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C12 · proof of concept

Why the fifteenth organization is different from the fifth.

A coalition or a listening exercise with fifteen organizations is not "three times as much work" as one with five. The number of coordination pairs grows with the square of the number of parties. Past twenty or so organizations, the work stops being more of the same and becomes something structurally different — a shift people inside it tend to feel before they can name.

Interactive: adjust a slider between 2 and 60 organizations. The diagram shows the nodes and every pairwise coordination link. The counters report the total number of links and an approximate hours-per-decision figure.
Organisations 15
Coordination links 105
Hours per decision cycle 18
Coordination graph Network diagram with 15 nodes arranged in a circle and every pair of nodes connected by a thin line. 105 links total.

15 organizations, 105 links, about 18 hours per decision cycle.

2 60

Drag to change the count. Arrow keys work too.

Moving from 5 organizations to 15 is a tripling of parties and a tenfold increase in coordination pairs. From 15 to 50 is a three-fold increase in parties and a twelve-fold increase in pairs. Somewhere in that range, coordination-as-individual-relationships stops being feasible, and the work has to be carried by something else — a coded synthesis, a backbone organization, a public atlas, a convening body with a fixed role.

This is why the same listening method at 15 organizations and at 58 organizations produces structurally different artifacts. The difference is in what the math of coordination permits.

Source. Link count is elementary combinatorics: the number of pairs among N parties is N(N−1)/2. The hours-per-decision figure is a conservative heuristic — approximately ten minutes of pairwise contact per link per decision cycle, which reduces to links ÷ 6. Heuristic and framing adapted from John Kania & Mark Kramer, "Collective Impact," Stanford Social Innovation Review (Winter 2011); and the Bridgespan Group, "Transformative Scale: The Future of Growing What Works" (2015).