What is optimal group size for solving hard problems?

by on January 22, 2018 at 1:01 am in Economics, Education, Law, Philosophy, Political Science, Uncategorized | Permalink

Galesic, M., Barkoczi, D., & Katsikopoulos, K. (2018). Smaller crowds outperform larger crowds and individuals in realistic task conditions. Decision, 5(1), 1-15.

Decisions about political, economic, legal, and health issues are often made by simple majority voting in groups that rarely exceed 30–40 members and are typically much smaller. Given that wisdom is usually attributed to large crowds, shouldn’t committees be larger? In many real-life situations, expert groups encounter a number of different tasks. Most are easy, with average individual accuracy being above chance, but some are surprisingly difficult, with most group members being wrong. Examples are elections with surprising outcomes, sudden turns in financial trends, or tricky knowledge questions. Most of the time, groups cannot predict in advance whether the next task will be easy or difficult. We show that under these circumstances moderately sized groups, whose members are selected randomly from a larger crowd, can achieve higher average accuracy across all tasks than either larger groups or individuals. This happens because an increase in group size can lead to a decrease in group accuracy for difficult tasks that is larger than the corresponding increase in accuracy for easy tasks. We derive this non-monotonic relationship between group size and accuracy from the Condorcet jury theorem and use simulations and further analyses to show that it holds under a variety of assumptions. We further show that situations favoring moderately sized groups occur in a variety of real-life situations including political, medical, and financial decisions and general knowledge tests. These results have implications for the design of decision-making bodies at all levels of policy.

I have heard a number of CEOs and directors claim that organizations change fundamentally once they start exceeding fifty employees, a number only slightly above the cited optimum here.  But if only for reasons of sales and marketing and branding, it does in fact make sense, on net, for many institutions to exceed that number of employees.

Here is the paper, and for the pointer I thank the excellent Kevin Lewis.

1 Brett January 22, 2018 at 1:26 am

I could believe the “50 employees” figure. If you figure that a manager could supervise 7-10 people, then the number of managers could be small enough that you could meet with them in a single conference room – and the overall employee number is still small enough that you could theoretically know all of them reasonably well. Once you start getting well above that, you have too many managers to supervise and need managers to supervise the managers, and you’re no longer able to personally know all the employees and take an active hand in hiring.

Although I wonder what the optimum group size is for resolving escape rooms . . .

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2 Greg Esres January 22, 2018 at 2:07 am

My one-time doing an escape room, we had six people and we all got into each other’s way. But none of us knew each other well and we had no organization. So the optimum number clearly depends on the composition of the group, the sorts of tasks they’re being asked to accomplish, and how they’re organized. Probably a lot of other factors, too.

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3 Matthew Young January 22, 2018 at 2:00 am

The Army knows, eight man squads.

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4 Peldrigal January 22, 2018 at 6:48 am

The size of the squad is determined by how many can fit into an armored vehicle designed to certain specs, not the other way around.

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5 procrustes January 29, 2018 at 12:10 am

Peldrigal – your comment on specific squad sizes right now might be true (conversely the defence procurement people may have had squad size of 8 as one of the specs for the procurement). However, I think you’re missing the wider point. Section or squad sizes have typically been of 8 to 10 or more, going back decades before armoured vehicles, were common. Matthew’s point is relevant regarding institutions having some ideal size.

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6 Ali Choudhury January 22, 2018 at 4:13 am

https://signalvnoise.com/posts/995-if-youre-working-in-a-big-group-youre-fighting-human-nature

From a post on Antony Jay’s book “Corporation Man”: .

When you’ve got a small group, you don’t need to constantly formalize things. You communicate and you know what’s going on. If you have a question about something, you ask someone. Formalized rules, deadlines, and documents start to seem silly. Everyone’s already on the same page anyway.

Ten-groups
According to British author Antony Jay, there are centuries of evidence to support the idea that small groups are the most efficient. In “The Corporation Man,” he talks about how humans have worked in small groups, usually five to fifteen people, as hunters and farmers for hundreds of generations. The ideal group size is a ten-group:
He found the most efficient to be organised in groups of eight to fourteen people which he came to call ‘ten-groups’, each group free to find its own way towards a target set for it within the general objects of the corporation…

“The basic unit is [a group] which varies from three to twelve or fifteen in number, and perhaps optimizes somewhere around ten; that this group is bound together by a common objective, and that the bond of trust and loyalty thus formed can become an extremely powerful uniting force; that the group needs to decide on (or at least take part in deciding on) its own objective, and to work out for itself how that objective shall be achieved…”

He offers up interesting examples to back up the theory, from sports teams to juries to army squads:

Jay draws attention to units of around this size in many fields beyond the corporation. A committee works best with about ten members; if it grows much beyond that size the extra people do not take a fully active part. Nearly all team games use a group of about ten on each side. Juries have 12 members and the Jewish minyan 10. In an army, organization often decides life and death, and under this pressure armies, too, adopt a basic unit of about ten; the British army, the US army, the ancient Roman army and that of Genghiz Khan, in fact every long-standing successful army, has built up its larger formations from squads or sections of about this size.

