With the development of new technologies, more than 3.8 billion users communicate on various social media platforms through word of mouth (WOM) [1]. This provides new channels for expressing opinions and exchanging information among group users, greatly facilitating our daily lives [2]. Users of social media platforms typically share interests, discuss popular topics, and acquire relevant information [3]. Online users prefer to make decisions based on opinions and information from social media platforms. Social media has become the primary way to disseminate public opinion [4]. Public opinion on social media has affected many fields such as enterprises, individuals, national security, and social stability [2]. For instance, the spread of social media information allows users to understand the process of popular events [5]. It can also help enterprises expand the scope of their products or businesses [6] and encourage the government to improve work efficiency to better fulfill government functions [7]. At the same time, the negative effect of complexity, diversity, and suddenness of public opinions is typically ignored. For example, rumors about COVID-19 have confused people worldwide, and Tesla’s brake failure has had a huge negative impact on the company involved. From the above analysis, it can be seen that the spread of public opinion on social media may have huge economic value but may also have a negative impact. Therefore, monitoring the dissemination of public opinion on online social networks is important.
Although social network platforms are independent, the observed network and dynamic features are isolated and different. These networks are interdependent and linked to a complex network—information, goods, and news flow through this complex network [4]. Coupled systems exist not only in physical and committed networks, but also in virtual social media networks. For example, online users typically use multiple social platforms, such as WeChat and Weibo, to exchange information; they also use Twitter and Facebook to share their opinions and communicate. Users are accustomed to using multiple online social media platforms to disseminate information and share opinions. Therefore, public opinion spreads rapidly on multiple social network platforms rather than being confined to a single closed network. With the continuous improvement in social networking platform functions and the growth of users, the dissemination process of multiple social networks exhibits increasingly complex features. For example, Tesla’s brake failure information spread on multiple platforms, such as WeChat, Weibo, and today’s headlines, which further increased the scope and duration of information. In addition, social network users (nodes), as information carriers, directly determine the propagation path of the information in a social network. Users obtain information from multiple channels on multiple social platforms and spread it across all social networks. If information dissemination cannot be effectively controlled and managed, it may lead to information distortion [4], which causes the dissemination of a black hole.
There have been many important achievements in the research on the opinion spread of individual populations on social networks [8], [9]. Opinion dynamics can be used to model and analyze the behavior of individuals interacting with and exchanging opinions on social networks. French (1956) introduced an opinion-dynamic model to discuss how individuals influence each other during an interaction. The model was further expanded to the French–DeGroot model [10]. Subsequently, scholars have proposed many improved DeGroot models that provide profound insights into the dynamic spread of public opinion. The Hegselmann–Krause (HK) and Deffuant–Weisbuch (DW) models use bounded confidence to analyze how individuals interact with others who have similar opinions [11], [12]. Opinion dynamics models are often used to analyze real-world communication phenomena [13], [14], [15]. These models clearly describe the process of dissemination and evolution of opinions, thereby increasing our understanding of the public opinion diffusion mechanism [16]. With the rapid development of communication technology, the spread of public opinion has become increasingly dynamic and complex, making it difficult to describe this dissemination process [2].
Previous studies have mostly focused on the public opinion dissemination mechanism on single-layer social media platforms; few studies have explored the dissemination of public opinion on multi-layer social media platforms. Current social media platforms exhibit the phenomenon of mutual communication in coupled networks. Accordingly, it is essential to build a multi-layer communication model for public opinion based on a multi-platform network [17].
Scholars have made significant efforts to develop management strategies for disseminating public opinion. At present, the management strategy for public opinion minimizes negative impacts and maximizes positive impacts. Regarding negative information and rumors, existing studies have mainly analyzed the propagation path of public opinion to minimize its negative impacts [8], [18]. Simultaneously, they explored how to enhance the influence of public opinion by maximizing the scope of information dissemination [6], [19], [20].
The above studies were implemented to manage public opinion on single-layer network platforms; however, public opinion management on coupled networks needs further improvement. Public opinion will show information attenuation in the process of spreading, particularly in multi-layer networks [4]. Therefore, the opportunity for the intervention of public opinion management in coupled networks is very important. Regulators face significant communication risks, particularly in the case of an explosion of negative public opinion in the coupling network. Therefore, exploring information attenuation in public opinion dissemination in a coupled network and exploring opportunities for regulatory intervention are important topics in current research on public opinion dissemination.
