Like many physicists, Stefan Thurner doesn’t like spending his time in long meetings. But after his employer — the Medical University of Vienna — underwent a major restructuring several years ago, he found that the time he had to devote to committees and other administrative tasks increased fivefold.

To understand why, Thurner and fellow physicists Peter Klimek and Rudolf Hanel turned to the British historian C Northcote Parkinson, who studied how the British Navy was once administered. Parkinson, who died in 1993, discovered a strong correlation between a committee’s ability to make a good decision, and its size. In particular, Parkinson found that committees with more than about 20 members are much more ineffectual at making decisions than smaller groups — something he dubbed the “coefficient of inefficiency”.

While many organizations are aware of the 20 person rule, Thurner and colleagues had not been able to find any reference to a mathematical explanation of the coefficient. So they set out to first empirically verify Parkinson’s law and then develop a mathematical model to describe it (arXiv:0804.2202v1 ) .

Governance Indicators

To do so the team looked at the governing cabinets of 197 countries worldwide. These bodies contain anywhere from five members (Liechtenstein and Monaco) to 54 members (Sri Lanka). The effectiveness of each cabinet was gauged using four parameters: the UN’s Human Development Indicator (HDI) — which assesses the health, wealth and education of people in a country — and three measurements used by the World Bank to calculate its Worldwide Governance Indicator.

The team found a very strong negative linear relationship between cabinet size and each of the indicators. In other words, countries with larger cabinets tended to have poorer HDIs than those with smaller cabinets, for example. According to Thurner, the statistical significance of their finding is orders of magnitude better than what is usually considered a good result in the social sciences.

The team also discovered that for all four indicators, most countries with above average scores have less than 20 cabinet members, which appears to support Parkinson’s law.

Cultural factors

There were important exceptions however. For example, Australia, Canada and New Zealand – which have high governance scores — have cabinets with 27, 32 and 27 members respectively. These three countries have similar political systems and cultures and Thurner hopes to collaborate with social scientists to understand if such factors affect the behaviour of committees.

Once they had verified Parkinson’s observations, the team developed a mathematical model to help them understand why 20 is a special number. Each cabinet member is defined as a node in a network. The state of a node (for or against an issue) can be influenced strongly by a subset of other members. This subset could represent a faction in a cabinet such as a political party. A node can also be influenced weakly by other nodes outside of its subset — reflecting the fact that a member can also be swayed by the opinions of a more distant colleague.

The dynamics of a cabinet with a fixed number of members was simulated by starting the model with each node in a specific state. The state of a node is then flipped if enough of its influencers are in the opposite state. This process is repeated many times until the system settles into a stable configuration of coalitions of “fors” and “againsts”. This process is repeated for every possible initial configuration and all the outcomes are used to define a “ dissensus” parameter that quantifies the inability of a cabinet to reach a majority consensus. The larger the dissensus, the less able a cabinet is to reach a consensus.

The team used this technique to study virtual cabinets with 5-35 members and found that the dissensus parameter climbed steadily with increasing cabinet size until 20 members — beyond which the rate of increase slows by a factor of two. This seems to indicate that the dynamics of the cabinet change just where, and how, Parkinson predicted.

Multiple factions

Thurner and his colleagues believe that this change occurs at the point where a cabinet can support multiple independent factions — something that could impair its ability to make good decisions.

Thurner hopes that the team’s research could help committee-driven organizations such as the European Union create effective decision making bodies. This will become more difficult as the EU admits more members (there are currently 27). Indeed, the EU is considering reducing the number of commissioners on its executive council from 27 to 18, to avoid the curse of Parkinson’s coefficient of inefficiency.