# Modeling Multidimensional Public Opinion Polarization Process under the Context of Derived Topics

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Model Construction

_{1}, x

_{2}, x

_{3}, …, x

_{n}), which is a point in n-dimensional space. The x

_{n}belongs to the interval (0, 1), and x

_{n}obeys N ~ (0.5, 0.2), mapping in the interval (0, 1). Set attitude (<0) as 0 and the attitude (>1) as 1. In this way, the initial attitude of most individuals is relatively neutral, while only a few individuals hold extreme attitudes. This assumption is consistent with the attitude distribution of groups in the real world towards certain kinds of events.

_{0}, and the nodes are connected randomly.

_{1}new nodes are added to the network each time, and a connection is established with m

_{0}nodes in the initial network, that is, m

_{1}new edges are added each time. The connection probability of the newly added nodes connecting the nodes in the initial network is positively correlated with the original node degree, and the resulting undirected network graph with node size N is generated.

_{mn}of topic m and topic n is equal to 0. If “No”, then Step6 is executed, otherwise Step9 is executed.

_{m}and f

_{n}of topic m and topic n is 0, if “No” then execute Step 8, otherwise execute Step9.

#### 3.1. Individual’s Support Degree of the nth Dimensional Topic ${S}_{n}\left(i\right)$

#### 3.1.1. Topic Correlation Coefficient ρ_{mn}

#### 3.1.2. Influence Intensity of Different Dimensional Topic ${E}_{n}^{m}$

_{mn}. When ρ

_{mn}> 0, the mth dimensional topic has a positive influence on the nth dimensional topic. When ${e}_{n}^{m}$ > 1, it means that the influence of the mth dimensional topic is much greater than that of the nth dimensional topic. For convenience, the default maximum value of ${e}_{n}^{m}$ is 1.

#### 3.1.3. The Influence of External Intervention Information ${F}_{n}^{mn}$

_{mn}, and f

_{m}. f

_{m}> 0 represents the external positive information of the mth dimensional topic, while f

_{m}< 0 represents the external negative information of the mth dimensional topic. $sin(\frac{\mathsf{\pi}}{2}\ast {f}_{m})$ is increasing in the interval [−1, 1] and the domain is [−1, 1], whose changing trend is consistent with the influence of external invention information on an individual’s support. When f

_{m}< 0, there is a negative correlation between topic m and topic n. At this point, the external information of the mth dimensional topic will have a completely opposite influence on the nth dimensional topic.

#### 3.2. Interaction Rule of Multidimensional Attitude

- when $\sqrt{\sum {\left({\dot{x}}_{n}\left(i\right)-{\dot{x}}_{n}\left(j\right)\right)}^{2}}<{d}_{1}$$${\ddot{x}}_{n}\left(i\right)={\dot{x}}_{n}\left(i\right)+\mu \left({\dot{x}}_{n}\left(j\right)-{\dot{x}}_{n}\left(i\right)\right)$$$${\ddot{x}}_{n}\left(j\right)={\dot{x}}_{n}\left(j\right)+\mu \left({\dot{x}}_{n}\left(i\right)-{\dot{x}}_{n}\left(j\right)\right)$$
- when $\sqrt{\sum {\left({\dot{x}}_{n}\left(i\right)-{\dot{x}}_{n}\left(j\right)\right)}^{2}}>{d}_{2}$$${\ddot{x}}_{n}\left(i\right)={\dot{x}}_{n}\left(i\right)-\beta \left({\dot{x}}_{n}\left(j\right)-{\dot{x}}_{n}\left(i\right)\right)$$$${\ddot{x}}_{n}\left(j\right)={\dot{x}}_{n}\left(j\right)-\beta \left({\dot{x}}_{n}\left(i\right)-{\dot{x}}_{n}\left(j\right)\right)$$
- In other cases, the attitude values of individual i and j remain unchanged, which is expressed as follows:$${\ddot{x}}_{n}\left(i\right)={\dot{x}}_{n}\left(i\right)$$$${\ddot{x}}_{n}\left(j\right)={\dot{x}}_{n}\left(j\right)$$

## 4. Simulation Experiment

#### 4.1. The Influence of Individual Participation Topic Status on the Multi-Dimensional Public Opinion Polarization Process

_{1}= 0.3, d

_{2}= 0.55, μ = 0.25, β = 0.1, the opinion confidence C of individual i obeys N~(0.5, 0.2), mapping in the interval [0, 1]. In order to observe the evolution of multi-dimensional public opinions, the correlation of topics in different dimensions is set to be strongly negative, with the evolution time T = 50. In this paper, the evolution results of three-dimensional topics are taken as an example for analysis, and the conclusion can be extended to other multi-dimensional situations.