Based on the above discussion, this study developed opinion dynamics HK models in which individuals interact with others using a three-stage cascade model on multi-layer social media platforms. As opinions evolve, each agent maintains a certain degree of adherence to their initial opinions and simultaneously determines the weight of opinion influence based on the node distance in multi-layer social networks. The proposed model considers information attenuation and the influence of opinion leaders in multi-layer social networks, and can describe a public opinion dissemination environment more closely.
The contributions of this study are the following:
(1)The process of information propagation attenuation in multi-layer social networks was considered for the first time in this study. The influence weights between nodes were calculated by introducing the distance between nodes in a multi-layer social network, and the weights were determined using a three-level opinion transfer network considering information attenuation. This model reflects the real phenomenon of information transmission in multi-layer social networks and enriches studies on information propagation in multi-layer social networks.
(2)This study considers the influence of two competitive opinion-leader subgroups on three-level nodes in a multi-layer social network and proposes a three-stage cascaded opinion dynamic model. Through random simulation, the propagation rule of competitive opinions in real multi-layer social networks was revealed. This is of great significance for enterprises to promote products in multi-layer social networks and regulators to grasp the rules of public opinion dissemination in multi-layer social networks.
The remainder of this paper is organized as follows: Section 2 describes opinion leaders and the information dissemination process. Section 3 presents the weight of public opinion transmission in a multi-layer social network and the effects of opinion leaders in a social network. Section 4 provides details and discusses the simulation results. Finally, Section 5 presents the conclusions of this study.
介绍
