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Abstract

Based on dynamic group decision theory of herd mentality, this study analyzed pedestrian violation mechanism and focused on the interaction views of pedestrian violation under the influence of herd mentality. For a typical signalized intersection in Yangzhou of China, a dynamic group decision-making model of pedestrians’ illegal crossing is established with opinion dynamics theory and scale-free network. Opinion leaders were considered and introduced in this model to capture the limitations of individual homogenization. Then, MATLAB was used to simulate and present the dynamic evolution process of decision makers. Results suggested that under the general conditions, the group decision results are closely related to the initial degree of knowledge, and once a few people lead the violation, there would be a greater probability of an illegal group crossing in the intersection. More importantly, the results gave a clear dynamic evolution process of the viewpoint and provided reference for similar research and a good guide for the management of violation crossing.

Keywords

Traffic safety dynamic group decision-making MATLAB simulation conformity violation opinion leader

Introduction

Pedestrians running a red light in a group are common in the urban traffic of most countries, which is usually caused by the herd mentality. This violation behavior always troubles traffic managers because it may cause the serious loss of property and casualties. Actually, some pedestrians do not want to run a red light. They often deviate from their original choices to make decisions that are consistent with group behavior preferences, due to interactions between pedestrians’ behavior decisions.¹ This behavior can be explained by the theory of dynamic group decision (GDM) in management science.

GDM was first proposed by Black in 1948, but the process, rules, and performance have been studied for more than 200 years. It is an important research topic of management science. As a broad form of decision-making, its theories and methods are very important and widely used in political, economic, cultural, and military management activities. Depending on whether the decision state changes, the GDM can be divided into static group decision and GDM. In reality, many decision-making problems usually have dynamic characteristics, so dynamic group decision-making is more valuable in practical problems. For analyzing the dynamic behavior of pedestrians, the GDM theory is applied in this study as well.

In this study, all pedestrians who reach the intersection during a red light will form a decision-making group, where each individual is a decision maker whose behavior is tentative, and as the behavior of others influences their own behavior, everyone’s plans are dynamically adjusted until the final decision is made. A novel method is proposed to study the violation behavior by introducing GDM theory. This method demonstrates the dynamic evolution process of individual decision-making and is of great significance for studying the characteristics and rules of violation, improving effective management and traffic safety.

Literature review

Group decision-making

Concerning the GDM, the existing research is mainly composed of two categories. One is based on economics and operations research to study algorithms and models with mathematical methods. Chu² used the social network analysis (SNA) method to establish the social characteristics of the experts, where fuzzy preference relations were utilized to address the GDM problem. Bai et al.³ proposed a new method of dynamic fuzzy multi-attribute group decision-making using dynamic fuzzy evaluation matrix and got the best supplier with the ordered entropy weights. Yao et al.⁴ presented a fault diagnosis method based on Bayesian network and GDM. Haghani and Sarvi⁵ applied the nested logit model to study the decision-making process of people, particularly the crowd exit-choice behavior, during emergency evacuation.

The other focuses on social psychology and organizational behavior are to observe and analyze the interaction between groups through experimental methods. A large number of experimental studies found that the group interaction process will be affected by many factors, such as different environment,^6,7 leadership style,⁸ the range of the preference spectrum,⁹ uncertainty preferences,¹⁰ group decision rules, and other factors.¹¹

Pedestrians’ illegal crossing based on herd mentality

For a long period of time, the research on pedestrians’ illegal road crossing has been focused on road facilities (the size of the intersection, vehicle position, time gap, etc.)^12–14 and pedestrian characteristics (age, sex, character, etc.).^15,16 In recent years, more and more scholars have adopted different methods to study the phenomenon of illegal crossing based on herd mentality.

Li et al.¹⁷ built a psychological threshold model about the behavior recognition process based on herd mentality and discussed the influence of different connections between groups on conformity behavior. Wu et al.¹⁸ constructed the evolutionary game model of pedestrians’ crossing behavior under the influence of herd mentality. Karamouzas and Overmars¹⁹ presented a simulation method for small-group walking behavior and described how group members interact with each other. He et al.²⁰ put forward a dynamic exchange grouping model and analyzed the influence of peer group on pedestrian flow dynamics using a simulation experiment. Yang et al.²¹ proposed a group decision conformity behavior evolution model based on cellular automata.

