Public Opinion Evolution Analysis Model Integrating Network Game Theory and Opinion Dynamics, Its Establishment Method and Application

Abstract

The present invention discloses a public opinion evolution analysis model that integrates network game theory and opinion dynamics, as well as its establishment method and application, belonging to the field of social network analysis technology. The public opinion evolution analysis model in the present invention combines social network game theory and opinion dynamics theory, and constructs a mathematical model of public opinion evolution (POEM) based on relevant theories in social science while considering more comprehensive factors. It realizes the scientific simulation of the psychological activities of individuals in the process of public opinion dissemination, breaking through the two major limitations of single behavior statistics in traditional network game models and the lack of behavioral characterization in opinion dynamics models; and uses uncertainty mathematical theory to characterize the psychological trends and decision-making behaviors of social individuals in the process of public opinion evolution, more accurately depicting the impact of individual dissemination behavior on the evolution of social public opinion.

Description

Technical Field

[0001] The present invention relates to the technical field of social network analysis, and in particular to a public opinion evolution analysis model integrating network game theory and opinion dynamics, as well as an establishment method and application thereof. Background Art

[0002] Public opinion management has always been a crucial issue in public administration. Analyzing public opinion evolution trends based on social networks and mathematical models has become a current research hotspot. This approach provides crucial decision-making support for government, businesses, and other organizations involved in public opinion management, and is therefore of great significance. In sociology, a social network refers to a collection of social actors and their relationships. Specifically, a social network consists of multiple nodes (social actors) and the connections between them (the relationships between actors). As a mature analytical perspective, social network analysis effectively captures the relationships between members of society. With the rise of the internet, especially mobile social media, the ways individuals interact have become more diverse, and the influence of social media influencers on individual attitudes has become more complex, leading to the diverse forms of social networks. In public opinion management research, social networks are often used to depict the information flows between social actors and form the foundation for constructing models for public opinion evolution and management. With the development of the internet and the increasing education level of the public, unstable factors within social networks are increasing, making public opinion management increasingly difficult.

[0003] There are two typical schools of thought in modeling the evolution of public opinion based on social networks: the evolutionary analysis of group communication behavior based on network games and the evolutionary analysis of group opinion tendencies based on opinion dynamics. Network game theory, a typical theory for multi-player game scenarios, has been widely applied to games between researchers and corporate groups. In network game theory, players typically exist as nodes and engage in games based on relationships represented by network edges. The resulting gains influence their behavioral decisions, and the equilibrium state of the game evolution is analyzed by counting the proportions of individual actions. Opinion dynamics models are primarily conducted in directed social networks, often using quantitative opinion tendencies to represent individual and group opinion tendencies. By dynamically updating individual opinion tendencies through network structure and different opinion updating rules, the evolutionary trends of group opinion are simulated. It is not difficult to find that public opinion evolution analysis based on network game theory primarily studies the equilibrium state of public opinion evolution by counting the proportion of individuals adopting certain behaviors, while opinion dynamics theory primarily analyzes the trends of public opinion evolution by observing numerically measured group opinion attitudes. While both theories can support the analysis of public opinion evolution under certain conditions, they cannot directly depict the relationship between public opinion attitudes and individual communication behaviors, and they can only reflect the trend of public opinion evolution from a single perspective. Furthermore, in the field of communication research, various scholars have proposed a wealth of public opinion management strategies. However, the effectiveness of these strategies often needs to be explored in real-world public opinion management operations. Therefore, modeling public opinion management strategies and exploring their effectiveness through simulation experiments has become a pressing issue in the field of public opinion management. Summary of the Invention

[0004] In response to the above-mentioned problems, the present invention aims to provide a public opinion evolution analysis model that integrates network game and opinion dynamics, as well as its establishment method and application. It uses uncertainty mathematical theory to characterize the psychological trends and decision-making behaviors of social individuals in the process of public opinion evolution, and more accurately characterizes the impact of individual communication behavior on the evolution of social public opinion.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] The method for establishing a public opinion evolution analysis model that integrates network gaming and opinion dynamics includes the following steps:

[0007] S1: Construct a model of individual influence differences in the process of public opinion dissemination;

[0008] S2: Based on the individual influence difference model, a decision-making model of individual bilateral behavior game based on social network game is constructed to determine individual behavior strategies, including expressing opinions and keeping silent;

[0009] S3: Based on the individual behavior strategy selection results in step S2, when the individual chooses to express his or her opinion on the reachable neighbors, an improved opinion dynamics model based on individual behavior, that is, a public opinion evolution analysis model, is constructed to determine the individual's opinion value.

[0010] Furthermore, the individual influence difference model described in step S1 is expressed as

[0011]

[0012] Where p i Represents any node v i The influence value, PR i Represents node v i PageRank value, PR j Represents node v j PageRank value, v j For individual v i Neighbors, V={v1,v2,…,v n} represents the set of nodes in the social network, and n represents the number of nodes.

[0013] Furthermore, the specific operation of step S2 includes the following steps:

[0014] S201: Construct a problem model of individual behavior game, specifically

[0015] Γ={G,{δ i (t)|v i ∈V},{π ij (t)|v i ∈V,v j ∈N i},{o i (t)|v i ∈V}}

[0016] Where G = (V, E) represents a social network with n nodes and m edges, and E = {e1, e2, ..., e ι} represents the edge set in the social network; δ i (t) = [δ ij (t)] 1×|V| For individual v i The strategy vector at the evolution time t, δ ij (t)∈{S1,S2} represents individual v i At the evolution time t, for individual v j The strategies adopted, S1 and S2 represent the two strategic options of expressing opinions and keeping silent respectively; π ij (t) represents individual v i At the evolution time t, the neighbor individual vj The psychological benefits obtained from the game, N i Represents node v i The set of all neighbors of i (t) represents the node v i At the moment of evolution t, the opinion value is expressed in the interval [0,1], with max(o)=1, min(o)=0, and o i (t)→1 represents the individual's positive attitude towards public opinion, o i (t)→0 means that the individual has a negative attitude towards public opinion;

[0017] S202: Determine the payoffs of a bilateral game between individuals;

[0018] S203: Determine the update rule of individual benefits;

[0019] S204: Construct a decision-making model for individual bilateral games and determine individual behavioral strategies.

[0020] Furthermore, the benefits of the bilateral game between individuals in step S202 include benefits between homogeneous individuals and benefits between heterogeneous individuals. Homogeneous individuals include audience-audience and authority-authority, and heterogeneous individuals include audience-authority.