随着新技术的发展，超过38亿用户通过口碑（WOM）[1]在各种社交媒体平台上交流。这为群体用户之间表达意见和交换信息提供了新渠道，极大地便利了我们的日常生活[2]。社交媒体平台的用户通常分享兴趣，讨论热门话题，并获取相关信息[3]。在线用户更倾向于根据社交媒体平台上的意见和信息做出决策。社交媒体已成为传播公众舆论的主要方式[4]。社交媒体上的公众舆论影响了许多领域，如企业、个人、国家安全和社会稳定[2]。例如，社交媒体信息的传播使用户能够了解热门事件的过程[5]。它还可以帮助企业扩大其产品或业务的范围[6]，并鼓励政府提高工作效率，更好地履行政府职能[7]。同时，公众舆论的复杂性、多样性和突发性的负面影响通常被忽视。例如，关于COVID-19的谣言已经让全世界的人感到困惑，特斯拉的刹车失灵事件对涉事公司产生了巨大的负面影响。从上述分析可以看出，社交媒体上的公众舆论传播可能具有巨大的经济价值，但也可能产生负面影响。因此，监控在线社交网络上公众舆论的传播是重要的。
尽管社交网络平台是独立的，但观察到的网络和动态特征是孤立和不同的。这些网络是相互依赖的，并连接到一个复杂的网络——信息、商品和新闻通过这个复杂网络流动[4]。耦合系统不仅存在于物理和承诺网络中，还存在于虚拟社交媒体网络中。例如，在线用户通常使用多个社交平台，如微信和微博，来交换信息；他们也使用推特和脸书来分享他们的意见和交流。用户习惯于使用多个在线社交媒体平台来传播信息和分享意见。因此，公众舆论在多个社交网络平台上迅速传播，而不是被限制在单一的封闭网络中。随着社交网络平台功能的不断完善和用户数量的增长，多个社交网络的传播过程表现出越来越复杂的特征。例如，特斯拉刹车失灵的信息在微信、微博和今日头条等多个平台上传播，进一步扩大了信息的范围和持续时间。此外，社交网络用户（节点）作为信息载体，直接决定了社交网络中信息的传播路径。用户从多个社交平台上的多个渠道获取信息，并将其传播到所有社交网络。如果信息传播不能得到有效控制和管理，可能会导致信息失真[4]，这会导致信息传播的黑洞。
在社交网络上个体群体的意见传播研究方面已经取得了许多重要成果[8]，[9]。意见动态可以用来模拟和分析个体在社交网络上互动和交换意见的行为。法国（1956）引入了一个意见动态模型来讨论个体在互动过程中如何相互影响。该模型进一步扩展到法国-德格鲁特模型[10]。随后，学者们提出了许多改进的德格鲁特模型，为公众舆论的动态传播提供了深刻的洞见。赫塞尔曼-克劳斯（HK）和德芬特-韦斯布奇（DW）模型使用有界信心来分析个体如何与持有类似意见的他人互动[11]，[12]。意见动态模型通常用于分析现实世界的沟通现象[13]，[14]，[15]。这些模型清晰地描述了意见的传播和演变过程，从而增加了我们对公众舆论传播机制的理解[16]。随着通信技术的快速发展，公众舆论的传播变得越来越动态和复杂，使得描述这一传播过程变得困难[2]。
以往的研究大多关注单层社交媒体平台上的公众舆论传播机制；很少有研究探讨多层社交媒体平台上的公众舆论传播。当前的社交媒体平台表现出耦合网络中的相互通信现象。因此，基于多平台网络构建公众舆论的多层通信模型是必要的[17]。
学者们已经做出了重大努力来开发传播公众舆论的管理策略。目前，公众舆论的管理策略旨在最小化负面影响并最大化正面影响。关于负面信息和谣言，现有研究主要分析了公众舆论的传播路径，以最小化其负面影响[8]，[18]。同时，他们探索了如何通过最大化信息传播的范围来增强公众舆论的影响[6]，[19]，[20]。
上述研究是在单层网络平台上实施的，以管理公众舆论；然而，耦合网络上的公众舆论管理需要进一步改进。公众舆论在传播过程中会显示出信息衰减，特别是在多层网络中[4]。因此，耦合网络中公众舆论管理的干预机会非常重要。监管者在耦合网络中面临重大的沟通风险，特别是在耦合网络中负面公众舆论爆发的情况下。因此，探索耦合网络中公众舆论传播的信息衰减和监管干预的机会是当前公众舆论传播研究中的重要课题。
基于上述讨论，本研究开发了意见动态HK模型，其中个体在多层社交媒体平台上使用三阶段级联模型进行互动。随着意见的演变，每个代理在保持对初始意见的一定程度的坚持的同时，还根据多层社交网络中的节点距离确定意见影响的权重。所提出的模型考虑了多层社交网络中的信息衰减和意见领袖的影响，能够更接近地描述公众舆论传播环境。
本研究的贡献如下：
（1）本研究首次考虑了多层社交网络中信息传播衰减的过程。通过引入多层社交网络中节点之间的距离来计算节点之间的影响权重，并使用考虑信息衰减的三级意见转移网络来确定权重。该模型反映了多层社交网络中信息传输的真实现象，并丰富了多层社交网络中信息传播的研究。
（2）本研究考虑了两个竞争的意见领袖子群对多层社交网络中三级节点的影响，并提出了一个三阶段级联的意见动态模型。通过随机模拟，揭示了现实多层社交网络中竞争性意见的传播规则。这对于企业在多层社交网络中推广产品和监管者掌握多层社交网络中公众舆论传播的规则具有重要意义。
本文的其余部分安排如下：第2节描述了意见领袖和信息传播过程。第3节介绍了多层社交网络中公众舆论传播的权重和社交网络中意见领袖的影响。第4节提供了细节并讨论了模拟结果。最后，第5节提出了本研究的结论。