#### 4.1.1. The Influence of Individual Participation in Different Number of Topics on the Multi-Dimensional Public Opinion Polarization Process

#### 4.1.2. The Dynamic Influence of Opinion Leaders and Topic Correlation Coefficient on the Number of Topics that Individuals Participate in

#### 4.2. The Influence of Individual Opinion Confidence and Interaction Times on the Multi-Dimensional Public Opinion Polarization Process

#### 4.2.1. The Influence of Individual Viewpoint Confidence on the Multi-Dimensional Public Opinion Polarization Process

#### 4.2.2. The Influence of Individual Interaction Times on the Multi-Dimensional Public Opinion Polarization Process

#### 4.3. The Influence of Topic Correlation Coefficient on the Multi-Dimensional Public Opinion Polarization Process

#### 4.3.1. The Influence of Topic Correlation on the Multi-Dimensional Public Opinion Polarization Process

#### 4.3.2. The Influence of Topic Correlation on the Multi-Dimensional Public Opinion Polarization Process

#### 4.4. The Influence of External Intervention Information on the the Multi-Dimensional Public Opinion Polarization Process

#### 4.4.1. The Influence of External Intervention Information on the Topic Derivation Process

#### 4.4.2. The Influence of External Intervention Information on the Multi-Dimensional Multi-Stage Public Opinion Polarization Process

_{1}= 0.5 of the first dimensional topic at time between 0 and 50, and f

_{2}and f

_{3}at time between 50 and 100 are set as −0.8, −0.6, −0.4, −0.2, 0, 0.2, 0.4, 0.6 and 0.8, respectively, so as to discuss the changes of multi-dimensional public opinion polarization process when the external information of topic 2 and topic 3 at time between 50 and 100 is involved simultaneously. The setting of other parameters is the same as above, and the result is shown in Figure 20.

_{2}and f

_{3}, the attitude polarizability of topic 1 decreased sharply, while that of topic 2 and 3 increased accordingly. This indicates that the intervention of external information in different dimensions at different times will further form the multi-dimensional and multi-stage polarization of public opinion, and the more relevant topics and information intensity released by the information means that extent of public opinion inversion is greater. Therefore, in public opinion control, relevant departments should release authoritative information in a timely fashion about hot events, guide the public opinion to a certain correct dimension, and avoid the continuous impact caused by the event.

#### 4.4.3. The Combined Analysis of External Intervention Information and Topic Correlation

_{1}is set to 0.5. At the time moments between 50 and 100, the external information intensity f

_{3}is set to 0.2, 0.4, 0.6 and 0.8, respectively, to observe the change of the polarizability of topic attitude in each dimension. In order to simplify the simulation process, only the situation when external positive information involved is analyzed here, and the conclusion can be extended to other cases. The results are shown in Figure 21.

## 5. Empirical Analysis

#### 5.1. Selection of Empirical Cases and Data Acquisition

#### 5.2. Data Processing

#### 5.3. Analysis of Results

_{1}= 0.2 (indicating the intensity of external information related to Tencent) was set in the simulation. f

_{2}= 0.5 (indicating the intensity of external information related to Laoganma); f

_{3}= 0.1 (represents external information relevant to Nanshan District Court). At the same time, the correlation of topics in three dimensions is set as follows: the topic of “Tencent” and “Laoganma” shows strongly negative correlation; the topic of “Laoganma” and “Nanshan District Court” shows strongly negative correlation; the topic of “Tencent” and “Nanshan District Court” shows moderately positive correlation. Other parameters are set as follows: the individual point confidence C is subject to N ~ (0.5, 0.2) and mapped to [0, 1], indicating that most individuals’ point confidence is general. d

_{1}= 0.15, d

_{2}= 1.15, μ = 0.35, β = 0.15; Interaction time T = 20; the result is shown in Figure 25.

## 6. Conclusions

- When there is a negative correlation among multi-dimensional topics, as the opinion of participants from different dimensions is gradually the same, the conflict between multi-dimensional topics will weaken the overall polarization effect of public opinion, while when there is a positive correlation between multi-dimensional topics, the polarization effect of public opinion will be correspondingly enhanced.
- When there is a negative correlation between multi-dimensional topics, with the increase of opinion confidence of an individual, the interaction between topics of different dimensions will weaken accordingly, thus enhancing the effect of public opinion polarization.
- When multi-dimensional topics are positively correlated, the participation of a certain proportion of opinion leaders can promote more individuals to participate in the discussion of multi-dimensional topics. However, when multi-dimensional topics are negatively correlated, the interaction between different dimensional topics will cause individuals to give up their support for a certain dimensional topic, thus reducing their participation in multi-dimensional topics.
- The intervention of external intervention information in different dimensions at different times will further form the multi-dimensional and multi-stage public opinion polarization phenomenon; however, the influence of external intervention information on multi-dimensional topics is constrained by the topic correlation coefficient, i.e., when multi-dimensional topics are negatively correlated, the intervention of external intervention information has a stronger influence on the multi-dimensional public opinion polarization process.

