How many members can a committee have and still be effective?

Cyril Northcote Parkinson argued that beyond about 20 members, groups become structurally unable to come to consensus.  You can read more of Parkinson’s insights on work from Parkinson’s Law: And Other Studies in Administration

Below is an excerpt from Mark Buchanan’s article  in issue 2690 of New Scientist magazine, page 38-39.

“A look around the globe today, courtesy of data collected by the US Central Intelligence Agency, indicates that Parkinson might have been onto something. The highest executive bodies of most countries have between 13 and 20 members. “Cabinets are commonly constituted with memberships close to Parkinson’s limit,” says Thurner, “but not above it.” And that is not all, says Klimek: the size of the executive is also inversely correlated to measures of life expectancy, adult literacy, economic purchasing power and political stability. “The more members there are, the more likely a country is to be less stable politically, and less developed,” he says.
Why should this be? To find out, the researchers constructed a simple network model of a committee. They grouped the nodes of the network – the committee members- in tightly knit clusters with a few further links between clusters tying the overall network together, reflecting the clumping tendencies of like-minded people known to exist in human interactions. To start off, each person in the network had one of two opposing opinions, represented as a 0 or a 1. At each time step in the model, each member would adopt the opinion held by the majority of their immediate neighbours.
Such a process can have two outcomes: either the network will reach a consensus, with 0s or 1s throughout, or it will get stuck at an entrenched disagreement between two factions. A striking transition between these two possibilities emerged as the number of participants grew – around Parkinson’s magic number of 20. Groups with fewer than 20 members tend to reach agreement, whereas those larger than 20 generally splinter into subgroups that agree within themselves, but become frozen in permanent disagreement with each other. “With larger groups, there’s a combinatorial explosion in the number of ways to form factions,” says Thurner.
Santo Fortunato, a physicist who works on complex networks at the Institute for Scientific Interchange in Turin, Italy, thinks the result is convincing evidence for Parkinson’s conjecture. But he would like to see further testing. “The outcome might well change significantly if you change the shape of the social network, or the way people’s opinions influence one another,” he says.
So might this kind of work offer a rational way to optimise our decision-making bodies? One curious detail provides an intriguing slant on this question. In the computer simulations, there is a particular number of decision-makers that stands out from the trend as being truly, spectacularly bad, tending with alarmingly high probability to lead to deadlock: eight.
Where this effect comes from is unclear. But once again, Parkinson had anticipated it, noting in 1955 that no nation had a cabinet of eight members. Intriguingly, the same is true today, and other committees charged with making momentous decisions tend to fall either side of the bedevilled number: the Bank of England’s monetary policy committee, for example, has nine; the US National Security Council has six.
So perhaps we all subliminally know the kind of things that Parkinson highlighted and the computer simulations have confirmed. As Parkinson noted, we ignore them at our peril. Charles I was the only British monarch who favoured a council of state of eight members. His decision-making was so notoriously bad that he lost his head.