[0021] Furthermore, in step S203, individual v is used i The true satisfaction Π at the evolution time t i (t) represents the actual benefit of the individual at a certain evolutionary moment, then Π i (t) is expressed as

[0022]

[0023] Among them, γ∈(0,1) is the memory sensitivity coefficient, Indicates that at the time t of evolution, individual v i The interaction satisfaction obtained through the game with neighbors, Indicates that at the time t-1 of evolution, individual v i The interaction satisfaction obtained through the game with neighbors, and ò i (t)∈{-1,0,1} is a Boolean variable used to judge the external cognitive pressure on the individual, and m represents the impact of group cognitive pressure on individual satisfaction;

[0024] It represents the proportion of all external opinions received by an individual at time t that are similar to his or her own opinions. ξ∈[0.5,1] is the group pressure threshold, which is used to judge the impact of group pressure on individual satisfaction.

[0025] Furthermore, the bilateral game decision model described in step S204 is expressed as

[0026]

[0027] Where, Represents individual v i For reachable neighbors v j The subjective probability of selecting strategy S1, strategy S1 is "expressing opinions"; the subjective probability of individuals selecting strategy S2 is Strategy S2 is “remain silent”; the fuzzy evaluation vector of the individual on strategies S1 and S2 measured by Score1 and Score2 is W B =[w1,w2,w3] is the fuzzy weight vector considering the three factors of individual satisfaction, influence difference and individual opinion polarity. R represents the fuzzy relationship matrix of the individual for strategies S1 and S2.

[0028] in, x1=Π i (t-1); x2=p i -p j ; υ i (x i )=1-μ i (x i )i=s,p,po.

[0029] Furthermore, the specific operation of step S3 includes the following steps:

[0030] S301: Based on uncertainty theory, from the perspective of individual v i Determine the set of trusted neighbors among the neighbors who express their opinions in, Indicates direct access to node v i Neighbor set, N i Represents node v i The set of all neighbors of ;

[0031] S302: Combine individual v i Current views on individual v i The influence of neighbors who express opinions, determining the update rules of individual opinions, and constructing an improved opinion dynamics model based on individual behavior:

[0032] when When , the update rule of individual opinions is

[0033] Then at time t, individual vi The view value o i (t) is expressed as

[0034] in, Represents individual v i At the evolution time t, the opinion value after being affected by the outside world, α i (t) represents individual v i The sensitivity factor at the evolution time t, and

[0035] Represents individual v i The ratio of the number of credible neighbors to the number of neighbors who can influence their opinions at time t, Indicates that at time t, i The set of neighbors who express opinions, β i ∈[0,1] represents individual v i The change threshold of the sensitivity factor; Δo ji (t) represents individual v i With the former neighbor v j The difference in opinion values ​​at time t; ω ij represents the influence weight of neighbors’ opinions; φ i (t) represents the polarization increment when individual opinions become polarized, which is expressed as λ∈(0,max(o)) is the polarization coefficient;

[0036] when hour,

[0037] Furthermore, the present invention also includes a public opinion evolution analysis model established using the establishment method as described above.

[0038] Furthermore, the present invention also includes the application of the public opinion evolution analysis model as described above in formulating public opinion management strategies.

[0039] Furthermore, the public opinion management strategy includes information blocking, forced intervention and gradual guidance.

[0040] The beneficial effects of the present invention are:

[0041] 1. The present invention innovatively integrates the network game model with the opinion dynamics, and constructs a mathematical model based on relevant theories in social sciences while considering more comprehensive factors, thus realizing a scientific simulation of the psychological activities of individuals in the process of public opinion dissemination. Simulation experiments show that the public opinion evolution model proposed by the present invention is more scientific and reasonable in depicting the general laws of public opinion evolution. From the perspective of real public opinion management, the model can not only provide support for managers to monitor the trends of opinions and attitudes on social networks, but also support the dynamic observation of individual voice behavior trends. This effectively makes up for the shortcomings of the network game model and the opinion dynamics model, and provides a scientific method for the evolution, analysis and management of public opinion.

[0042] 2. Methodologically, the proposed model innovates by combining online game theory with complex network dynamics models, and also simulates psychological activity based on uncertain mathematical models. While providing a scientific and robust method for analyzing the evolution of public opinion, it further models and analyzes the effectiveness of public opinion management strategies. This approach possesses significant practical value and can provide theoretical insights for research in areas such as group decision-making and public administration. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Schematic diagram of the strategy combination relationship in the two cases of unidirectional edge connection and bidirectional edge connection in the present invention.

[0044] Figure 2 is the sensitivity factor α of individuals to external opinions at different initial moments in the simulation experiment of the present invention i (0) Impact on the evolution results. Simulation results diagram.

[0045] Figure 3 This is a simulation result diagram showing the influence of different polarization coefficients λ on the evolution results in the simulation experiment of the present invention.

[0046] Figure 4 This is a simulation result diagram of the influence of different approximate viewpoint judgment thresholds τ on the evolution results in the simulation experiment of the present invention.

[0047] Figure 5 This is a graph showing the experimental results comparing the effects of different public opinion management strategies in the simulation experiment of the present invention.

[0048] Figure 6 This is a comparative experimental result diagram of dynamic models from different viewpoints in the simulation experiment of the present invention. DETAILED DESCRIPTION

[0049] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0050] Example 1:

[0051] Example 1 provides a method for establishing a public opinion evolution analysis model that integrates network gaming and opinion dynamics, which specifically includes the following steps:

[0052] S1: Construct a model of individual influence differences in the process of public opinion dissemination;

[0053] In the present invention, a social network consisting of n nodes and m edges is defined as G = (V, E), where V = {v1, v2, ..., v n} represents the node set in the social network, n represents the number of nodes, E={e1,e2,…,e ioιa} represents the set of edges in the social network, and iota represents the number of edges. The nodes in the social network represent individuals in the process of public opinion dissemination. These individuals can be individuals or some official or unofficial "organizations". Their roles in the social network jointly promote the dissemination of public opinion. The edges in the social network represent the public opinion dissemination relationship between these individuals. This relationship can be unidirectional or bidirectional. Therefore, this invention adopts a directed network to represent the social network. Use N i Represents node v i The set of all neighbors of Indicates direct access to node v i The neighbor set of Indicates that all nodes v i The neighbor set pointed to. Set o i (t) represents the node v i The opinion value at the evolution time t. This opinion value represents the tendency of an individual to hold a certain opinion on a certain public opinion and is the core indicator of public opinion evolution and management. The [0,1] interval (i.e. max(o)=1, min(o)=0) is used to represent the range of individual opinion values, and o is set i (t)→1 represents the individual's positive attitude towards public opinion, o i (t)→0 means that the individual has a negative attitude towards public opinion.