- Although this paper considers the interaction between topics in different dimensions and defines the topic correlation coefficient to describe it, it does not give a specific calculation method, so it is necessary to artificially determine the correlation coefficient between topics in different dimensions. Therefore, in follow-up research, big data and AI technology can be used to comprehensively analyze various factors among topics of different dimensions and calculate the correlation coefficient between topics.
- As the spread of social hot events is usually a dynamic process, individuals participating in the discussion of events in the network will enter and exit, so it is necessary to consider the increase and withdrawal mechanism of nodes in the network and study the phenomenon of multi-dimensional public opinion polarization in the dynamic network.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**The influence of opinion leaders on the number of topics that individuals participate in under different topic correlation coefficients.

**Figure 7.**The influence of topic correlation coefficient on the number of topics that individuals participate in.

**Figure 8.**Histogram of group attitude distribution under individual view confidence with different distributions.

**Figure 9.**Polarizability curves of group attitude under individual view confidence with different distributions.

**Figure 11.**The relationship of individual viewpoint confidence, individual interaction times and attitude polarizability.

**Figure 15.**Attitude polarizability when the topic correlation coefficients are randomly distributed.

**Figure 16.**Histogram of group attitude distribution under different external information intensity at different moments.

**Figure 17.**The polarizability curve of group attitude under different external information intensity at different time.

**Figure 18.**Histogram of group attitude distribution at different moments under different information intensity.

**Figure 19.**The polarizability curve of group attitude at different time under different information intensity.

**Figure 20.**The attitude polarizability of external information intervention in topic 2 and topic 3 at different moments.

**Figure 21.**The relationship between external information intensity, topic correlation coefficient and attitude polarizability.

**Figure 26.**The distribution chart of public opinion proposed by the literature [25].

$C\left(i\right)$ | opinion confidence of individual i |

d_{1} | assimilation effect zone distance |

d_{2} | repulsion effect zone distance |

μ | assimilation parameter |

β | repulsion parameter |

ρ_{mn} | relevant parameter between the mth dimensional topic and the nth dimensional topic |

${f}_{m}$ | external information intensity of the mth dimensional topic |

${x}_{n}\left(i\right)$ | the attitude value of individual i to the nth dimensional topic |

${\dot{x}}_{n}\left(i\right)$ | attitude value presented by individual i after the change in support for the nth dimensional topic |

${\ddot{x}}_{n}\left(i\right)$ | attitude value of individual i after the interaction with individual j |

${S}_{n}\left(i\right)$ | Individual’s support degree of the nth dimensional topic |

${e}_{n}^{m}$ | the impact of the mth dimensional topic on the nth dimensional topic |

${E}_{n}^{m}$ | the intensity of the impact of the mth dimensional topic on the nth dimensional topic |

${F}_{n}^{m}$ | the intensity of the impact of external intervention information of the mth dimensional topic on the nth dimensional topic |

Topic Correlation Coefficient ρ_{mn} | The Degree to Which the mth Topic Is Related to the nth Topic |
---|---|

ρ_{mn} ∈ [−1, −0.8) | Extremely strong negative correlation |

ρ_{mn} ∈ [−0.8, −0.6) | Strong negative correlation |

ρ_{mn} ∈ [−0.6, −0.4) | Medium negative correlation |

ρ_{mn} ∈ [−0.4, −0.2) | Weak negative correlation |

ρ_{mn} ∈ [−0.2, 0) | Extremely weak negative correlation |

ρ_{mn} = 0 | Independent |

ρ_{mn} ∈ (0,0.2] | Extremely weak positive correlation |

ρ_{mn} ∈ (0.2,0.4] | Weak positive correlation |

ρ_{mn} ∈ (0.4,0.6] | Medium positive correlation |

ρ_{mn} ∈ (0.6,0.8] | Strong positive correlation |

ρ_{mn} ∈ (0.8,1] | Extremely strong positive correlation |

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**MDPI and ACS Style**

Chen, T.; Wang, Y.; Yang, J.; Cong, G.
Modeling Multidimensional Public Opinion Polarization Process under the Context of Derived Topics. *Int. J. Environ. Res. Public Health* **2021**, *18*, 472.
https://doi.org/10.3390/ijerph18020472

**AMA Style**

Chen T, Wang Y, Yang J, Cong G.
Modeling Multidimensional Public Opinion Polarization Process under the Context of Derived Topics. *International Journal of Environmental Research and Public Health*. 2021; 18(2):472.
https://doi.org/10.3390/ijerph18020472

**Chicago/Turabian Style**

Chen, Tinggui, Yulong Wang, Jianjun Yang, and Guodong Cong.
2021. "Modeling Multidimensional Public Opinion Polarization Process under the Context of Derived Topics" *International Journal of Environmental Research and Public Health* 18, no. 2: 472.
https://doi.org/10.3390/ijerph18020472