That mention of the Roman army takes us back some two thousand years, and Jay traces the ten-group back still farther, back to the foraging communities. The ten-group, found today as a structural unit in successful corporations began, he argues, as the male hunting-group of pre-agricultural times, still with us and still functional.

Groups this size succeed because they have mutual dependence and a common objective:

This group displays qualities in addition to its size. Small enough for the contribution of each member to make a noticeable contribution, in order to function it needs mutual dependence, a common objective and a single criterion of success for them all; as the hunting band fed or went hungry together so members of the modern ten-group must receive praise, blame and material rewards collectively for the unit to function at its best.

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7 federal system January 22, 2018 at 4:38 am

545 people

435 Congresspeople
100 senators
1 President
9 Supreme court justices

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8 So Much For Subtlety January 22, 2018 at 5:29 am

Didn’t C Northcote Parkinson have a large section on this in one of his books? In my experience he is absolutely right about the size of committees that work – anything much over 15 is pointless.

I should also point out that Parkinson’s book was published in 1955 and yet he predicted that the Royal Navy would one day have more admirals than ships. Which is pretty much where the Royal Navy is right now. And to think people laughed …..

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9 Karl Lembke January 22, 2018 at 3:05 pm

He did indeed.
In his semi-empirical fashion, he observed that the maximum useful size for a cabinet or privy council seemed to be between a dozen and a score. When a body becomes large enough that a person has to rise to be heard, the function of the body seems to shift from producing useful results to following proper procedure.
At this point, the executive creates a smaller council from the most useful members of the larger body, and it splits off to do useful work outside of the usual meeting hours.

As evidence, he cited the growth of various councils over time, showing that once they reached a critical number of about a score, the rate of growth took off, and a new smaller council would appear shortly thereafter.

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10 harpersnotes January 22, 2018 at 7:29 am

There is of course an interaction between optimal size and average cognitive ability in the group. No doubt GMU macroeconomist Garrett Jones would have some thoughts, as might psychometrics researcher Timothy C. Bates. If I might hazard some conjectures, higher average cognitive ability likely pushes the optimal group size upward, but in practice probably also goes with more difficult problems being addressed. The interactions could be, well, complex. (The model in my mind at the moment is The Manhattan Project.)

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11 Engineer January 22, 2018 at 8:15 am

8-10 seems about the optimum size for engineering teams, in my experience (mostly software, but some hardware and chemistry too). Teams were often smaller, but usually that meant longer than optimal schedules. With more than about a dozen, the team usually split into two teams.

A lot of that is the intro-team communication overhead. A rule of thumb I found as a young manager was that when the team got too large to have lunch together every day, you had to start writing a lot more things down.

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12 Doug January 22, 2018 at 10:35 am

Amazon has the famous “two pizza” rule, where a team meeting is limited to the number of people that could be fed by no more than two pizzas.

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13 edgar January 22, 2018 at 11:32 am

Psychologists discover The Calculus of Consent. Progress.

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14 Jonathan S January 22, 2018 at 1:19 pm

Wouldn’t the simple answer be: how difficult is the problem that is being solved?

As Bryan Caplan points out in his “Myth of the Rational Voter”, crowds aren’t necessarily correct, particularly in areas where they may not be well-informed. Some sort of meritocratic technocracy would seem to be the best solution for solving difficult problems, and then the group size would be dependent on how many specialists would be optimal for solving the problem.

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15 Karl Lembke January 22, 2018 at 3:12 pm

I read somewhere that the effective IQ of a group increased roughly as the number of members in the group. This seems reasonable, since in a larger group, individuals will be able to fill in gaps in the knowledge of other individuals, and some problems can be portioned out so each member can work on a different piece of the solution.

However, this depends on effective communication among the members of the group (the issue Parkinson identified in his book), and there’s also the issue that people with high IQs are much more likely to know about the exceptional cases that may cloud the issue. (Example: Which planet is closer to Earth? (a) Mars; (b) Venus; (c) It depends.)

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16 harpersnotes January 22, 2018 at 6:43 pm

For whatever it’s worth, one of the more recent studies on group IQ — Runs mostly counter to the earlier claims of non-IQ factors having most of the influence on group level cognitive performance. Three studies with 312 people. “Contrary to prediction, individual IQ accounted for around 80% of group-IQ differences.” Timothy Bates and Shivani Gupta “Evidence for IQ as the origin of collective intelligence in the performance of human groups.” February 2017 in Intelligence. http://www.research.ed.ac.uk/portal/en/publications/smart-groups-of-smart-people(4e291196-abaa-41d7-be94-582e2a542c32).html ..

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