In addition, many scholars have contributed to the study of dynamic group decision-making and pedestrians’ illegal road crossing. It is visible that the elements in the GDM theory can fit well with the needs of the research on illegal group road-crossing behavior. However, so far, there have been few scholars using group decision-making theory to study on the interaction between individuals in pedestrian violation. At the same time, in some decision-making models mentioned above, some studies, in order to simplify the modeling, ignored the differences among individuals and homogenized the decision-making individuals, which reduced the accuracy of decision-making and the correspondence with reality.

This research aimed at constructing the model of dynamic group decision-making on pedestrian traffic violation and exploring the mechanism of this behavior based on herd mentality, and then, introducing opinion leader and revealing the evolution process of individual decision. Results can explore the pedestrian herd crossing violation of law in typical intersection, provide the basis for the development of traffic management and intervention measures, and can be useful and significant ideas and reference for the simulation of other intersections.

Framework

Analysis on the behavior mechanism of pedestrians’ illegal crossing

The intersection of Jiangyang West Road and Hanjiang Mid Road in Yangzhou, China was chosen as the survey site. Both the roads are urban main roads, and the nearby land is mainly for recreation and accommodation which attracts large traffic flow. It was observed that there was a more obvious phenomenon of pedestrians’ illegal crossing in this intersection than others. This study interpreted the decision-making process of pedestrians’ illegal crossing behavior in group, as shown in Figure 1.

Figure 1.

Behavior mechanism of pedestrians’ illegal crossing based on herd mentality.

All pedestrians arriving at this intersection during a red light form a decision-making system. Each of them has their own initial decision plan whether to go across the street illegally or not based on the factors such as traffic situation, traffic lights, whether they are in a hurry or not, and so on. However, each pedestrian will be affected by others’ decisions to adjust the original plan. This is the process for the pedestrians to learn information from others, and this process will continue until the final decision plan is formed.

The GDM concept model of the crowd violation

In the GDM model, the opinion dynamics and knowledge learning theory are combined to examine the decision-making process of pedestrian crossing in terms of microscopic view.

The dynamics mainly studies the process of individual opinion change, and its three elements are the expression of opinion, the mechanism of local communication, and the environment in which the evolution is located.²² The expression of opinion is usually abstracted as variables or interval, such as postgraduate/employment/abroad, with 1, 2, 3; what’s more, the interval [0, 1] is used to describe the degree of perceived danger from “very dangerous” to “very safe.” The mechanism of local communication is a criterion for interaction between individuals, guides the exchange of information, and is conducive to a clear presentation of the dynamic process of decision-making. The environment in which evolution is located is the medium of dynamic interaction between group views. Introducing the theory of opinion dynamics into the dynamic group decision-making model helps to show the dynamic evolution of pedestrians’ opinions and make up for the shortcomings of traditional group decision-making models, which cannot show the dynamic adjustment process of individual views.

Different subjects have different definitions about the meaning of knowledge. In this study, knowledge learning is defined as the utility judgment of the cross street information. Is it a violation of the traffic rules now? Do the others cross the street? Is it dangerous to go now? Am I in a hurry to do something important? The behavior of others has a great influence on the process of knowledge learning because of the psychology of the herd.

On the basis of previous studies, this article constructs a GDM concept model of the crowd violation, which is demonstrated in Figure 2. The concept model consists of three elements, which are the knowledge generation model, the interactive object generation model, and the knowledge transfer model. The knowledge generation model can determine the initial value of each individual’s view. Interactive object generation model is used to select objects that interact with each other. Not everyone is going to interact with other people. The premise is that the difference between the two views is within a certain threshold. Just as a man who hates carrots, no matter how many other people choose to eat carrots, he will not make a decision to eat carrots. Only when someone does not repel carrots, the choice of others may affect him. The model of knowledge transfer is to form a new distribution of group views after a round of interaction between individuals. It can make group consensus judgment and see whether it has reached the convergence of group opinions. Based on that, it decides whether the outcome of the final group decision is to be output or the next round of interaction between individuals, in turn.