[0054] In information sharing on social media, individuals with higher influence on social media will increase the prominence of information and users' recognition of information. Similarly, in the internal communication and community awareness of a specific organization, personal influence has a certain impact on information satisfaction. This shows that in the evolution of public opinion on social networks, there are clear differences in the roles played by individuals with different influences in the process of public opinion dissemination. This difference mainly depends on the status of the individual in information dissemination, that is, the position of the individual in the social network, which is closely related to the structure of the social network. In this invention, this role is quantitatively represented by the indicator of "influence", and the PageRank value of the node is used to measure the influence of the node. The PageRank algorithm is an iterative algorithm. After multiple rounds of iterations, the PageRank value of each node will tend to a stable value:

[0055]

[0056] Where PR i (z) represents node v i The PageRank value after the zth iteration, 1-q is the damping coefficient, |V| is the total number of nodes contained in the graph, which is the same as n; after obtaining the PageRank value of each node, the PageRank value of the node is normalized to obtain the PageRank value of any node v i The influence value p i for

[0057]

[0058] The influence of an individual is an important factor in conducting games and interacting with opinions. According to the authority effect or authority suggestion effect in social networks, people, under the influence of security psychology and recognition psychology, will have more trust in the opinions and attitudes of authorities, and the ideas of authorities can be spread more. In real social networks, the influence of high-influence individuals on neighboring individuals is usually higher than the influence of average-influence individuals on neighboring individuals. In the process of information dissemination and public opinion evolution, individuals can identify high-influence neighbors around them under normal conditions. Taking into account the differences in decision-making and cognition of individuals in social networks, different individuals can be divided into two roles: "authorities" and "audiences" according to the size of their influence. In reality, there is no very clear boundary between these two roles. For the sake of convenience, the present invention takes the top 10% of the influence value as the authorities, and the rest of the individuals are audiences.

[0059] S2: Based on the individual influence difference model, a decision-making model of individual bilateral behavior game based on social network game is constructed to determine individual behavior strategies, including expressing opinions and keeping silent;

[0060] Specifically, S201: Construct a problem model of individual behavior game;

[0061] The game of public opinion evolution is mainly used to simulate the behavior of individuals in the process of public opinion evolution. In this invention, the problem model Γ of the individual behavior game is constructed based on the binary network hybrid strategy, which is specifically expressed as:

[0062] Γ={G,{δ i (t)|v i ∈V},{π ij (t)|v i ∈V,v j ∈N i},{o i (t)|v i ∈V}}(3)

[0063] Normally, the person being shared with only needs to show concern and recognition to greatly stimulate the satisfaction of the sharer and thus inspire more sharing behaviors. The higher the satisfaction of the sharer, the better the actual effect of sharing. In fact, the spread of public opinion in social networks is driven by the behavior of individuals spreading their opinions, and this behavior is also accompanied by changes in individual emotions. At the same time, the emotions of individuals will also determine their behavior in spreading opinions. Therefore, in this invention, the measurement indicator "satisfaction" is defined and regarded as the benefits generated by gaming behavior. Satisfaction refers to the measure of the psychological benefits caused by different behavioral interactions during the gaming process between an individual and his neighbors. Let Π i (t) is individual v i Satisfaction at evolution time t.

[0064] Define δ i (t) = [δ ij (t)] 1×|V| For individual v i The strategy vector at the evolution time t, δ ij (t)∈{S1,S2} represents individual v i At the evolution time t, for individual v j The strategies adopted, S1 and S2 represent the two strategic options of expressing opinions and keeping silent. Let c(v i )={0,1},c(v i )=0 means individual v i For the audience, c(v i )=1 indicates that the individual is an authority. For the convenience of representation, the symbol It is used to indicate that at time t, c(v i ) Type individual v i Choose a strategy of expressing an opinion or keeping silent, π ij (t) represents individual v iAt the evolution time t, the neighbor individual v j The "psychological" benefits obtained from gambling.

[0065] Because the information connections between individuals in a social network are directed, not all individuals can effectively express their opinions to their neighbors. This means that when an individual chooses S1, since they can only receive information from their neighbors but cannot effectively disseminate their opinions to them, their expression of opinions will be "ineffective." Therefore, the present invention defines the following two judgment rules to address this characteristic:

[0066] (1) When any individual v i Choose a neighbor v j When expressing their views, if the two are connected by the middle v i Can point to v j , then v i v j The effective strategy is S1, otherwise v i v j The effective strategy is S2.

[0067] (2) When any individual v i Choose a neighbor v j When you remain silent, even if there is v i Point to v j The edge, v i v j The effective strategy is also S2.

[0068] In order to more intuitively illustrate the judgment rules of effective strategies, the present invention is Figure 1 Individual v i and its neighbors v j As an example, the strategy combination relationship under the two cases of one-way connection and two-way connection is shown. The solid line directed connection represents that the individual expresses his opinion to the neighbor when there is a one-way information transmission relationship with the neighbor, and the dotted line directed connection represents that the individual remains silent to the neighbor when there is a one-way information transmission relationship with the neighbor. Figure 1 middle, In this case, v i and its neighbors v j The effective strategy is S1.

[0069] S202: Determine the payoffs of a bilateral game between individuals;

[0070] According to the "uses and gratifications" theory of communication, from the perspective of the audience, people's motivation for participating in mass communication is that these contacts satisfy certain needs of individuals. Therefore, it can be considered that in the process of public opinion evolution, the psychological benefits between individuals mainly depend on whether their own opinions are recognized, that is, whether there are differences in opinions between individuals. The differences in opinions between individuals are divided into two situations: "similar opinions" and "contradictory opinions". i and its neighbors v j Taking the viewpoint value at the time t of evolution as an example, let the viewpoint approximation threshold be τ, then when o j (t)∈[o i (t)-τ,o i (t)+τ], the two views are considered similar. At the time, I thought the two views were contradictory.

