Noted social scientist Mark Mizruchi of the University of Michigan claims in his book that since the end of WWII, the boards of corporate America have begun to disintegrate, in that the overlapping of such boards, where the overlap is of members that hold positions across boards, has severely decreased. He then goes on to claim that this destabilization of the corporate elite will lead to negative effects on the US economy, as those who hold power will not operate cooperatively and with a generally unified position for the improvement of US industry [as a note, this post will deal only with his first statement – that the boards themselves have started to destabilize] . As one can see, this type of hypothesis is a direct extension of the work we did on bipartite graphs in class several weeks ago, and actually would include board members that we looked at such as Steve Jobs.
In order to test the validity of the Mizruchi hypothesis, several mathematical and computational scientists from the US and France set about trying to determine the statistically signifiant change of the core of US company boards – the DOW Jones 30 – over the period from 2001-2010. A small caveat to their statistical analysis is that the DOW Jones 30 evolves over time, and thus in order to truly try and create plausible metrics of statistical significance, the authors needed to increase their sample size to 43, which totals all companies who were on the DOW Jones 30 anytime between 2001 and 2010 and had board memberships. They then analyzed all board members of these 43 companies and created a bipartite graph where each foci is sized according to its degree centrality and each number represents a unique interlocked board member, as seen below.
After this analysis, they then sought about creating a projected graph where the resultant network would be a 1-mode network showing edges between foci. In order to demonstrate the extent of interlocking throughout these boards, they also use weighted edges, where the weight of the edge is directly proportional to the number of directors any two nodes share. This graph can be seen below.
From these initial observations they then conducted tests of statistical significance to determine any measurable variation of several metrics, among them the average degree and clustering coefficients of nodes, using an application of Bayesian Probability modeling, as seen below.
They concluded that, contrary to Mizruchi’s proposed theory, the boards of these companies have remained quite stable over their time span, as the confidence intervals generated for the mean of the difference between 2001-2010 all contained 0, thus not allowing any inference that the interlocking nature of corporate boards has destabilized to any real degree.