Figure 2.

The dynamic group decision concept model of the crowd violation.

Modeling

In the investigation of the selected intersection, it is found that the phenomenon of pedestrians’ illegal crossings based on herd mentality is more obvious, and the number of people who arrived in a red light period is about 20 people, and thus the initial number of models set is 20. In the basic setting model, a scale-free network as an interactive media is used to build a knowledge generation model and formulated as an interactive object generation model with deffuant boundary trust theory, and the knowledge transfer threshold and consistency criteria are set in the knowledge transfer model. This study focused on the conditions which easily lead to the conformity violation crossing behavior, and so a lot of simulations on whether to introduce opinion leaders and the different numbers of opinion leaders have been done. At last, a representative comparison of the two simulations’ outcomes is presented.

Knowledge generation model

The setting of individual initial views

The initial number of individuals to interact is 20, each individual is represented by $x_{i} (i = 1, 2, . . ., 20)$ . At time $t$ , the view of the member $i$ is expressed as $x_{i} (t)$ . Its value can be discrete or an interval, but few individuals in the group can guarantee the absoluteness of the viewpoint, and the form of interval can represent the degree of cognition better and more reasonable, and so in this article, the value of $x_{i} (t)$ is set as interval [0, 1], where 0 means he felt he had to abide by the traffic rules and 1 means he thought he had to run the red light and cross the street illegally. In the contrast simulation, the $x_{i} (t)$ of the opinion leader is set to 1, and the others are random digits.

Group preference setting

When the model is established, it is particularly important to set the rules of preference adjustment. There are differences in personality and knowledge between each individual, which will lead to distinct levels of interaction. Therefore, this study used the scale-free network as the carrier of evolution. Different from the general rules of the network, it will not only evolve over time but also can set the status of different degree of individual influence. The main idea of this network model is to first set a connected network with $m_{0}$ initial nodes, and then, as time progresses, a new node is added and connected to other nodes in each step, until the nodes are generated sufficiently. The process of node connection following the node degree optimization rule, the greater the node degree, the greater the probability of being selected to connect becomes, will result in the greater influence in the network.

The initial value of node degree is shown in Figure 3, and according to the scale-free network principle, MATLAB and Pajek software were used to build the scale-free network shown in Figure 4. The network initially had 3 individuals, but the number increased with time and finally reached 20.

Figure 3.

Initial node degree value.

Figure 4.

Scale-free network of $n = 20$ and $m_{0} = 3$ .

Interactive object generation model

Deffuant model is one of the most widely used opinion dynamics models. It follows the principle of “border trust,” that is, to set up a trust threshold (trust boundary) in advance. When two individuals interact and if the opinion difference between the two persons exceeds the threshold, the two opinions do not change. If the difference is within the threshold range, there will be an opinion interaction. This model can be used to determine the generation of interactive objects.

It is shown as follows: two random individuals $i$ and $j$ , at time $t$ , have opinions $x_{i} (t)$ and $x_{j} (t)$ , respectively, and the interactive threshold is $ε$ , and if $| x_{i} (t) - x_{j} (t) | < ε$ , then, at the time $t + 1$ , the opinions of $i$ and $j$ are, respectively

x_{i} (t + 1) = x_{i} (t) + μ [x_{j} (t) - x_{i} (t)]

(1)

x_{j} (t + 1) = x_{j} (t) + μ [x_{i} (t) - x_{j} (t)]

(2)

where $μ$ is a convergent parameter usually ranging from 0 to 0.5.

Knowledge transfer model

Setting knowledge transfer threshold

In the previous section, equations (1) and (2) are used to calculate the updated opinion value, where parameter $μ$ is convergent parameter, determining the distance that an interactive individual moves to the other’s opinion. The theoretical research shows that $μ$ does not affect the final convergent value and only has an impact on the speed of convergence. The greater value will lead to the faster speed, and so according to experience, $μ = 0.5$ . The existing research assumes that the threshold of all the individuals in the group is equal. Although the difficulty of the simulation is reduced, the difference between individuals is ignored. The differences between the members in the decision-making group include background of their knowledge, belief, character, and so on, and so the threshold of the interaction should be different. In this study, pedestrians who arrived at the intersection were originally random, and the obvious difference between individuals was the opinion leader.

