Emergent Discrimination and Polarization in Multi-Agent Systems

Nestor Caticha; João Henrique Sant'Ana; Felippe Alves; Davi Bastos Costa; Mariana Mercucci; Juan P. Neirotti; Otavio Citton; Renato Vicente

cs.MAOct 15, 2026

Emergent Discrimination and Polarization in Multi-Agent Systems

Authors: Nestor Caticha, João Henrique Sant'Ana, Felippe Alves, Davi Bastos Costa, Mariana Mercucci, Juan P. Neirotti, Otavio Citton, Renato Vicente

Organizations: Instituto de Estudos Avançados, Universidade de São Paulo, São Paulo, Brasil · TELUS Digital Research Hub, CIAAM, Universidade de São Paulo, São Paulo, Brasil · Data Science Institute, University of Chicago, Chicago, USA · Bernoulli Institute, University of Groningen, Groningen, Netherlands

Abstract

We study theoretically how discrimination and polarization can emerge in a population of learning agents. Each agent uses an adaptive linear decision layer to map a language-model embedding of an issue to a binary opinion and maintains an evolving estimate of how much it trusts every other agent. Through pairwise interactions, agents update both their decision weights and trust estimates using an online Bayesian rule derived from teacher-student learning over a noisy channel. In-context-learning experiments with large language models qualitatively reproduce the predicted opinion and trust updates. We then assign each agent one of two arbitrary group labels, A or B, and model group bias by allowing a fraction $f_b$ of agents to shift its perceived agreement with each message by a strength $b$ , a bias steering prejudice, depending on whether the sender and receiver share a label. We use order parameters from statistical mechanics to connect these local dynamics to collective states and transitions. Starting from uniformly random initial conditions, simulations reveal a rich phase diagram in the $(b,f_b)$ plane, comprising four collective states: spin-glass frustrated out-group favoritism, nondiscriminatory polarization, discrimination with opinion alignment, and discrimination without opinion alignment. Which state emerges depends on both the strength and prevalence of the bias. These results show how simple local learning dynamics can generate qualitatively distinct forms of polarization and discrimination, underscoring the need for population-level safety analysis of multi-agent systems. They also suggest measurable order parameters for characterizing analogous collective states in human societies.

Figures & tables

Figure 1: Four collective states and representative populations. Left: the phase diagram in the space of bias strength

b

and the fraction

f_{b}

of biased agents, obtained from societies of

N=100

agents by averaging two realizations at each point of a

300\times 300

grid. In (I) out-group favoritism leads to a frustrated, in the sense of spin glass, structure of trust relations and opinions. In (II), polarization , opinion and trust form two camps unrelated to class. In (IIIa), both trust and opinion are highly correlated with class; in (IIIb),

b

is so high that irrespective of opinion, trust and class are correlated. Right: one representative

N=100

population from each phase. Each arrow is an agent’s opinion (top) or outgoing trust profile (bottom), projected onto two dimensions. Color denotes class and filled markers denote biased agents. Formal definitions and the full phase analysis are given in Section 4.2 .

Figure 2: Evidence landscape and modulation functions. Left: Minus the log-evidence $-\ln Z$ . Online SGD follows its negative gradient toward higher-evidence regions and away from the dissonant configurations where evidence is low. Center and right: the opinion and trust modulation functions, $F_{w}$ and $F_{\mu}$ . Learning and unlearning occurs in the low evidence regions which represent cognitive dissonance, i.e. when the emitter agrees (respect. disagrees) with a receiver that it distrusts (respect. trusts). Even in those low evidence regions the large changes occur mainly in one sector where the field is less in magnitude. This blame attribution to a sector resembles the algorithm of least action Mitchison and Durbin (1989) , which was shown to be quite limited by Kabashima (1994) and was optimized in Simonetti and Caticha (1996) Copelli and Caticha (1995) for the parity and committee machines.

Figure 3: Opinion and trust updates under in-context learning. The backgrounds show the analytic functions and the points show the measured changes divided by one global fitted scale for each experiment. The opinion experiment (left) contains $550$ measured changes, with $94.7\%$ sign agreement and rank correlation $r_{s}=0.90$ . The trust experiment (right) contains $712$ measured changes, with $86.0\%$ sign agreement and correlation $r=0.85$ .

Figure 4: Effect of the prejudice bias. Learning is driven by flows that decrease dissonance in the evidence landscape. The arrows components are proportional to the learning modulations

F_{w},F_{\mu}

at the receiver’s field

h_{w}

and

h_{\mu}

induced by learning the emitter’s opinion. Left: More tolerant:

b<0

increases the basin of attraction of agree/trust . Center:

b=0

. Right : Less tolerant:

b>0

increases the basin of attraction of disagree/distrust .