在数字经济中，社交网络，如Twitter和微博，已经成为最大的信息门户[1]。用户可以通过这些社交平台与朋友和追随者分享信息。信息反映了产品、公司和服务，使信息流动更加迅速；而信息的影响力对于许多公司来说是关键[2]。在社交网络中，用户对某些实体的意见通过他们的互动和表达方式得到反映[1,3]，这导致了信息的更快传递。此外，消费者对特定实体的意见对于信息扩散变得很重要[4]。虽然消费者的日常互动是社交营销的基础，但由于复杂的动态因素，很难预测互动对产品销售的影响[5]。因此，了解消费者的意见对于组织和公司来说变得至关重要[6]。在信息传播过程中，一些被称为意见领袖的社交媒体用户可以对其他用户的观点和决策行为施加相当大的影响[7]。在Twitter上，49%的受访者依赖意见领袖的产品推荐，40%的用户购买意见领袖推荐的产品[8]。在用户对产品或服务的态度形成过程中，意见领袖可以改变用户的信念并影响购买决策。这是一种营销策略，意见领袖通过社交网络向他人推荐产品或服务。大量研究表明，意见领袖对意见传播过程有深远的影响[9]。罗杰斯[10]发现，与意见形成未影响意见领袖相比，意见领袖在有追随者的社交网络中传播意见的速度更快。在社交电子商务中，口碑（WOM）这一大众媒体传播方式有效地影响了消费者购买采用的过程[7]。通过口碑，意见领袖通过意见分散影响其他消费者[11]。研究发现，意见领袖对平均消费者购买决策的差异程度是由意见领袖和消费者之间的文化背景和产品关注点差异造成的[12]。意见领袖愿意与消费者使用口碑传播。先前的研究发现，意见领袖通常通过口碑传播向其他消费者提供购买决策的产品信息和建议，从而影响对产品的信念、态度和行为。然而，由于有多个意见领袖推荐竞争产品，因此研究消费者在做出购买决策时如何与多个意见领袖互动以及分析影响意见领袖权力的关键因素非常重要。
此外，意见领袖的反馈基于个人特质偏好，可能与其他消费者无关，使得追随者很难判断产品[13]。由于社会压力和支持，意见领袖顺应他人的期望，精心选择和传播信息，从而影响消费者的决策过程[14]。然而，企业仍然专注于产品设计和影响未知消费者的购买决策，而不是专注于意见领袖的产品采用和推荐。在社交网络中，信息的传播是一个复杂而动态的过程。虽然以前的研究使用意见动力学模型来调查社交媒体平台上的意见传播机制[9,15-16]，但很少有人探索意见领袖的产品信息传播过程。为了探索这一过程以及对消费者购买决策的影响，本研究基于意见动力学模型考察了意见领袖的动态影响。以前的研究在意见动力学方面取得了很大进展；然而，仍然存在以下局限性：1）在意见动力学过程中，意见领袖受到目标广告或产品的影响，形成个人意见，并通过互动将这种意见传达给其他消费者。因此，应考虑广告或产品的影响。2）现有研究只考虑意见领袖对关注者的影响。但在意见影响过程中，意见领袖对目标广告或产品信息的投放会成功，关注者会根据有界置信度规则调整意见。因此，信息传递概率的影响需要调查。为了克服这些局限性，本研究构建了一个新的多信息意见领袖，并基于有界置信度原理分析了社交网络中关注者的意见动态模型。这些方法影响目标广告和信息传递概率。此外，本研究分析了意见领袖对意见的采纳和传播与跟随意见演变的过程之间的关系。本研究旨在（1）探索公众意见领袖的信息采用、传播过程及其对消费者的影响；（2）帮助企业更好地了解意见领袖的影响，并在社交平台上实施营销策略。该研究通过构建一个集成的有界信心模型来定量分析广告强度与以前的定性分析相比的影响，从而为研究做出贡献。此外，它分析了当最初支持产品广告的消费者较少时，如何提高广告的投放效率。文章的其余部分组织如下。第2节提供了意见领袖的理论背景和有界信心原则。第3节为多个信息意见领袖和意见追随者构建了一个新的有界信心意见动力学模型。第4节通过计算机模拟呈现结果，以研究多意见领袖的影响和追随者意见的演变。第5节总结了这项研究。
2 文献综述
2.1 意见领袖研究领域的各种背景提供了意见领袖的定义[17]。意见领袖是一个有吸引力的人，具有突出的精神、身体和社会特征，并在特定领域拥有可靠的知识[18]。此外，意见领袖具有更高的社会经济地位，因为大众媒体的曝光率增加，与变革推动者的密切接触，这影响了社交媒体参与者[19]。值得注意的是，意见领袖通过提供产品或服务的购买推荐来影响对其他个人的影响。这种影响直接影响消费者的购买决策[20]。因此，意见领袖是在意见更新过程中具有确定的、坚定不移的目标意见，打算影响追随者的意见，并且不受追随者意见影响的代理人[9]。在意见扩散中，大众媒体中的意见和信息通过意见领袖的调节作用进行传递[7]。因此，意见领袖通过意见交流过程对他人的决策具有突出的影响力[21]。社会互动的复杂性和动态性使得预测经济结果变得困难。为了解决这个问题，多智能体模拟模型使用意见动力学进行实验，探索意见领袖在社交网络中的影响传播机制[7]。在意见动力学领域，意见领袖被定义为由一个或多个个体连接的易于被其他成员跟随的群体[22]。使用计算机模拟，意见领袖被发现在达成群体共识方面是有效的[23]。即使个人不知道他们的信息如何与他人进行比较，或者不知道他们是属于多数群体还是少数群体[24]，情况也是如此。