Therefore, we set different number of opinion leaders (pedestrians who take the lead in crossing the road illegally) and give these individuals greater interaction thresholds, that is, no matter what other people’s views are, these leaders will not change their own decisions, and the other individuals’ interaction threshold are evaluated at random values below 0.5.

The setting of decision consistency judgment condition

Our study set 20 decision makers in a decision-making group. The opinion of decision maker i at time t is $x_{i} (t) \in (0, 1)$ , $i = 0, 1, 2, . . ., 20$ . The opinion of all decision makers is $x_{i} (t) = {x_{1} (t), x_{2} (t), . . ., x_{20} (t)}$ , and the average view of the group is $c (t)$ , then, the following formula can be used to find the consistency value of this decision

y (t) = \sum_{i = 1}^{20} \frac{| x_{i} (t) - c (t) |}{c (t)}

(3)

where $y (t)$ reacts to the degree of differences in group decision results. The views of group members would be concentrated as the value of $y (t)$ decreases, namely, the decision consistency is going to be much better with the decrease of $y (t)$ . Besides, the consistency threshold $ξ_{1}$ is set up. When $y (t) < ξ_{1}$ , the decision made in the group has reached consensus. When $y (t) > ξ_{1}$ , the members of the group will further interact with each other and constantly update their views. Due to a serious violation of the road crossing phenomenon in the selected investigation, the value of $ξ_{1}$ was tested and adjusted in simulation for the more obvious convergence results.

Results and discussion

Simulation of initial setting model

In this study, MATLAB software and Pajek software are used to simulate and visualize the graphics. The process is as follows:

Set the total number of individuals in the network $N = 20$ ;

Randomly select two individuals i and j, according to formula (1) and (2), to update their views;

Adjust consistency threshold $ξ_{1}$ and obtain more obvious results of opinion convergence.

The simulation results are depicted in Figure 5.

Figure 5.

Simulation results with initial values: (a) group initial view distribution map, (b) group final view distribution map, and (c) dynamic evolutionary of group view.

A total of 20 individual initial points of view were generated randomly by MATLAB, with a mean value of 0.445. After 70 iterations, the final point of view converges, the value is about 0.45, and Figure 5(c) shows the dynamic evolution of the viewpoint. It can be inferred that the final view of the group has a certain connection with the mean value of the initial point of view. In real life, the probability of final decision-making about whether or not to cross the road illegally depends on the average level of traffic law–abiding consciousness of the group. This is in conformity with the reality: increasing the awareness of law-abiding is the most basic and vital countermeasure to reduce traffic accidents.

Simulation with the introduction of opinion leaders

From the microcosmic perspective of herd behavior, the beginning is triggered by several leaders, and then, a group would follow these leaders. The leader’s point of view is usually clear, which has a great effect on the process of decision-making. In the simulation, these individuals are embodied by setting key parameters. The opinion leader node degree value is set to a larger value so that it can play a key guiding role of public opinion; the interactive threshold is also set to a larger value, indicating that the pedestrian is more likely to interact with others; convergence parameter is set to a smaller value, which means that the pedestrian’s will is too strong to change his opinion. The evolution criteria are adjusted as follows:

The general individual opinion is evenly distributed on [0, 1], while the initial opinion value of the opinion leader is 1, the interaction threshold of opinion leader $ε_{j} = 0.8$ , and the convergent parameter $μ = 0.1$ .

Randomly select two individuals $i$ and $j$ , according to formula (1) and (2), to update their views;

Adjust consistency threshold $ξ_{1}$ and obtain more obvious results of opinion convergence.

At the same time, different number of leaders is set up to explore the influence it has on the final point of view and the speed of convergence. The simulation results are shown in Figure 6.

Figure 6.

Simulation results with opinion leaders: (a) group initial view distribution with opinion leaders, (b) group final view distribution with opinion leaders, and (c) dynamic evolution of group views with opinion leaders.

