Symmetry breaking in collective decision-making through higher-order interactions

TL;DR

The paper tackles how higher-order interactions shape symmetry breaking in collective decisions between two equivalent options. It develops a simplicial-contagion model with autonomous adoption, analyzed via mean-field equations and simulated on random and empirical simplicial topologies, revealing when deadlock gives way to consensus. Key findings include continuous and discontinuous transitions, bistability, and tricritical points, with higher-order ($D=2$) recruitment enabling symmetry breaking that pairwise interactions alone cannot achieve. These results offer a framework for designing distributed decision protocols in artificial swarms and deepen understanding of social systems where group interactions are pivotal.

Abstract

Collective decision-making is a widespread phenomenon in both biological and artificial systems, where individuals reach a consensus through social interactions. While traditional models of opinion dynamics and contagion focus on pairwise interactions, recent research emphasizes the importance of including higher-order group interactions and autonomous behavior to better reflect real-world complexity. In this work, we introduce a collective decision-making model inspired by social insects. In our framework, uncommitted agents can explore options independently and become committed, while social interactions influence these agents to prefer options already accepted by the group. Our model extends classical contagion models by incorporating multiple, mutually exclusive options and distinguishing between pairwise and higher-order social influences. Using simulations and analytical mean-field solutions, we show that higher-order interactions are essential for breaking symmetry in systems with equally valid options. We find that pairwise communication alone can cause decision deadlock, but adding group interactions allows the system to overcome stalemates and reach consensus. Our results emphasize the important roles of autonomous behavior and higher-order structures in collective decision-making. These insights could help us better understand social systems and design decision protocols for artificial swarms.

Figures (4)

• Figure 1: Mean field value of the active population, $\rho_{sb,+}^*$, for the case of two contagions spreading without spontaneous adoption ($\pi = 0$) in the parameter space defined by the pairwise and three-wise spreading intensities, $(\lambda_1, \lambda_2)$. The consensus state is given by $|m^*| = \rho_{sb,+}^*$. The dot-dashed line indicates the discontinuous transition at $\lambda_1^{c,\pi = 0} = 2\sqrt{\lambda_2}-\lambda_2$, while the shaded area delineates the bistability region.
• Figure 2:
• Figure 3: Simulations on a Random Simplicial Complex (RSC) with $\langle k \rangle = 20$ and $\langle k_2 \rangle = 6$. (a) No spontaneous adoption scenario, $\pi = 0$: three different values of the three-body spreading strength are shown ($\lambda_2 = 0$, red squares; $\lambda_2 = 0.8$, beige triangles; $\lambda_2 =2.5$, blue circles), while varying the two-body spreading strength $\lambda_1$. Since the simulations agree with the mean field results, we have $|m^*| = \rho^*$. (b) and (c) depict the spontaneous adoption scenario with $\pi = 0.05$. Two different values of the three-body spreading strength are shown ($\lambda_2 = 1.5$, red squares; $\lambda_2 = 3.9$, blue circles). Other simulation parameters are $r = 0.05$, $N = 2000$.
• Figure 4: Simulations on a Simplicial Complex built from a real dataset based on time-aggregated face-to-face interactions in a high school. We use the same parameters as in the RSC simulations. (a): The active population $\rho^* = |m^*|$ with no spontaneous adoption $\pi = 0$ and group recruitment strengths $\lambda =0.0, \; 0.8, \; 2.5$. (b) and (c) show $\rho^*$ and $|m^*|$, respectively, for spontaneous adoption $\pi = 0.05$ and group recruitment strengths $\lambda = 1.5, \; 3.9$. The system size of the simplicial complexes generated from the data is $N = 1611$, with an average node degree $\langle k_1 \rangle = 33.2$ and an average simplicial degree $\langle k_2 \rangle = 10.9$.