Figure 5: Order parameters over the $(b,f_{b})$ plane . $R_{\mu,c}$ measures trust–class alignment, $R_{c,w}$ opinion–class alignment, and $R_{w,\mu}$ opinion–trust alignment. Each panel averages two $N=100$ realizations at each point of a $300\times 300$ grid.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Two slices of the general field. Left: the $(a,f_{a})$ plane. Right: the $(c,f_{c})$ plane. Colors encode the order parameters defined in the text.

Figure 7: An unbiased society splits in two. Eight realizations with independently sampled initial conditions, each with

N=400

agents at

b=0

and a simple agenda, before and after

500

interactions per ordered pair, with their pairs pooled:

638\,400

unordered pairs for the opinion overlap and

1\,276\,800

ordered pairs for the trust. Blue is the initial state, red the final one. Opinion overlap starts unimodal at zero, of width

1/\sqrt{K}

as random vectors in

K=30

dimensions require, and ends bimodal; trust starts spread across the interior and ends saturated at

\pm 1

, so the split in trust is built by the dynamics and not supplied by the initial condition. The positive and negative peaks correspond to pairs within and across the two camps, respectively.

symbol	meaning	value	provenance
$K$	dimension of the issue embedding	$30$	fixed by the agenda-complexity setup
$\Delta t$	interactions per ordered pair	$500$	stability check (see below)
$C_{0},V_{0}$	initial uncertainties	$I$ , $1$	uninformative prior
$\mu_{0}$	initial distrust	$\mathcal{U}(-1,1)$	unstructured initial trust

Appendix

Table 8

experiment	$N$	$P$	parameter sampling	realizations	updates per realization
main phase diagram	$100$	$5$	$300\times 300$ grid in $(b,f_{b})$	$2$ /point	$4\,950\,000$
complex-agenda diagram	$40$	$100$	$200\times 200$ grid in $(b,f_{b})$	$1$ /point	$780\,000$
general-field slices	$40$	$5$	two $200\times 200$ grids	$1$ /point	$780\,000$
unbiased polarization	$400$	$5$	$b=0$	$8$ total	$79\,800\,000$
finite-size check	$20,30,40,60$	$5$	five selected points	$12$ /point	$500N(N-1)$
IIIb lifetime test	$40$	$5$	selected points	$12$ /point	up to $1\,560\,000\,000$

Appendix

Table 9

Figure 8: Correlations and phase diagram for the complex agenda ( $\alpha=3.3$ ), simulated with $N=40$ on a $200\times 200$ grid with one realization per point. The first three panels show $R_{w,\mu}$ , $R_{\mu,c}$ , and $R_{c,w}$ over the $(b,f_{b})$ plane; the right panel combines them as RGB channels to identify the four collective states. Compared with Figure 5 , $R_{c,w}$ now tracks $R_{\mu,c}$ over most of the $b>0$ half, so region (IIIa) occupies most of the discriminatory regime.

Figure 9:

\langle|\rho|\rangle

saturates the Cauchy–Schwarz bound of equation 20

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AI agents increasingly operate as part of interacting systems rather than in isolation. As agents exchange information and jointly make decisions, their interactions can improve collective reasoning but may also produce herding, polarization, or amplify shared biases. Understanding and predicting these collective dynamics is therefore important for designing effective and aligned multi-agent systems. Here, we study over 10,000 communities of language-model agents that repeatedly exchange messages and revise their opinions across objective mathematics questions and subjective political statements. Despite substantial diversity in possible behavior, the individual and group dynamics can be represented by three characteristic regimes: indifference, polarization, and consensus. AI agents start indifferent and build conviction as they interact. On objective questions, communication improves collective accuracy, while on subjective questions it often drifts group opinions toward the right in the political spectrum. We explain these observations with a statistical-mechanics formalism in which agents stochastically favor lower social pressure. Given only initial opinions, our model predicts individual trajectories, outperforms all standard baselines, generalizes to unseen community graphs, and reproduces the observed group archetype distributions. Our fitted model parameters reveal the mechanics underlying our key observations: i) communities operate below the critical social temperature, which explains conviction buildup; ii) attractive ties outweigh repulsive ones, which favors consensus; and iii) agents holding the correct answer exert the strongest pull, which drives truth-seeking. Overall, our results demonstrate that collective behavior of AI agents, like that of other complex systems, follows compact and predictive dynamical laws.

Abstract

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