[0071] The similarity and deviation of opinions between individuals are the direct factors affecting satisfaction. This invention will analyze them from the perspectives of the game between homogeneous individuals (no difference in individual influence) and the game between heterogeneous individuals (difference in individual influence). Under the premise that there is no difference in influence between individuals, the game between individuals can be regarded as a kind of interpersonal communication with relatively equal status. In interpersonal communication on the Internet, when an individual obtains similar opinions expressed by his neighbors, the individual's satisfaction will be positively improved, otherwise it will be negatively declined. Define a as the increment of positive improvement, and b as the increment of negative decline. When an individual's opinion is opposed and recognized by other individuals at the same time, the individual tends to pay more attention to the negative impact caused by opposition, and despise the positive impact caused by recognition. Therefore, the following assumptions are made in this invention:

[0072] Hypothesis 1: When any individual receives similar opinions from their neighbors, the absolute value of the positive increment in their satisfaction will be much smaller than the absolute value of the negative increment in their satisfaction when they receive contradictory opinions from their neighbors. This also means that the relationship between a and b satisfies |a|<<|b|, a>0, b<0.

[0073] In another scenario, when an individual expresses their opinions unilaterally to their neighbors, they may develop two perceptions: one is that their neighbors "acquiesce" to their opinions, which in turn positively increases their satisfaction; the other is that their opinions are "ignored" by their neighbors, which negatively decreases their satisfaction. However, the formation of these two perceptions is not fixed, depending on various factors such as individual personality and intentions. Their impact on individual satisfaction is relatively minor, so the absolute value of this impact is represented by c. In this paper, the two perceptions of an individual in this scenario are randomly represented.

[0074] Under conditions where there are large differences in influence between individuals, the scope of information dissemination by highly influential individuals in social networks will expand. In this case, the game between individuals with different levels of influence is formed in the environment of mass communication. In social networks in the social media era, the emergence of powerful and flexible digital communication tools has made mass communication information more permeable than ever before, but the corresponding impact of mass communication on individuals is less than that of interpersonal communication. Define that when an authority observes similar opinions expressed by the audience, the positive increment in satisfaction obtained by the authority is f, and when the authority observes contradictory opinions expressed by the audience, the negative increment in satisfaction obtained is g. Similarly, let the positive increment in satisfaction of the audience when they obtain similar opinions from the authority be d, and the negative increment in satisfaction when they obtain contradictory opinions from the authority be e. Based on the difference in influence between the two, the following assumptions can be made:

[0075] Hypothesis 2: Because of the status difference between the authority and the audience, the authority will underestimate the influence of the audience's views, while the audience will attach importance to the influence of the authority's views.

[0076] Based on this assumption, the relationship between different satisfaction increments is: |f|<|a|<|d|, |g|<|b|<|e|.

[0077] Let's further consider the case of one-way opinion expression between individuals with varying influence. In reality, this difference in influence creates a "gap" between the audience and the authority, making them less sensitive to the impact of their neighbors' "acquiescence" and "ignorance" on their satisfaction. Let h be the absolute value of the impact on the satisfaction of the individual expressing the opinion when opinions are expressed one-way between the authority and the audience. Then, h < c.

[0078] Based on the above analysis, under different bilateral game scenarios, the relationship between individual satisfaction and its impact is shown in Equation (4). The meanings of various parameters are shown in Table 1.

[0079]

[0080] Table 1 Meaning of parameters of satisfaction

[0081]

[0082] definition Represents individual v i At the evolution time t, the neighbor individual v j The strategy combination of the game includes the following AC cases for the benefits between homogeneous (audience-audience, authority-authority) individuals, and the following DF cases for the benefit matrix between heterogeneous individuals.

[0083] Scenario A:

[0084] In this case, the game payoff between any two individuals is as follows:

[0085]

[0086] For two individuals in a game, interactions with similar views will produce a "mutual recognition" effect, which will increase the satisfaction of both parties. Conversely, interactions with opposing views will produce a "mutual negation" effect, causing the satisfaction of both parties to decrease.

[0087] Case B:

[0088] by Taking as an example, the satisfaction increments of the two are shown in the following formula (6).

[0089]

[0090] In this case, v j Received v i The influence of the two people’s opinions on satisfaction is determined by the similarity between their opinions. i From the perspective of neighbor v j No response, which means v i You might think v j "Default" to his own point of view, or he may think that v j "Ignore" your own point of view. Take the product of rand{-1,1} and c as v i The impact of satisfaction is measured in a random manner, thereby measuring the two possible perceptions. The same applies to other combinations in situation B.

[0091] Case C:

[0092] Case C is simpler than cases A and B. In this case, both individuals and their neighbors remain silent and do not interact with each other. The increment of satisfaction between the two is π ij (t) and π ji (t) is shown in the following formula (7).

[0093] π ij (t)=π ji (t)=0(7)

[0094] Situation D:

[0095] Case D represents the situation where both the audience and the authority choose to express their opinions at the same time. For example, at this time individual v i For the authority, vj For the audience, the benefits of both are shown in the following formula (8).

[0096]

[0097] Case E:

[0098] In this case, the authority and the audience each choose different strategies to combine: For example, at this time individual v i For those who are authoritative in expressing their opinions, j v i If the neighbor of the audience remains silent, the game benefits of both parties are as shown in the following formula (9).

[0099]

[0100] In another case v i Next, individual v i To keep silent authority individuals, v j is the audience neighbor who expresses the opinion, then v i and v j The benefits can be expressed as above formula (8) and (9) respectively.

[0101] Case F:

[0102] At this point, both the authority and the audience remain silent, which is consistent with situation C. There is no interaction between the two parties. The satisfaction with the communication of opinions and the interaction effect of both parties are the same as formula (7).

[0103] S203: Determine the update rule of individual benefits;

[0104] The individual's benefit at an evolutionary moment is not just the sum of the benefits gained from the bilateral game with all neighbors, but also includes the "group pressure" formed by the neighbor group's opinions on the individual's cognition. That is, when the group opinion is considered to be contrary to the existing view, the group pressure will force the individual to modify the original view and succumb to the group opinion. To measure the impact of this group opinion, suppose that at time t, i The set of neighbors who express opinions is For v i Express opinions and v i A set of neighbors with similar opinions satisfies the following relationship: Therefore, among all the external opinions received by an individual at time t, the proportion of opinions similar to its own is Expressed as

[0105]

[0106] Similarly, the proportion of the opposite view is Define ξ∈[0.5,1] as the group pressure threshold to determine the impact of group pressure on individual satisfaction. i (t)∈{-1,0,1} is a Boolean variable used to judge the external cognitive pressure on the individual.

[0107]

[0108] At the time t of evolution, any individual v i The interaction satisfaction obtained through the game with neighbors Π i Inter (t) is expressed as

[0109]

[0110] Equation (12) shows that the satisfaction gained by an individual through opinion interaction is composed of the cumulative impact of all bilateral game satisfaction and the influence of external cognitive pressure. m represents the impact of group cognitive pressure on individual satisfaction. Compared with bilateral games between individuals, group cognitive pressure has a stronger impact, so |m|>>|e|, m>0.

