products on offer result in large differences in income for their sellers.

For the model to apply, the products on offer must be imperfectly substitutable. In music, that might mean that you would never think of giving up your first pressing of Belle and Sebastian’s Tigermilk for the complete works of Ant & Dec, even though Ant & Dec ultimately and inexplicably released three studio albums with a cumulative length of two hours and seventeen minutes, much more than Tigermilk’s forty-one minutes.

Rosen explicitly mentions the law in his paper when describing these imperfect substitutes.

If a surgeon is ten percent more successful in saving lives than his fellows, most people would be willing to pay more than a ten percent premium for his services. A company involved in a $30 million law suit is rash to scrimp on the legal talent it engages

In this context, this might mean that barristers who appear more are simply very slightly better than their peers, and as such “sell more” legal representation, because consumers attach disproportionate weight to having the top barrister compared to saving their money.

Preferential attachment: Rosen’s paper started from the idea of differences in quality. Preferential attachment doesn't need anything like that to get going. Rather, it operates on the Matthew effect — “For everyone who has will be given more”. Academic articles which get a good haul of citations in their first year will go on to gain more citations, even if on some objective measure of quality they’re poor papers.

In this context, preferential attachment suggests that lawyers who have appeared x times before the Supreme Court will get more briefs, simply from the fact of their already having appeared x times.

Although preferential attachment doesn't need quality, it’s often lurking in the background. Maybe initial divergences in citation counts or appearances happened just because those papers were good papers, or because those lawyers were high quality advocates.

Given a power law distribution, it’s hard to work out whether it’s the result of preferential attachment or superstar economics. You would either need some independent and objective measure of quality, or a completely exogenous intervention which manipulates, say, the number of times a song has been played or an article cited or a lawyer featured.

So it’s not clear from this pattern whether

— superstar lawyers really are superstars in the sense suggested by Rosen, or

— whether the market for lawyers needed someone to be a superstar, and some lucky lawyers were the first out of the gate.

Does this matter?

It matters if you're trying to pick a lawyer. If you think that superstar economics is at work, then you should definitely pick the lawyers who appear most. If you think that this story can be told entirely in terms of preferential attachment, save yourself some money and go for a jobbing barrister. I'm sure they'll be grateful for it.