The red points in the figure represent opinion leaders. Their initial values are all above 0.9. In the process of simulation, it is found that when the number of opinion leaders is three, there is a more obvious convergence and faster convergence rate, as shown in Figure 6. The mean initial point of view is 0.489, and the opinion converges near 0.674 through the interaction of nearly 50 steps. Even if the mean value of the initial group is less than 0.5, under the action of three leaders, the final opinion value is concentrated at about 0.674. It means at that intersection, only a few illegal crossing leaders will affect the other pedestrians with wait-and-see attitude to a great extent, which would lead to the group violations.

Conclusion

In this article, a dynamic group decision-making theory is applied to study the phenomenon of pedestrians’ illegal crossing based on herd mentality. The typical signalized intersection in the city of Yangzhou, China was analyzed in the actual situation. The main conclusions are as follows:

The internal mechanism of pedestrians’ illegal crossing was analyzed based on the influence of herd mentality, and the GDM concept model of the crowd violation is constructed with the previous research.

The specific traffic problems were studied in combination with many fields of knowledge, such as herd psychology, opinion dynamics, knowledge learning, and so on. The scale-free network was used as the evolution medium, and the deffuant boundary trust model is the judging standard for the interactive objects. The knowledge transfer threshold and consistency criterion of the model were set up so that they can better explain the phenomenon of pedestrians’ illegal crossing behavior.

In the proposed model, the opinion leader was introduced, which breaks through the limitation of the homogeneity of the individual. Using MATLAB tools, the evolution of the individual views was dynamically rendered, and results showed that in the absence of the role of opinion leaders, master degree of group decision results largely depended on the initial knowledge of the group. What’s more, in the intersection of Jiangyang West Road and Hanjiang Mid Road in Yangzhou China, during a red light, if the number of pedestrians is 20 and among them, 3 lead to cross the road illegally, a large possibility of group violations can be caused.

To reduce the violation behavior, two major countermeasures can be taken, which are as follows:

Reduce the benefits of illegal behavior; pay attention to risk awareness education; carry out lectures on traffic knowledge in schools; and use modern media to increase traffic accident education and traffic law propaganda.

Increase external punishment, and equip the traffic police and recruited volunteers at the intersection to assist the management. At the same time, the violations shall be exposed and fined. Use a variety of punishment education means, such as increasing the amount of fine, recording the violation record for personal credit system reference, and so on. Of course, all kinds of punishment measures should combine the actual situation of the local.

The research ideas of this article are suitable for the general intersection, and the research results are beneficial to take pertinent measures to counter this group violation phenomenon. Future studies can further understand the difference between people’s knowledge level and take the details of each individual’s traffic concept, time, and safety benefits into consideration in the model so that they can better simulate the reality.

Footnotes

Handling Editor: Martin Baumann

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The study is supported by the National Key Research and Development Program: key projects of international scientific and technological innovation cooperation between governments (grant no. 2016YFE0108000); the Natural Science Foundation of Jiangsu Province, China (grant no. BK20171426); the Natural Science Foundation of Zhejiang Province, China (grant no. LY17E080013); project of the Jiangsu association of higher education (grant no. 16ZD010); and the Opening Fund of Key Laboratory of Urban ITS Technology Optimization; and Integration Ministry of Public Security, China (grant no. 2017KFKT03) and the Project of Ministry of Housing and Urban-Rural Development of China (grant no. 2014-K1-016).

ORCID iD

Zhuping Zhou

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Pedestrians’ violation behavior model based on group decision-making

Abstract

Keywords

Introduction

Literature review

Group decision-making

Pedestrians’ illegal crossing based on herd mentality

Framework

Analysis on the behavior mechanism of pedestrians’ illegal crossing

The GDM concept model of the crowd violation

Modeling

Knowledge generation model

The setting of individual initial views

Group preference setting

Interactive object generation model

Knowledge transfer model

Setting knowledge transfer threshold

The setting of decision consistency judgment condition

Results and discussion

Simulation of initial setting model

Simulation with the introduction of opinion leaders

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References