By Carlos Paes
What this note is for
This note presents a small agent-based model of the scapegoat mechanism and asks for comments on one claim in particular: that the model is ready to move from theoretical exposition toward explanation. The order in which the work was done matters for that claim, so it comes first.
The model was built before any data were collected. It started from René Girard’s account of the mechanism — a group in crisis converging on a single victim, the unanimity of the expulsion, the order that follows — and reduced that account to the few rules that could be written in NetLogo, to see what those rules do on a network when population, closure and skepticism are varied. In the vocabulary of Edmonds et al. (2019), that is theoretical exposition: the behaviour of a set of mechanisms, characterised by systematic runs, with no particular empirical target in view.
The data came afterwards. O Mecanismo (omecanismo.org) now follows eight Brazilian online pile-ons, from 2014 to 2025, day by day as mention networks on Twitter/X, published without naming anyone, the target included. The eight episodes share a shape, and it is the shape the model had been producing: a diffuse baseline, a trigger, a convergence on one account, a peak, the target leaving the centre, and a residue in which the network does not go back to what it was. Because the model was not fitted to the cases, the resemblance was not engineered. Whether it is enough to call the model an explanation of the cases is the open question, and the reason for writing.
The shape the cases have
Each case has two different days of interest: the day with the most posts, and the day on which the mention network comes closest to a star, with one account at the centre. In seven of the eight cases these are not the same day. In the 2022 case of a broadcaster, the crowd peaks on the first day after the trigger, but the network only takes the shape of a star on the sixth, when the volume has already fallen and what remains is organised around the target. In the 2014 case the order is reversed: the star forms on the seventh day and the largest crowd arrives on the twelfth. The crowd and the star are two events, and a mechanism that only produced a peak would miss the cases; it has to produce the star at a moment of its own.
The model in four rules
Thirty to a hundred agents sit on a small-world ring, the Watts–Strogatz skeleton taken from the Small Worlds model in the NetLogo library. Each agent carries a quantity called tension, which builds up and propagates between neighbours. A saturated agent transfers its tension onto a target — transfer rather than accusation, because it is tension changing place, with no content and no merit attached. Not any agent: only one at maximum tension whose neighbours are all at maximum tension can start a transfer. The leader of the accusation is not a cool strategist standing outside the crisis; it is the most tensioned agent in the most tensioned pocket of the network, and once poles amount to one agent in twenty the transfers come from the poles themselves. The target is not chosen at random either. The transfer looks first for an isolated agent — one with fewer than two ties — then for an agent already marked by an earlier transfer, then for one at middle distance in the network, neither neighbour nor stranger, and only in the last resort for anyone. Isolation is the model’s victimary sign, and it feeds on itself: once marked, the target loses the tie that brought it closest to the pole, and the isolated agents of the network attach themselves to the marked. A transfer either takes — the network follows it, the one who transferred becomes an amplifying pole and the target stays marked — or it does not. Once the marked targets exceed one tenth of the population and a pole exists, the expulsion occurs: one marked target leaves, the rest adhere to the pole — that is the mimetic step, new ties with the agent who started the transfer — and a new agent takes the empty place. Three parameters: population; closure, which lowers the chance that the network creates new ties (in the code the parameter is called friendliness and means the opposite; the name was kept in the code and changed on the page); and skepticism, the probability that a transfer which attracted no adhesion is blocked.
Where each rule comes from
It would be easy, and misleading, to present every rule above as Girardian, so the provenance is stated plainly.
From the theory, as design decisions taken before any code was written:
- Mimetic crisis → tension that accumulates in each agent and propagates to its neighbours, until whole pockets of the network are saturated.
- The first accuser → only a saturated agent surrounded by saturated agents can transfer: the accusation starts where the crisis is densest.
- Victimary signs → the transfer looks first for an isolated agent, one with fewer than two ties.
- Polarisation on a single victim → the transfer lands on one target, which stays marked.
- Mimetic contagion → adhesion to the one who transfers: new ties with the pole.
- Unanimity → the adhesion of the rest of the network to the pole at the expulsion, reached once the marked targets exceed one tenth of the population.
- Catharsis → the discharge: at every transfer that gains adherents the tension of the whole network drops to zero, in full at the expulsion. This last rule is what gives the tension curve its saw-tooth form.
Auxiliary assumptions, chosen to make the simulation run and not attributable to Girard or to anyone else:
- the expulsion threshold — one tenth of the population marked as targets;
- the skepticism probability and its range (50 to 99);
- the preference of a new transfer for a target already marked once, and for targets at middle distance (three to five steps away);
- the rule that, once poles amount to one agent in twenty, new transfers come from the poles themselves;
- the replacement of the expelled agent by a new one with four ties;
- ties with no direction and no weight, and no memory of who left.
Nothing in the theory speaks of tenths, of twentieths or of four ties.
From a library: the small-world ring, reused under its licence.
Left out on purpose: learning, algorithmic amplification, and any defender of the target. Not following a transfer is not neutral, though. Since the expulsion depends on a threshold of marked targets, every transfer the network does not follow marks nobody and counts against the unanimity, and so does every transfer that skepticism blocks. The model has no defence, but it has abstention — the network declining to follow a transfer — and abstention is what protects.