[0111] In a typical complex network game model, the payoffs of players at the current evolutionary moment depend solely on their current game outcome and only affect their strategy choices at the next moment. However, in the context of public opinion evolution, individuals retain a certain "memory" of satisfaction, a "sensory" factor, which means that historical payoffs also influence their strategy choices. Therefore, the following basic assumptions can be proposed in this invention:

[0112] Hypothesis 3: The satisfaction of an individual at any moment in the evolutionary process consists of two parts: the interaction satisfaction at the current moment and the historical satisfaction, and the individual has a certain degree of forgetfulness about historical benefits.

[0113] The individual v i The true satisfaction Π at the evolution time t i (t) is defined as a time function as shown in the following formula (13). It should be noted that, in order to measure the impact of the evolution process, the present invention sets the real satisfaction of any individual at the initial moment Π i (0)=0, which has been ignored in formula (13).

[0114]

[0115] Among them, γ∈(0,1) is the memory sensitivity coefficient, which has the following property: as the evolution time t increases, individuals will pay more attention to their own recent benefits and ignore previous benefits. This also reflects the process of individuals forgetting the perceptual benefits during the evolution process. When γ→1, individuals The greater the proportion of an individual's past satisfaction in their current gains, the stronger their memory of past satisfaction. When γ→0, individuals prioritize recent gains over past gains. True satisfaction is the actual gain of any individual at a specific evolutionary moment. It measures the psychological satisfaction gained by individuals through gaming during the public opinion dissemination process and is the primary motivation for individuals to engage in gaming.

[0116] S204: Construct a decision-making model for individual bilateral games and determine individual behavioral strategies;

[0117] Current research on complex network games often uses the Fermi rule to single out individual payoff differences as a single factor influencing strategy selection. This is reasonable in certain scenarios. In this paper, individual satisfaction with opinion dissemination is one of the drivers of their gaming behavior. In the context of public opinion evolution, factors influencing individual strategy selection are not limited to this. Therefore, this paper specifically analyzes these influencing factors and constructs a decision-making model for individual bilateral games. Furthermore, the behavior of any individual expressing opinions in a social network is inherently determined by a "chaotic" psychological process. This psychological process depends not only on observable deterministic factors but also on factors such as individual personality and psychological state, resulting in significant uncertainty. The probability of strategy selection is inherently highly subjective, making it difficult to measure using conventional probabilistic statistical methods. To address this characteristic, this paper draws on the principles of fuzzy comprehensive decision-making theory, viewing the individual decision-making process as a process of selecting "options," namely, the process by which individuals determine whether to choose strategy S1 or S2.

[0118] For individual satisfaction, define the reference quantity x1=Π i (t-1) is used to measure the degree of motivation for the individual to choose S1. Obviously, higher satisfaction will encourage individuals to express their opinions more frequently. Since x1 does not strictly belong to the interval [0,1], we refer to the idea of ​​membership function in fuzzy comprehensive evaluation and convert the individual's tendency to choose S1 caused by satisfaction into μ s (x1) is defined as shown in the following formula (14).

[0119]

[0120] From formula (14), we can see that for any individual at any evolutionary moment, μ s (x1)∈[0,1], and when μ sWhen (x1)→1, it means that the satisfaction will make the individual have a strong tendency to choose S1. s When (x1)→0, it means that the satisfaction makes the individual extremely inclined to choose S2. Similarly, let the reference quantity for measuring the influence difference be x2=p i -p j , that is, the difference in influence between an individual and its reachable neighbors. i The influence is higher than that of its reachable neighbor v j When v i will tend to v j Select S1, otherwise there is no tendency to choose S1. This characteristic can be characterized by the ReLU function. Therefore, the tendency coefficient μ of the individual to choose S1 caused by the influence difference is p (x2) is shown in the following formula (15).

[0121]

[0122] From formula (2), we can see that the influence of any individual is in the interval (0,1), so the tendency coefficient μ p (x2) also satisfies: μ p (x2)∈(0,1]. This means μ p (x2) can be used to measure the impact of individual influence differences on their tendency to choose S1.

[0123] Further considering the polarity of individual opinions, according to the definition of opinion value, a reference value x3 is set to measure the individual v i The viewpoint polarity at time t, x3, is specifically expressed as shown in the following formula (16).

[0124]

[0125] Setting μ po (x3) is the coefficient of the individual's tendency to choose S1 due to opinion polarity. In the real evolution of public opinion, individuals with strong emotions about a public opinion event are more likely to express their opinions to their neighbors, and this tendency will show a significant attenuation as their emotions weaken. Individuals with neutral attitudes tend to observe their neighbors' opinions silently, and a small increase in polarity will not significantly increase their tendency to express their opinions. Therefore, there is a close positive correlation between the increase in opinion polarity Δx3 and the increase in their tendency to express their opinions. That is, as opinion polarity increases, the membership of strategy S1 becomes more sensitive to opinion polarity. Therefore, Obviously, according to formula (16), x3∈[0,1], so this property can be simplified by a quadratic function, then μ po (x3) is shown in the following formula (17).

[0126]

[0127] According to the influence of the three factors on the individual's tendency to choose S1, in the scenario of binary mixed strategy game, the individual's tendency to choose S1 and S2 is strictly opposite. i (x i )∈[0,1], therefore, the tendency coefficient υ of individual choice S2 caused by the three factors i (x i ) is expressed as:

[0128] υ i (x i )=1-μ i (x i )i=s,p,po(18)

[0129] Define the fuzzy weight vector of the three factors as W B =[w1,w2,w3], construct the fuzzy relationship matrix R of the individual for strategies S1 and S2 as

[0130]

[0131] Adopt the currently recognized comprehensive effect Operator synthesis weight vector and fuzzy relationship matrix (where ). As shown in the following formula (20), the fuzzy evaluation vector of the individual on strategies S1 and S2 measured by Score1 and Score2 can be obtained.

[0132]

[0133] In an individual bilateral game, the strategy choice of an individual can be viewed as a “subjective probability” resulting from the strategy “evaluation”. This probability characterizes the individual’s strategy decision-making process. By normalizing the elements in the fuzzy evaluation vector, we can obtain the individual v i For reachable neighbors v j The subjective probability of choosing strategy S1 for:

[0134]

[0135] At any evolutionary moment, the individual's strategy choice for its reachable neighbors will be determined by the subjective probability By the same token, the subjective probability of an individual choosing strategy S2 is The above formula (21) is also the bilateral game decision-making model constructed in this invention. This model accurately simulates the psychological factors that affect strategy selection in the process of public opinion dissemination, and represents the individual's strategy selection tendency through subjective probability, which can more reasonably characterize the individual's behavioral choices in the process of public opinion dissemination.

