August 22, 2008

Quantifying Inefficiency

Parkinson's law (or more properly, laws) are often regarded as humorous (true) statements about bureaucracy. The paper arXiv:0808.1684 Parkinson's Law Quantified: Three Investigations on Bureaucratic Inefficiency by Peter Klimek, Rudolf Hanel and Stefan Thurner demonstrates that they can be simulated fairly well.

They make an intriguing diagram of cabinet size vs. human development index and political stability for different countries. Clearly countries with 20+ cabinet members tend to be worse off than those with small cabinets.

The reason for the 20 people cut-off is revealed in another simple model. Cabinets are modelled as small-world networks where members take on the opinion of the majority of their neighbours. For small cabinets everybody convinces everybody. For larger cabinets the likelihood of getting stuck in a divided state increases linearly with size, with some form of breakpoint at 20. There is also a high tendency for size 8 cabinets to get stuck.

Further models of careers give numeric estimates of when bureaucracies tend to grow (essentially for all reasonable probabilities of promotion and number of subordinates) and how the age of retirement affects organisational efficiency. It turns out that there is an optimum retirement age that keeps experienced officials yet avoids having too many jealous and inefficient non-promoted officials. This grows with the number of levels of non-promoted subordinates.

All in all, it is a nice way of quantifying a few of the common-sense observations. I doubt adjusting retirement ages to organisation structures work well since other parameters (e.g. levels of resentment) may change faster, but the opinion formation model of cabinets seem to be something anybody involved in meetings and organisations should keep in mind. Most likely a way of increasing the number of contacts between cabinet members (increasing k in their notation) is a good way of improving opinion convergence.

BTW, Sweden has 22 members of cabinet. Oh dear.

Posted by Anders3 at August 22, 2008 05:52 PM