Understanding how group interactions influence opinion dynamics is fundamental to the study of collective behavior. In this work, we propose and study a model of opinion dynamics on $d$-uniform hypergraphs, where individuals interact through group-based (higher-order) structures rather than simple pairwise connections. Each one of the two opinions $A$ and $B$ is characterized by a quality, $Q_A$ and $Q_B$, and agents update their opinions according to a general mechanism that takes into account the weighted fraction of agents supporting either opinion and the pooling error, $α$, a proxy for the information lost during the interaction. Through bifurcation analysis of the mean-field model, we identify two critical thresholds, $α_{\text{crit}}^{(1)}$ and $α_{\text{crit}}^{(2)}$, which delimit stability regimes for the consensus states. These analytical predictions are validated through extensive agent-based simulations on both random and scale-free hypergraphs. Moreover, the analytical framework demonstrates that the bifurcation structure and critical thresholds are independent of the underlying topology of the higher-order network, depending solely on the parameters $d$, i.e., the size of the interaction groups, and the quality ratio. Finally, we bring to the fore a nontrivial effect: the large sizes of the interaction groups, could drive the system toward the adoption of the worst option.

翻译：理解群体交互如何影响观点动态是研究集体行为的基础。本研究提出并分析了一种在$d$-一致超图上的观点动力学模型，其中个体通过基于群体的高阶结构而非简单的成对连接进行交互。两种观点$A$和$B$分别由质量参数$Q_A$和$Q_B$表征，个体根据一种通用机制更新其观点，该机制综合考虑支持各观点的加权个体比例以及交互过程中信息损失的代理参数——汇集误差$α$。通过对平均场模型的分岔分析，我们识别出两个临界阈值$α_{\\text{crit}}^{(1)}$和$α_{\\text{crit}}^{(2)}$，它们界定了共识状态的稳定性区域。这些解析预测通过在随机超图和无标度超图上进行的大规模基于个体的仿真得到验证。此外，分析框架表明分岔结构和临界阈值与高阶网络的基础拓扑无关，仅取决于参数$d$（即交互群体规模）和质量比。最后，我们揭示了一个非平凡效应：过大的交互群体规模可能驱动系统采纳更劣选项。