[0136] Further, step S3: Based on the individual behavior strategy selection result in step S2, in individual v i For reachable neighbors v j When choosing to express opinions, an improved opinion dynamics model based on individual behavior is constructed, that is, a public opinion evolution analysis model, to determine the individual v i point of view value.

[0137] Based on the existing public opinion propagation phenomenon and relevant social psychology theories, this paper constructs an improved opinion dynamics model based on individual behavior to fit the evolution of individual opinions in social networks. Specifically, it includes the following steps:

[0138] S301: Determine the set of trusted neighbors based on uncertainty theory;

[0139] The selective exposure theory points out that when the audience is exposed to mass communication activities, they will treat any media and content differently, tending to be exposed to media or content that is consistent with or close to their existing positions, views, and attitudes, and avoid those that are contrary to their existing views. Based on this theory, it can be inferred that there are two factors in judging the trust of neighbors in the process of public opinion dissemination: the first is the similarity or difference of views. Individual opinions are not blindly influenced by all of their neighbors, but tend to selectively accept the opinions of neighbors that are similar to their own; the second is the influence of neighbors. An individual's trust in the opinions of his neighbors does not depend entirely on the similarity of their views, but also on the influence of the neighbors. Individuals will have more trust in the opinions of highly influential neighbors. Define individual v i The set of trusted neighbors at time t of evolution is: The opinions of individuals in the trusted neighbor set can influence v i Opinions have an effective impact.

[0140] The present invention adopts uncertainty theory to determine whether an individual's neighbors belong to its trusted neighbor set, and constructs the opinion difference credibility function ψ o (x4) represents the degree of trust that the individual regards the neighbor as a “trustworthy neighbor” due to the difference in opinion between the individual and any previous neighbor. Similarly, the influence trust function ψ can be constructed p (x5) represents the degree of trust in the individual's predecessor neighbor due to the influence of the individual's predecessor neighbor. Define the uncertain variables x4 = |Δo ij (t)|=|o i (t)-o j (t)| and x5=p j Obviously x4,x5∈[0,1], where Δo ij (t) represents individual v i With the former neighbor vj The difference in opinion values ​​at time t.

[0141] The spread of public opinion in social networks has the following characteristics: individuals have higher trust in neighbors with similar opinions, and as the difference in opinions increases, the trust level of individuals in neighbors will decline significantly. On the other hand, individuals have higher trust in neighbors with high influence, and as the influence increases, the difference in trust in neighbors will decrease. This characteristic can be abstracted into mathematical concepts, and the trust function of opinion difference can be expressed as ψ o (x4) and the influence credibility function ψ p (x5) is defined as a concave function on the interval [0,1]. Therefore, the first-order and second-order derivatives of the two belief functions have the following characteristics:

[0142]

[0143] Based on the characteristics shown in formula (22) above, combined with the normativeness, duality and subadditivity axioms that the credibility operation should satisfy, the opinion difference credibility function and influence credibility function can be constructed as shown in the following formulas (23) and (24).

[0144]

[0145] In the belief function, are the sensitivity coefficients of opinion difference reliability and influence reliability, respectively. When both tend to 1, it means that the individual has a high sensitivity to the reliability caused by opinion difference and influence, and vice versa. In this invention, considering the characteristics of the reliability function, we set Further considering the working principle of the two factors, the trust caused by the two factors has no essential connection, but it is possible that the trust caused by the two factors will lead to trust or distrust of the neighbors. However, the "trust" caused by a single factor is relatively one-sided. For example, consider the trust of an individual in a previous neighbor. If this previous neighbor has a very high influence, but his views are almost completely contrary to those of the individual. At this time, it cannot be unilaterally considered that the individual is greatly inclined to trust the previous neighbor, because there is a large difference between their views; on the contrary, when the influence of this previous neighbor is weak, but his views are almost completely consistent with those of the individual, it cannot be determined with certainty that the individual will be greatly inclined to trust the neighbor, because the authority of this neighbor's views is questionable. Therefore, in the present invention, it is determined that if and only if the difference in views and the influence of neighbors can lead to an individual's trust in neighbors, that is, the event "due to similar views, individual v i Trust its predecessor neighbor v j " and the event " due to v j High influence, individual v i Trust its predecessor neighbor vj When it happens at the same time, According to the product axiom of uncertainty theory, the joint distribution of these two events is the confidence of their simultaneous occurrence. for

[0146]

[0147] Among them, "∧" means taking the smaller operation. Obviously, This satisfies the reliability range. i Previous neighbor v j Is it v i When the trusted neighbor is , a random number rand∈[0,1] can be generated first. When v j Treated as v i Trusted neighbors.

[0148] S302: Combine individual v i Current views on individual v i The influence of neighbors who express opinions, determine the updating rules of individual opinions, and build an improved opinion dynamics model based on individual behavior;

[0149] In the real interaction of opinions, there is a phenomenon that more similar opinions will make an individual stick to his or her original opinion, while fewer similar opinions will increase the individual's self-doubt and make him or her give up sticking to the original opinion. In order to describe this phenomenon, the present invention defines α i (t) is the individual's sensitivity factor to external opinions, and α i The larger the (t) is, the more sensitive the individual is to external opinions and the less persistent the individual is in the initial opinions. i The ratio of the number of credible neighbors to the number of neighbors who can influence their opinions at time t As a measure of approximate opinion, the individual v i Sensitivity factor α at evolution time t i The calculation method of (t) is

[0150]

[0151] where β i ∈[0,1] is the individual v i The change threshold of the sensitivity factor is When this threshold is exceeded, the individual's sensitivity factor will decrease, which means that the individual has deepened his adherence to the current view due to receiving more credible opinions. On the contrary, the individual's sensitivity factor will increase, which means that the individual has doubted the current view due to receiving fewer credible opinions. iThe value range of (t) is For and α i (t)∈(0,1), that is, for any node at any time, α i The value of (t) is between 0 and 1.

[0152] At any moment in evolution, there are two driving forces for the update of individual views: one from the outside and the other from the individual's self-cognition. From the perspective of the time sequence of influence, the change of individual self-cognition often depends on external influences. First, consider the external driving force. For any individual v i At the evolution time t, the opinion value after being affected by the outside world is updated to when When , the update rule is as shown in formula (27).

