The Caliban-Partition Model
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 sole native islander 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.
Simulation Modes
Mode I: Animated
Picks a single group and runs interactions one by one. You see members (A, B, C...) sort into coloured subgroups each step, with the Caliban highlighted in red. Tracks running statistics and per-member isolation counts. Good for building intuition about how often a given group size produces exclusion.
Mode II: Head-to-Head
Runs two groups simultaneously, by default n=5 (prime) vs n=6 (factorisable), and plots their welfare trajectories side by side. You can watch the factorisable group steadily pull ahead as the Caliban penalty accumulates over hundreds of interactions.
Mode III: Rotation Tracker
Tests whether the Caliban role distributes fairly across all members over time. Shows per-member bar charts, a coefficient of variation measuring fairness, and a heatmap of who was isolated when. Over enough interactions, the counts should converge toward uniformity.
Mode IV: Longitudinal Study
The big picture. Simulates all group sizes from n=3 to n=15 at once and plots their welfare trajectories on a shared chart. After the simulation completes, you can display a ranked table showing which group sizes produce the highest member utility. This directly replicates the analytical results from the paper through Monte Carlo evidence.
Model Parameters
You can adjust these in the collapsible panel below. The defaults match 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}.
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.
δ (Caliban penalty) is the utility cost of being isolated. The default of 5 means being a Caliban is far worse than the baseline benefit of being included (u_base = 2).
T (interactions) is the number of social gatherings to simulate. More interactions give the observed rates more time to converge to the predicted values.
Visibility Correction
The model includes a correction mechanism: in smaller groups, exclusion is more noticeable and more likely to be fixed. In a group of 3, there is a 50% chance someone notices and pulls the isolated person back in. In a group of 7, that drops to about 17%. When a correction happens, the simulation shows it in amber rather than green, so you can see the mechanism in action.