The model is archived at CoMSES Net (Paes, 2025), with its ODD description.
What the runs show
Five scenarios, twenty runs each with seeds 1 to 20, a ceiling of 1,500 steps, time aligned on the expulsion. The base scenario (population 60, closure 10, skepticism 75) reaches the expulsion in all twenty runs, at a median step of 546.5, with a median of 10 adhesions to the pole. Closing the network (closure 19) is the only change that stops the mechanism: ten of the twenty runs never reach the expulsion, and when they do the adhesion is the smallest of any scenario, 3.5. The closed network is at once the one that isolates the target most and the one that expels it least. Read back into the theory, that is what unanimity should cost: reorganising around a pole means making new ties, and a network that makes none accumulates transfers without ever converting them into anything.
Opening the network (closure 0) and raising skepticism to 95 both bring the expulsion forward, to median steps of 279.5 and 278, by two different routes. New ties speed up adhesion; blocking weak transfers leaves only the ones that take. Skepticism, in this model, protects whoever would have been marked by mistake, not whoever is marked by everyone. With thirty agents everything is faster, median step 190, because three agents are a tenth of the network.
One result was not written into the rules. In every scenario modularity and local cohesion fall during the episode and have not recovered a hundred steps after the expulsion, even with the replacement of the expelled agent. One cascade destroys more structure than ordinary interaction rebuilds. Nothing in the code asks for this; it is the model’s residue, and it matches the order-after of the theory without having been programmed.
The question
What would be required to accept the move from theoretical exposition to explanation? At present the comparison with the cases rests on a shared sequence of stages and on two measures that exist on both sides, concentration of attention and degree centralisation; a third, local cohesion, has no empirical counterpart, because the model’s network is the substrate (who knows whom) while the cases’ networks are the episode itself (who mentioned whom that day). Would a pattern-by-pattern comparison be enough? Three patterns already have a measure on both sides: the star at a moment of its own, apart from the crowd; the closed network that isolates most and expels least; and the structure that does not come back — with a caveat, because in the cases fragmentation falls between the first and the last days with a network of thirty accounts or more in five of the seven cases that have them, and rises in the other two. Two more could be measured: several marked before one is expelled, since the model needs more than a tenth of the network marked (about twenty transfers in the base scenario) and three of the eight cases have a secondary target; and the target isolated in the fabric while central in the episode — the model’s victimary sign, which in the cases appears as a person at the centre who is talked about far more than talked to. One pattern could count against the model as written: the discharge. In the model the expulsion resets the tension at once; in the cases, of the five with a sanction inside the collection window, three (2014, 2019 and the 2022 broadcaster) have about half of the collected posts after the day of the sanction — two of them sampled with a daily ceiling, which flattens the shares — and in 2014 the largest crowd arrives six days after it. Either the sanction is not the expulsion, the expulsion being the target leaving the centre rather than the institutional act, or the model’s discharge is too fast. Or does explanation require tying the mechanisms themselves to evidence, and if so, what evidence would count? One such tie is untested: the model predicts that the first accusers come from an already saturated pocket, which in the cases would mean accounts already engaged in related disputes before the trigger; four of the eight cases have data from before the trigger. Suggestions on what to measure, what to vary, and what would falsify the claim are what this note is for.
The run data for the five scenarios are available by e-mail. The site’s research pages — theory, model, method and the cases in summary — are in English at omecanismo.org/en/, with the five scenario charts labelled in English; the case pages are in Portuguese.
References
Edmonds, B., Le Page, C., Bithell, M., Chattoe-Brown, E., Grimm, V., Meyer, R., Montañola-Sales, C., Ormerod, P., Root, H. and Squazzoni, F. (2019). Different modelling purposes. Journal of Artificial Societies and Social Simulation, 22(3), 6. DOI:10.18564/jasss.3993
Girard, R. (1977). Violence and the Sacred. Translated by Patrick Gregory. Baltimore: Johns Hopkins University Press.
Girard, R. (1986). The Scapegoat. Translated by Yvonne Freccero. Baltimore: Johns Hopkins University Press.
Paes, C. (2025). An agent-based model of scapegoating (Version 1.0.1). CoMSES Computational Model Library. https://www.comses.net/codebases/44d0678d-1412-40d9-8a02-a857a5f1d81d/releases/1.0.1/
Watts, D. J. and Strogatz, S. H. (1998). Collective dynamics of “small-world” networks. Nature, 393, 440–442. DOI:https://doi.org/10.1038/30918
Wilensky, U. (1999). NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University. http://netlogo.org/
Wilensky, U. (2015). NetLogo Small Worlds model. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. http://netlogo.orghttp://netlogo.org
Paes, C. (2026) The crowd and the star: a small scapegoat model, eight pile-ons, and a request for suggestions. Review of Artificial Societies and Social Simulation, 4 Nov 2026. https://rofasss.org/2026/11/04/the-crowd-and-the-star/
© The authors under the Creative Commons’ Attribution-NoDerivs (CC BY-ND) Licence (v4.0)