[0153]

[0154] Among them, ω ij The form shown in formula (28) is the influence weight of the neighbor's opinion. This means that among the trusted neighbors who express their opinions, the opinions of individuals with higher influence will have a more significant impact.

[0155]

[0156] And when When individual opinions cannot be influenced by the outside world, there is On this basis, we further consider the internal driving force of individual opinions. Group polarization theory points out that the interaction of group opinions in social networks will lead to individual opinions tending to be extreme. The reason for this phenomenon can usually be explained by two theories: one is the persuasive argument theory, which believes that after listening to others' arguments supporting their original positions, people will become more convinced of their own opinions and thus take more extreme positions. The second is the social comparison theory, which believes that people evaluate their own opinions by comparing themselves with others. When people find that others have similar opinions to themselves in group discussions, they are unwilling to stay at the general level, but tend to take extreme positions to show that they are higher than the general level. In order to characterize this phenomenon, it is assumed that when individuals in a social network receive more similar opinions, their opinions tend to evolve in an extreme direction. Therefore, when an individual receives a majority of similar opinions, his opinions will become polarized. For this purpose, a polarization threshold η∈(0,1) can be set to determine whether the opinion polarization phenomenon occurs. According to the definition in formula (10) When satisfied: Then it is considered that polarization occurs. Further, let λ∈(0,max(o)) be the polarization coefficient, then the polarization increment φ when individual opinions are polarized i (t) can be expressed as

[0157]

[0158] When polarization does not occur, φ i (t)=0. Therefore, at time t, individual v i The viewpoint value satisfies formula (30):

[0159]

[0160] According to formula (27) and formula (30), we can get: and o i (t)∈(min(o),max(o)), that is, for any node at any time, the opinion value o i The values ​​of (t) are all between the upper and lower limits of the viewpoint value.

[0161] Example 2:

[0162] Example 2 provides an application of the public opinion evolution analysis model established by the establishment method in Example 1 in the public opinion management strategy.

[0163] In the context of a crisis, public opinion management aims to curb and reverse the evolving public opinion on major public opinion events. For example, in the event of a major disaster, the public's negative views on government response measures can be prevented. This prevents negative public opinion from harming normal social order, thereby improving society's crisis response capabilities. This paper proposes three strategies: information blocking, mandatory intervention, and gradual guidance for social network authority.

[0164] Information blocking: Information blocking is a common method of public opinion management. It involves controlling influential figures with negative attitudes within social networks to prevent the spread of negative information. The specific methods of information blocking can be divided into two steps: target identification and information blocking.

[0165] Step 1: Target identification. Identify the set L of authority figures holding negative opinions in the social network as the control target.

[0166] Step 2: Information blocking. For each element in the set L, set the probability of each element expressing an opinion about its successor to 0 and maintain it.

[0167] Information blocking is a low-cost and easy-to-implement method for public opinion management. Public opinion management departments can use social media platforms to block opinion leaders who spread negative views in the short term, thereby curbing the spread of negative views to a certain extent. However, because information blocking does not inject positive information into social networks, its actual effectiveness is relatively limited.

[0168] Forced intervention: Forced intervention can also be divided into two steps: target identification and opinion control.

[0169] Step 1: Target identification. Obtain the set L of all authorities.

[0170] Step 2: Opinion Control. For each individual in L, its opinion value is continuously controlled to be max(o) during the evolution process, and the probability of expressing its opinion value to subsequent neighbors is set to 1. In other words, it always releases extreme positive opinions to guide the audience during the evolution process.

[0171] Coercive intervention strategies can leverage extreme speech to guide audience opinion on social networks. Compared to information blockades, controlling authority figures requires more judicial, economic, and technological means, resulting in higher costs. However, compared to information blockades, coercive intervention strategies are gentler, leading to greater audience acceptance of policies. They can also shift the evolution of group opinion by disseminating positive information within social networks, making them suitable for application in the online media environment powered by internet technology.

[0172] Gradual guidance: Experimental studies on crisis communication have shown that positive interaction and effective communication have a significant impact on the evolution of public opinion. Through measures such as managing uncertainty, effective communication, understanding crises, and promoting communication ethics, crises can be transformed into opportunities in many cases. This positive communication is called gradual guidance. As an effective public opinion management strategy, the main principle of gradual guidance is to influence the authority through continuous and permeating influence, so that it can slowly influence the audience's views. Gradual guidance requires continuous observation of the average opinion value of all individuals during the evolution process. To support the implementation of actions on the controlled object. Set the guidance coefficient σ∈(0,max(o)] and the error threshold error to represent the process of progressive guidance. The steps of progressive guidance are as follows:

[0173] Step 1: Target identification. Obtain the authority set T.

[0174] Step 2: Conduct guidance. For each authority, increase σ based on its current opinion value and set the probability of expressing its opinion to subsequent neighbors to 1.

[0175] Step 3: Time update. The evolution time t is updated to t+1.

[0176] Step 4: Effect judgment. Is it true? If so, go to Step 2; otherwise, go directly to Step 3.

[0177] Compared to forced intervention, gradual guidance adopts a softer, slower, and more gradual approach to public opinion management, effectively and understandably shifting audience opinion. However, this approach incurs significant costs for public opinion monitoring and analysis, and requires dynamic adjustments to the opinions of authority figures.

[0178] Simulation experiment:

[0179] In order to better verify and analyze the public opinion evolution model and public opinion management strategy, this paper only discusses the situation where the average opinion is biased towards negative, so relevant processing is made in the setting of the initial opinion value. For the verification of public opinion management strategy, the main goal is to curb the negative evolution of public opinion and guide the public opinion to evolve towards positive. Among them, the average opinion value of the social network at any time of evolution is And the proportion of strategy S1 being selected These are the main parameters observed in this invention.

[0180] 1. Data Preparation

[0181] This simulation experiment selected four typical social network data for analysis:

[0182] (1) Congress-Twitter Dataset (ct). This network represents the Twitter interaction network of the House of Representatives and Senate of the 117th United States Congress. The underlying data is collected through the Twitter API, and the empirical diffusion probability is quantified based on the number of times a member retweets, quotes, replies, or mentions another member’s tweet.

[0183] (2) The soc-sign-bitcoin-otc dataset (OTC). This is a trust-whom network where people trade Bitcoin on the Bitcoin-OTC platform. This is the first explicitly weighted, signed, directed network available for research.

