The Scapegoat model

The Scapegoat model is an executable hypothesis: a program in which a few dozen agents — the parameter runs from 30 to 100; the scenarios on this page use 30 and 60 — linked in a network accumulate tension, transfer that tension onto a target and adhere to whoever transferred it, following simple rules. It does not reconstruct any of the cases documented on this site and proves nothing about people. What it shows is something else: that a small mechanism, without intention and without content, is sufficient to produce the shape the cases have — the convergence, the peak, the exit of the target and the residue.

The model’s network is the substrate: who knows whom. The phenomenon happens in the agents’ attributes — tension, transfer, adhesion. That is why, besides the video, the model appears here as curves over time: what is compared with the cases is the shape of the curve, not the shape of any network drawing.

Two terms of the model

The model has a vocabulary of its own, slightly different from the one used in the cases, because it describes operations rather than acts.

Tension transfer. What the cases call accusation is, in the model, a transfer: a saturated agent discharges onto a target the tension accumulated in its pocket of the network. There is no content and no merit — there is tension changing place. (The passing of tension between neighbours, which precedes this, is propagation.)

Expulsion. The decisive event, in which the target leaves the network and all the others reorganise around whoever transferred the tension. In mimetic theory this event is the founding collective violence — the expulsion of a victim by the group — and the rite is its repetition under controlled conditions. The model produces the event, not the repetition; that is why this page speaks of expulsion, not of rite.

How to read the curves

The time axis is aligned on the expulsion: zero is the step at which it occurs, negative numbers count the steps before it, positive numbers are the residue. This allows runs that reached the expulsion at different moments to be superimposed.

The solid line is a run with a fixed seed — reproducible step by step, the same as the video at the top of the page. The band in the background shows where the middle half (between the first and third quartiles) of twenty runs with different seeds fell; runs in which the expulsion did not happen before the ceiling of 1,500 steps stay out of the band and are counted separately.

The site’s canonical stages are marked on the chart and were mapped as follows (each case names its stages with the terms of its own episode, aligned to these):

One important detail, so as not to be misled by the tension curve: in the model, every tension transfer with adhesion resets the tension of the whole network to zero, not only the expulsion. That is why tension has a sawtooth shape — it rises, drops to zero at each transfer, rises again. What distinguishes the expulsion is not the fall in tension but what comes with it: the target leaves, the agents adhere to the amplifying pole and the marked targets return to zero.

Three of the network measures have counterparts in the cases — the site computes them, day by day, on the mention network of each episode: concentration and centralisation are in the cases side by side (in Portuguese); modularity appears in the line of figures of each stage, because it grows with the size of the network. The fourth has no counterpart:

• Concentration of attention: in the model, the share of accumulated transfers that fell on the most targeted agent. In the cases, the Gini index of attention.
• Centralisation: Freeman’s degree centralisation of the network of the agents present — 0 when all have the same number of ties, 1 in a perfect star.
• Modularity: of the communities detected by the Louvain method, at each step.
• Local cohesion: mean clustering coefficient — how many of each agent’s neighbours know one another. No empirical counterpart. In the model, the network is the substrate — who knows whom, before and after the episode — and cohesion measures that fabric. In the cases, what is observed is the day’s mention network, which is the episode itself, not the fabric beneath it; and in a star, clustering is zero by construction, which would make the curve fall for the wrong reason. So cohesion stays on the model’s side only, declared as such.

The model has no pole of contestation — nobody defends the target. What exists as an analogue, and is in the bottom panel, are the transfer attempts blocked by skepticism: weak transfers that the network refused.

The three parameters

• Population (30 to 100 agents). Larger networks dilute tension: more targets in proportion, each one under less pressure.
• Closure (0 to 19). The higher it is, the lower the chance that the network creates new ties — it stays close to the initial ring, with high local cohesion. In the source code it is called friendliness, with the name inverted; here we use the name that describes the effect.
• Skepticism (50 to 99). The probability that a transfer without adhesion is blocked. It protects by preventing the prior marking of targets: whoever has been targeted once is the preferred target of the next transfer.

The five scenarios vary one parameter at a time from the base scenario (population 60, closure 10, skepticism 75), with twenty runs each.

What the scenarios show

The figures below come from the hundred runs recorded for this page (twenty per scenario, seeds 1 to 20, ceiling of 1,500 steps). They are simulation results, not empirical data.

In the closed network, the expulsion often does not happen. With closure at its maximum, only 10 of the 20 runs reach the expulsion before the ceiling, and when they do, adhesion to the amplifying pole is the smallest of all scenarios (a median of 3.5 agents). In the base scenario, all 20 runs reach the expulsion, with a median adhesion of 10; in the open network, also all 20, with an adhesion of 15.5 — the largest. In the mimetic reading, the expulsion is unanimity: it requires the whole group to reorganise around the pole, and reorganising is creating new ties. A network that creates no ties accumulates tension transfers without ever converting them into unanimity — the tension is not resolved, it only repeats over marked targets. This complements, and does not contradict, the main result of the model’s parameter sweeps (“cohesion closes, openness dilutes”): cohesion concentrates the severity on whoever is targeted; openness is what allows the collective discharge. A closed network is, at the same time, the one that most isolates the target and the one least able to expel it.

In the open network and in the skeptical network, the expulsion comes earlier. The median step of the expulsion falls from 546.5 (base) to 279.5 (open) and 278 (skeptical). These are two different routes to the same effect: in the open network, new ties speed up adhesion; in the skeptical network, transfers without adhesion are blocked, only the ones that “take” remain, and the marking of targets concentrates. Skepticism protects against diffuse prior marking, but it does not prevent unanimity once it forms — it protects those who would be targeted by mistake, not those who are targeted by everyone.

In the small population, everything is faster. With 30 agents, the expulsion occurs at a median step of 190, with an adhesion of 6. One tenth of the network is three targets: the threshold is reached quickly. It is the simulated version of an old intuition of the theory: in small communities the mechanism appears more sharply, because unanimity is easier to obtain.

In every scenario, the network does not return to what it was. Modularity falls slowly over the run, and local cohesion decays and does not recover in the hundred steps after the expulsion, even with the replacement of agents. It is the structural residue: a single cascade destroys more structure than ordinary interaction rebuilds.

What the model does not do

Ties have neither direction nor weight. The tension transfer has no content: it is a change of role. There is no learning and no algorithmic amplification. The agent that leaves is replaced by a new one, with four ties — the model keeps no memory of who left. And the expulsion, as implemented, weighs little in the aggregate results; this is an acknowledged limitation.

The logic behind the rules — the tension transfer that closes the triangle against a third party — is drawn, without formulas, in A Forma (in Portuguese). The model is written in NetLogo; the model file and its ODD description are archived at CoMSES Net (version 1.0.1), and the data of each run can be requested by e-mail. The network skeleton — the initial small-world ring — follows the model of Watts and Strogatz (1998), in the implementation of the Small Worlds model from the NetLogo library (Wilensky, 2015), reused under a CC BY-NC-SA licence. NetLogo is by Uri Wilensky (1999).