Collective decision-making in biological and human groups often emerges from simple interaction rules that amplify minor differences into consensus. The bee equation, developed initially to describe nest-site selection in honeybee swarms, captures this dynamic through recruitment and inhibition processes. Here, we extend the bee equation into an agent-based model in which emotional valence (positive-negative) and arousal (low-high) act as modulators of interaction rates, effectively altering the recruitment and cross-inhibition parameters. Agents display simulated facial expressions mapped from their valence-arousal states, allowing the study of emotional contagion in consensus formation. Three scenarios are explored: (1) the joint effect of valence and arousal on consensus outcomes and speed, (2) the role of arousal in breaking ties when valence is matched, and (3) the "snowball effect" in which consensus accelerates after surpassing intermediate support thresholds. Results show that emotional modulation can bias decision outcomes and alter convergence times by shifting effective recruitment and inhibition rates. At the same time, intrinsic non-linear amplification can produce decisive wins even in fully symmetric emotional conditions. These findings link classical swarm decision theory with affective and social modelling, highlighting how both emotional asymmetries and structural tipping points shape collective outcomes. The proposed framework offers a flexible tool for studying the emotional dimensions of collective choice in both natural and artificial systems.

翻译：生物与人类群体的集体决策往往源于简单的交互规则，这些规则将微小的差异放大为共识。最初为描述蜂群巢址选择而提出的蜜蜂方程，通过招募与抑制过程捕捉了这种动态。本文将蜜蜂方程扩展为一个基于智能体的模型，其中情绪效价（正-负）与唤醒度（低-高）作为交互速率的调制器，有效改变了招募与交叉抑制参数。智能体根据其效价-唤醒状态映射出模拟的面部表情，从而得以研究共识形成过程中的情绪传染。我们探讨了三种情景：（1）效价与唤醒度对共识结果与速度的联合影响；（2）当效价匹配时，唤醒度在打破平局中的作用；（3）“雪球效应”，即共识在超越中间支持阈值后加速形成。结果表明，情绪调制可通过改变有效招募与抑制速率，使决策结果产生偏差并改变收敛时间。同时，内在的非线性放大机制即使在完全对称的情绪条件下也能产生决定性的胜出结果。这些发现将经典的群体决策理论与情感及社会建模联系起来，揭示了情绪不对称性与结构性临界点如何共同塑造集体结果。所提出的框架为研究自然与人工系统中集体选择的情绪维度提供了一个灵活的工具。