The 15-person threshold
Something changes when a group crosses 15 people. A birthday dinner for 8 is manageable. A wedding party of 12 is complex but solvable. But at 15, 20, or 30 people, the bill-splitting problem becomes qualitatively different. Not just harder—different in kind.
Social psychologist Ivan Steiner formalized this in his 1972 work on group productivity. Steiner’s Law states that actual group performance equals potential performance minus process losses. These losses come from two sources: motivation losses (social loafing) and coordination losses. Both accelerate non-linearly as group size increases.
Steiner’s Law:
Actual Productivity = Potential Productivity - Process Losses
where Process Losses = Motivation Losses + Coordination Losses
For small groups, coordination losses are minimal. Four people can glance at each other and know who’s doing what. But coordination links grow combinatorially. A group of 4 has 6 possible two-way communication links. A group of 20 has 190. The cognitive load of tracking who ordered what, who already paid, and who’s waiting for someone else becomes overwhelming.
The formula is n(n-1)/2, where n is the number of people. At 15 people, you have 105 potential coordination pairs. At 25 people, 300. This is why large group dinners feel chaotic: the communication complexity exceeds human cognitive capacity long before everyone gets their food.
Source: Steiner, Group Process and Productivity, Academic Press (1972).