March 13, 2004

Optimizing robust organizations

Peter Sheridan Dodds, Duncan J. Watts and Charles F. Sabel, Information exchange and the robustness of organizational networks, PNAS October 14, 2003 vol. 100 no. 21 12516-12521

A fun paper on how to create robust networks, with many applications for organisations. The question is how to organise links in the network so that it can both withstand the loss of key nodes/people and there is less chance of them getting overloaded. The best practical solution appears to be multiscale networks that mix hiearchy with cross-division interconnections.

How should an organisation be organised in order to work at its best? Usually communication is the bottleneck. If everybody communicates with everybody else the time spent on communicating soon overtakes the time spent on working (since the number of pairs of people grows quadratically while the amount of potential work only grows linearly with the number of members). If an executive manages the communication it becomes more efficient (he gives and receives information from everybody else, who can spend more time working). But now the executive is a bottleneck: if there are too many people under him he will be overwhelmed by the information flow. Adding higher levels partially solves the problem, allowing huge organisations. But there is a loss of robustness too: if the boss is sick or away, communications between different parts of the organisation breaks down. In the everybody-talks-to-everybody case there is no such risk.

The paper creates a model of networks starting with a hierarchical network extra links are added. The probability of the extra link between two nodes depends on their organisational distance (how far away are they on the hierarchical org chart) and their depth in the organisation. The results range (for different parameters) between random networks, local teams (people talk within the team), random interdivisional (people have extra links across divisions but few within), core-periphery (the top level has all the extra connections, but the rest is strictly hierarchical) and a multiscale mixture for intermediate parameters.

Then they tested the probability of overloading: information is sent between random pairs of nodes along the network and the total traffic across the network calculated. The congestion centrality is the amount of traffic at the most overworked node in the network. It turns out that there is a very narrow minimum corresponding to a kind of core-periphery structure that has the best performance (the higher-ups are good at distributing information among themselves, making themselves unlikely to be overloaded) and a broad minimum for the multiscale network. So while the organisation might be efficient in the core-periphery architecture, random changes in connectivity wrecks it easily. Hence it is not very robust.

Even more importantly, if highly connected nodes are deleted, the core-periphery and local-team networks fare very poorly. Random and interdivisional networks survive well, and the multiscale networks almost equally well. So the multiscale networks can survive both loss of nodes and overloading.

The moral seems to be that highly optimized networks are not very trustworthy in a messy reality where people meeting in the smoking room form important informal information conduits, executives get random colds and section 9 grows a bit beyond what is optimal for the overworked administrator far up in the hierarchy. Having interconnections across divisions, between levels and within teams becomes important in the core part of the organisation and as it grows they need to grow with it.

It is interesting to consider the similarities to other networks, like the brain. Here the peripheral systems bringing in and out information like the primary cortices are less densely interconnected as the higher association cortices. See for example
From sensation to cognition by M.M. Mesulam (Brain, Vol 121, Issue 6 1013-1052). Of course, in the brain everything is connected to everything else, but it is not implausible to think that the strength of the interconnections follow a pattern reminiscent of the paper by Dodds, Watts and Sabel.

Posted by Anders at March 13, 2004 07:54 PM

One interesting elaboration I'd like to see investigated is including the directionality of communication. In this model, the information flow appears to be unidirectional, which is unrealistic, if we are modeling hierarchical structures.

Do nodes that give 'orders' to other nodes waste time? Should there be 'listeners' to organize and disseminate node-layer traffic?

I would imagine that including directionality, and partial directionality would give more relevant results per human organization.

Posted by: Justin Corwin at March 14, 2004 05:44 AM

Yes, the current model is undirectional. Superiors are only there to distribute information (essentially acting as routers) rather than acting as managers.

Maybe one could model leadership as getting information for decisions: a superior receives information about the state of the world from subordinates, and then makes decisions based on it that propagate down. There is degradation in the signal going both ways (the SNAFU principle). Performance would be measured by how little distortion could be achieved. In this simple model the flatter the organisation, the better. Here there would be a trade-off between overloading managers and having few levels. Most likely the answer is randomly connected people, making sure information always has plenty of shortcuts.

A more elaborate analysis would assume that the organisation meets problems of varying size and frequency, requiring different amounts of information. Since small local problems are more likely, it seems reasonable that it would promote more more connections in the periphery than the core.

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