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TEN CONCEPT BRIEFS · Chapter I.07 — The Second Circle

One page each. A reader who reads only these ten pages has the chapter.

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BRIEF 1 — Simple and Complex Contagion

The idea. A fact spreads on one contact. A practice does not.

A simple contagion — a rumour, a price, a piece of news, a virus — transmits on a single exposure. One person tells you and you have it. A complex contagion needs reinforcement from two or more independent sources before a person will act, and it needs it because acting costs something: time, standing, the risk of being the only one doing a strange thing in a meeting.

Everything in a transition is a complex contagion. Nobody changes how they allocate capital because one colleague mentioned it once.

Worked example. You send a memo to forty people. Forty people now have the information — a simple contagion, complete in one hop. Three months later nobody has changed anything. The memo was never the mechanism. What would have changed behaviour is two colleagues, known to each other and to the reader, visibly doing it.

The figure. Centola and Macy's central result is that the long, weak, bridging ties that make information travel fast can make practice travel slower, because they deliver one signal each from unconnected places.

You already know this because you have never adopted a working habit from a newsletter, and you have adopted several from watching two people you respect use them.

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BRIEF 2 — The Adopter Bands, and Why There Is No Second Enthusiast

The idea. Rogers' five categories are a normal curve cut at the mean and at one and two standard deviations: innovators 2.5 percent, early adopters 13.5, early majority 34, late majority 34, laggards 16.

Turn the percentages into heads and something lands hard.

The figure. You need forty people before one innovator is expected and eighty before two are. In any group that fits round a table, you are the only one.

What follows. The second adopter cannot be another innovator, so stop looking for one. They come from the early-adopter band — one in 7.4 people — and that is a categorically different person: near the local norm, socially central, the person colleagues check with. Rogers is explicit that innovators are not that person; they are cosmopolite and marginal to the local system, which is exactly why their endorsement moves nobody.

You already know this because the colleague who agreed with you within thirty seconds is the colleague whose agreement nobody else finds interesting.

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BRIEF 3 — What the Second Adopter Is Worth

The idea. The Bass model gives the pull on the next undecided person as

  dF/dt  =  (p + qF)(1 − F)

where p is adoption from outside influence and q adoption from imitation. Across 213 published applications the means are p = 0.03, q = 0.38.

Worked example — a circle of twelve.

The figure. Every adopter adds the same absolute increment, q/N = 0.0317, to a base that keeps growing. So the first person who joins you slightly more than doubles the pull on everyone else, and no recruit afterwards ever changes the rate by as much again.

And a second figure worth carrying into budget meetings. Peak adoption arrives at t* = ln(q/p)/(p+q) = 6.19 periods, with 46.1 percent adopted. The same elapsed time on p alone — announcements, memos, presentations, no imitation — reaches 17.0 percent. Word of mouth does 2.72 times the work your communication does.

You already know this because you have watched a launch with a large budget do less than one respected person switching over in public.

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BRIEF 4 — Thresholds, and the Gap

The idea. A threshold is the number of others who must already be doing something before this person will. Granovetter's insight is that the outcome depends on the distribution of thresholds, not on their average.

Worked example — two circles of twelve.

  circle A   0  1  2  3  4  5  6  7  8  9 10 11     mean 5.500  ->  12 of 12
  circle B   0  2  2  2  2  2  2  2  2  2  2 11     mean 2.583  ->   1 of 12

Circle B's average threshold is less than half circle A's — it is more than twice as eager, by any summary statistic you would naturally compute — and it never moves. Ten of its twelve members need only two others. There is no route from one to two, because nobody in the room has a threshold of exactly 1.

The figure. Swap that one reluctant member at 11 for a single person at threshold 1, and the same circle goes to twelve of twelve.

What follows. Do not try to raise the enthusiasm of a group. Map the distribution, find the gap — the value at which nobody sits — and recruit one person into it. The gap is usually at one, two or three.

You already know this because you have sat in a room where everybody privately agreed and nothing happened, and you have watched one person's willingness to go first unlock the same room in a minute.

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BRIEF 5 — The Committed Three

The idea. A stalled circle needs a specific number of unconditionally committed people, and it is usually three.

Worked example. Circle C, thresholds 0 3 3 3 4 5 6 7 8 9 10 11:

One is a founder. Two is a pair of enthusiasts and it still stalls. Three is where the circle carries itself without anybody pushing.

The figure, arrived at twice. Centola, Becker, Brackbill and Baronchelli found experimentally that a committed minority overturned an established social convention once it passed roughly 25 percent of the group. Twenty-five percent of twelve is 3.0. Two methods that share no assumptions return the same integer.

The honest caveat. Agent-based models put the tipping fraction nearer 10 percent. In a group of twelve that is 1.2 people — which is you, which is where you already were. Where two estimates disagree, take the one that asks more of you: the cost of under-recruiting is the whole programme, and the cost of over-recruiting is one extra conversation.

