The many university rankings, from U.S. News and onwards, can sometimes seem rather capricious: choose a personalized set of variables—student to teacher ratios, alumni giving rates, and so forth—and then apply a very precise yet seemingly arbitrary set of weights to these variables in order to get a ranking. If you have ever been struck by the arbitrariness of such rankings, you are not alone.

So is there a better way? At least when it comes to graduate department rankings, there is a more principled method. In a new paper, published in the new journal Science Advances and titled "Systematic inequality and hierarchy in faculty hiring networks," co-authors Aaron Clauset, Dan Larremore, and I developed a new ranking methodology based on a simple idea: a school's prestige (and rank) is determined by where its graduates go. If a school is good, then lots of other schools will want to hire its graduates. Essentially, these movements—from where you get your PhD to where you are employed as faculty—form a network of connections between schools. Our method orders the schools such that these movements from PhD to faculty position between a worse-ranked school and a better-ranked school are minimized; the more highly ranked a school is, the more likely it is that other schools (generally of lower rank) want to hire its graduates.

In this way, this method not only ranks schools by using the decisions of experts in each field—the people who make the hiring decisions in each department—but it sidesteps the massive effort of universities that try to boost their scores in more traditional rankings such as U.S. News by pouring resources into variables that don't really matter to a school's output and seem superficial. This system is much harder to game—if you really want to get your department a higher ranking, you need to convince other schools to hire your graduates, which means raising your quality—but it also accords well with our intuitive notions of prestige.

Employing a massive data collection process—information on about 19,000 North American faculty in the areas of computer science, business, and history were collected—we were able test this method on different disciplines. And the schools that are more highly ranked are indeed ones we intuitively view as more prestigious. For example, in computer science, Stanford, Berkeley, and MIT are the top three.

But beyond the ranking methodology itself, you can also see how stratified academia really is:

Across disciplines, we show that faculty hiring follows a common and steeply hierarchical structure that reflects profound social inequality among institutions. Furthermore, we show that (i) doctoral prestige alone better predicts ultimate placement than authoritative rankings from the U.S. News & World Report and the NRC, (ii) female graduates generally place worse than male graduates from the same institution, and (iii) increased institutional prestige leads to increased faculty production, better faculty placement, and a more influential position within a discipline.

For example, a quarter of departments end up generating about three-quarters of all faculty, and if you get a faculty job, you can expect to have one at a school that is more than twenty rungs lower on the prestige ranking. Furthermore, this drop in rank is steeper for women than men.

The structure of this network of academics even has implications for how ideas spread in the academy:

A strong core-periphery pattern has profound implications for the free exchange of ideas. Research interests, collaboration networks, and academic norms are often cemented during doctoral training. Thus, the centralized and highly connected positions of higher-prestige institutions enable substantial influence, via doctoral placement, over the research agendas, research communities, and departmental norms throughout a discipline. The close proximity of the core to the entire network implies that ideas originating in the high-prestige core, regardless of their merit, spread more easily throughout the discipline, whereas ideas originating from low-prestige institutions must filter through many more intermediaries.

Dan Larremore has created some amazing interactive visualizations of the dataset, which show just how stark the imbalance between the top and bottom schools really is. For example, below is the movement in the field of history, with the blue lines showing movement down the hierarchy, red upwards, and gray as no change:

<a href="http://danlarremore.com/faculty/">Dan Larremore</a>

The massive sea of blue demonstrates how often graduates end up getting faculty jobs at lower-ranked schools. The big band on the upper left is the lower 119 schools, while the rest of the circle is for only the top 25 schools. The size of these bands represents how much they export in terms of graduates, showing that not only do the top 25 provide the faculty to over three-quarters of all schools but that graduates of the lower 119 schools are nearly always stuck in this bottom tier (because its mainly gray).

There's a lot in the paper and I'm really proud to have been part of the team. You can read the paper here. And if you want to play with the data or the code from the paper, you can do that too.