When a group of friends gets together, conversations naturally split into smaller clusters. Two people talk about one thing, two others talk about something else. But what happens when the numbers don't work out? In a group of five, the most natural split is two pairs, which leaves one person sitting there with nobody to talk to. That isolated person is what this model calls the "Caliban," after the solitary character in Shakespeare's The Tempest.
The Caliban-Partition Model (CPM) is a mathematical framework that predicts how often this isolation happens based on the size of the group. The core finding is that group sizes which divide evenly into pairs (4, 6, 8, 10, 12, 14) produce far fewer Caliban events than prime-sized groups (5, 7, 11, 13), because prime numbers cannot be split into equal subgroups without leaving someone out. This simulation lets you watch that prediction play out in real time through Monte Carlo sampling.
You can adjust these in the collapsible panel below. The defaults match the empirically calibrated values from the paper.
α (pair preference) controls how strongly conversations gravitate toward pairs. Higher values mean the partition {2,2,2} for n=6 becomes much more likely than {3,3}. Default: 2.2 (calibrated from observed pair/triad ratio of 274/126).
β (balance preference) controls how much the model favours equal-sized subgroups. Higher values penalise unbalanced splits like {5,1} relative to {3,3}.
γ (fragmentation) controls how unlikely it is that the whole group stays as one conversation. Higher values make fragmentation into subgroups almost certain for larger groups. Default: 5 (calibrated from ~8% unified partition rate).
δ (Caliban penalty) is the utility cost of being isolated. The default of 15 means being a Caliban is far worse than the baseline benefit of being included (u_base = 2).
κ (coordination cost) is the per-member cost of belonging to a larger group. Each member beyond n=3 adds κ to the coordination burden. Default: 0.07 (calibrated from the observation that no groups exceeded n=7, implying coordination costs make large groups suboptimal despite their lower Caliban probabilities).
T (interactions) is the number of social gatherings to simulate. More interactions give the observed rates more time to converge to the predicted values.
The model includes a correction mechanism: in smaller groups, exclusion is more noticeable and more likely to be fixed. The correction probability φ(n) = 1.45/(n−1)^0.71 is empirically calibrated from observational data. In a group of 3, there is an 89% chance someone notices and pulls the isolated person back in. In a group of 7, that drops to about 41%. When a correction happens, the simulation shows it in amber rather than green, so you can see the mechanism in action.
Select a mode and press Run to begin the simulation.