Social Influence and Consensus Building: Introducing a q-Voter Model with Weighted Influence

Pratik Mullick, Parongama Sen
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Abstract

We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the best of our knowledge. When the bias is neutral, the model is reduced to a mean-field voter model. We analyze the behavior and steady states of the system, identifying three distinct regimes based on the bias level: one favoring negative opinions, one favoring positive opinions, and a neutral case. In large systems, the equilibrium properties become independent of the size of the group, indicating that only the bias influences the final outcome. However, for small groups, the time to reach equilibrium depends on the size of the group. Our results show that even a small initial bias leads to a consensus where all agents eventually share the same opinion when the bias is not neutral. The system exhibits universal behavior, with critical slowing down occurring near the neutral bias point, marking it as a critical dynamical threshold. The time required to reach consensus scales logarithmically when the bias is non-neutral and linearly when it is neutral. Although short-term dynamics depends on group size for small groups, long-term behavior is governed solely by the bias.
社会影响与达成共识:引入具有加权影响力的 q-Voter 模型
我们研究了一个观点形成的动态模型,在这个模型中,一个人的观点会受到与一群其他参与者互动的影响。我们引入了对其中一种意见的偏见,据我们所知,这种偏见是以前从未考虑过的。当偏见为中性时,模型就简化为均值场选民模型。我们分析了系统的行为和稳定状态,根据偏差水平确定了三种不同的状态:一种偏向负面意见,一种偏向正面意见,以及一种中性情况。在大型系统中,平衡特性与群体规模无关,表明只有偏差会影响最终结果。然而,对于小群体来说,达到平衡的时间取决于群体的大小。我们的结果表明,如果偏差不是中性的,即使是很小的初始偏差也会导致共识,即所有代理最终都持有相同的观点。该系统表现出普遍行为,在中性偏差点附近出现临界减速,这标志着它是一个临界动力学阈值。当偏向非中性时,达成共识所需的时间按对数缩放,而当偏向中性时,则按线性缩放。虽然对于小群体来说,短期动力学取决于群体大小,但长期行为则完全由偏置决定。
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