You already know this because you have been the second person on something and felt how differently the third arrival landed.

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BRIEF 6 — Redundant Ties

The idea. For a complex contagion, the useful property of a network is not reach. It is redundancy — whether your contacts are contacts of each other.

The clustering coefficient measures it. On a ring lattice where each person is tied to their k nearest:

  C  =  3(k − 2) / (4(k − 1))

The figure. At k = 4, half of a person's neighbours are tied to each other, so a signal that reaches one of them reaches a second by a route the sender never had to take. That is reinforcement arriving free.

The uncomfortable part. Efficiency engineering removes exactly this. A well-designed communication network minimises redundant paths; a well-designed adoption network maximises them. The property that makes a network good at information makes it bad at practice, and you cannot optimise for both at once.

You already know this because the teams where things actually change are the ones where everybody already knows what everybody else is doing, and you have probably described that as inefficient.

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BRIEF 7 — The Star Trap

The idea. If you recruit people one at a time, privately, and they know you but not each other, you have built a star — and a star cannot carry a practice at any size.

Worked example.

The figure. Your own degree grows without limit. Every other person's degree stays at one, forever. With a reinforcement threshold of two, adoption among the spokes is zero at every size in that table.

Why this is the dangerous failure. Every visible metric improves while the thing dies. Reach rises. Attendance rises. The mailing list rises. Awareness surveys rise. Nothing propagates, and the numbers say the opposite.

The repair. Introduce your recruits to each other on a real task, without you present. It is not a nicety; it is the mechanism. Budget a month for it.

You already know this because you have been in a group where everybody knew the organiser and nobody knew anybody else, and you remember precisely how it felt when the organiser did not come.

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BRIEF 8 — The Coordination Ceiling

The idea. Reinforcement rises with n. Coordination cost rises with n². Those two lines cross, and the crossing is the size limit of a circle.

Worked example.

The figure. Dunbar's layers come at 5, 15, 50 and 150, scaling by a ratio close to three. Sixty-six channels and five minutes a head is about where a group stops being able to hold its own decisions.

What follows. Buurtzorg caps a nursing team at about twelve and splits it when it exceeds that. This is not a philosophy of teams. It is this table.

The thing to say out loud. A circle that doubles has not doubled its strength. It has quadrupled its coordination load, and it has done so while every member's share of attention halved.

You already know this because you can name the exact meeting size at which your organisation's conversations stop being conversations, and it is somewhere between eight and fifteen.

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BRIEF 9 — The Governance Minimum

The idea. Ostrom's eight design principles describe an established commons. A circle of six has no commons yet — it has a practice and a small shared budget. Four of the eight are the minimum, and they fit on one page.

The figure. Four sentences. Törbel's villagers wrote theirs in 1483 and the first provision was the boundary; the commons held for five centuries.

Why the meeting matters more than the document. Have everyone assent aloud, in the same room, at the same time. That event is itself a complex contagion: every person receives reinforcement from every other person simultaneously, which is the only moment in the life of a circle when that is true.

The alternative, named in 1972. Jo Freeman's argument is that a group which refuses explicit structure does not become structureless. It develops an informal elite that cannot be held to account, cannot be joined, and cannot be succeeded. Four written lines are cheaper than that by a very wide margin.

You already know this because you have been in the group with no rules and you could name its real decision-makers within a fortnight.

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BRIEF 10 — Split, Do Not Widen

The idea. Growth that preserves a practice is multiplication of small dense groups, never enlargement of one.

Worked example — what widening does. Students for a Democratic Society grew from a few hundred members in 1962 to something on the order of a hundred thousand by 1969 and disintegrated at its Chicago convention that June. Polletta traces the same arc through participatory-democratic movements repeatedly: decision-making that worked at twenty could not be scaled to two hundred, and the attempt to scale rather than multiply is what broke it. Occupy's general assemblies ran the experiment again in 2011 with the same outcome.

The figure that prices the alternative. Median US employee tenure was 3.9 years in January 2024. Treated as a constant hazard, that gives a 41.3 percent chance the founder's attention is gone within three years. Against a £150,000 cost to re-found an initiative from zero, the expected loss is £20,663 a year. Two named second owners at two hours a month cost about £5,120 a year — a 4.04× cover ratio. You buy the second owner for 25 percent of the risk it retires.

The three things that make a circle survive the founder.

1. A named successor who is already doing the job — chairing alternate meetings, named on half the artifacts.
2. The four written lines, so somebody other than you can point at them.
3. A split rule stated in advance: at what size, and who decides.

You already know this because every group you have watched survive a founder's departure had someone else already running half of it, and every one that did not survive was surprised.

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All figures in these briefs are computed in lib/verify/I_07.py and reproducible with python3 lib/verify.py I.07. Sources are in the chapter's Works Cited.