[0184] (3) Wiki-vote dataset (wv). A small percentage of Wikipedia contributors are administrators, users who have access to additional technical features that aid maintenance. In order for a user to become an administrator, a Request for Administration (RfA) is published, and the Wikipedia community decides who to promote to administrator through public discussion or voting. Approximately half of the votes in the dataset come from existing administrators, while the other half come from ordinary Wikipedia users.

[0185] (4) Email-Eu-core dataset (eec). This network is generated using email data from a large European research institution. If one person has sent at least one email to another person, there is an edge between them in the network. The network also contains links between members of the institution and people outside the institution.

[0186] These social networks, derived from real-world social relationships, represent the information connectivity between individuals. These networks all use directed edges to indicate the direction of information transmission between individuals, and the average degree of nodes within the networks is at varying levels. Specific network parameters are shown in Table 2 below. This means that these networks can be used to validate the effectiveness of various public opinion management strategies at varying scales and connectivity densities.

[0187] Table 2 Comparison of network parameters of four social networks

[0188]

[0189] 2. Parameter settings

[0190] The various parameters involved in the public opinion evolution model and management strategy are reasonably set based on the characteristics of real-world public opinion management. The specific parameter values ​​are shown in Table 3. At the same time, for intuitive comparison, the evolution time in this simulation experiment is set to 100.

[0191] In the consideration of the benefits of the bilateral game between individuals, the numerical value is set according to the analyzed properties. At the same time, this simulation experiment simplifies the consideration of the sensitivity factor of individuals to external opinions and sets the α of all individuals at the initial moment to i (0) is set to 0.5, which means that individuals consider external opinions and their own opinions to be equally important at the initial moment. On the other hand, this simulation experiment believes that when individuals implement strategic decisions, the satisfaction of their opinions and the polarity of their opinions are the core factors that determine whether they speak out. Therefore, they have a higher weight in the fuzzy decision-making process. For the opinion values ​​and bilateral strategies of individuals at the initial moment of evolution, this simulation experiment uses random initialization to generate them.

[0192] Table 3 Parameter settings in this simulation experiment

[0193]

[0194] 3. Numerical simulation experiments

[0195] This simulation experiment mainly analyzes some key parameters in the public opinion evolution model proposed by this invention that may affect the evolution results. These parameters include: the individual's sensitivity factor α to external opinions at the initial moment; i(0), the polarization coefficient λ of individual opinions, and the judgment threshold τ of approximate opinions. The sensitivity analysis conducted in this simulation experiment is mainly based on the natural evolution scenario of public opinion, that is, no intervention is imposed on the evolution of public opinion. In order to better observe the effect of evolution, this simulation experiment randomly generates strategies between individuals at the initial moment and randomly generates the initial opinion value of individuals in the interval (0, 0.95), which means that in the social network at the initial moment, the group opinion is slightly biased towards the negative.

[0196] 3.1α i (0) Impact on evolutionary results

[0197] At the initial moment, set the sensitivity factor α of all individuals to external opinions i (0) are α i (0)=0.1,α i (0)=0.4,α i (0) = 0.5 and α i (0) = 0.7, and the other parameters are the same as those in Table 3. i Under the condition of (0), 30 evolution experiments were conducted, and the average opinion value at each moment in these 30 experiments and the proportion of strategy S1 being selected were counted. The results are shown in the attached figure. Figure 2 As shown, from (a) to (d) are the average opinion values ​​of the four networks ct, otc, wv and eec, and from (e) to (h) are the proportions of S1 being selected for the four network strategies ct, otc, wv and eec.

[0198] Depend on Figure 2 From (a) to (d), we can see that α at different levels i (0) will lead to differences in the convergence of the average opinion value. Under the influence of polarization, the evolution of the average opinion value in the social network will tend to be extreme. i When (0) is small, individuals tend to stick to their own initial opinions, which makes the external opinions have less influence on them, resulting in a smaller gap between the average opinion value after convergence and the average opinion value at the initial moment. i When (0) is large, external opinions have a greater impact on individuals, resulting in a larger difference between the average opinion value after convergence and the average opinion value at the initial moment.

[0199] As for the selection ratio of strategy S1, it can be seen from (e)-(h) of the attached figure that the higher α i (0) leads to a higher proportion of individuals choosing strategy S1 in the evolutionary stable state, which is clearly reflected in the experiments of the otc dataset and the eec dataset. The experiments of the wv dataset and the ct dataset also show this trend to a certain extent. This is due to the higher αi (0) It will cause the opinions of most individuals in the social network to converge more quickly, making most individuals have higher satisfaction and opinion polarity, which will lead to their stronger willingness to express their opinions.

[0200] 3.2 The impact of λ on evolution results

[0201] In order to verify the influence of the polarization coefficient λ on the evolution results, this simulation experiment selected four cases of λ: λ = 0.2, λ = 0.4, λ = 0.6, and λ = 0.8. 30 simulation experiments were conducted under the same conditions. The evolution trends of the average opinion value and the proportion of strategy S1 selected were as follows: Figure 3 Among them, from (a) to (d) are the average opinion values ​​of the four networks ct, otc, wv and eec, and from (e) to (h) are the proportions of the selected strategies S1 of the four networks ct, otc, wv and eec.

[0202] From the attached Figure 3 As shown in Figures (a)-(d), in the experiments with the OTC and EEC datasets, increasing the polarization coefficient λ leads to a larger gap between the average opinion value in the stable evolutionary state and the average opinion value in the initial state, resulting in a greater polarity of the average opinion in the social network. In contrast, in the experiments with the WV and CT datasets, the polarization coefficient has no significant effect on the evolution of the average opinion value. This suggests that different network structures are sensitive to different levels of λ. Furthermore, because increasing λ increases the polarization of individual opinions, individuals with stronger opinion polarity will receive more similar opinions as evolution progresses, increasing their willingness to express their opinions. Meanwhile, individuals with weaker opinion polarity will receive more contradictory opinions, which will reduce their willingness to speak out.

[0203] From the attached Figure 3 As can be seen in Figures (e)-(h), different levels of λ lead to different convergence trends in the proportion of S1 selected in different social networks. This is due to the differences between different social networks. However, λ has a relatively small impact on the evolutionary equilibrium state, indicating that in the public opinion evolution model proposed in this paper, individual strategic choices are highly robust to different λ conditions.

[0204] 3.3 The influence of τ on evolution results

[0205] To further test the effect of the approximate opinion judgment threshold τ on the evolution results, τ was set at three levels: τ = 0.2, τ = 0.3 and τ = 0.4. The average results of 30 simulation experiments in different social networks are as follows: Figure 4Among them, from (a) to (d) are the average opinion values ​​of the four networks ct, otc, wv and eec, and from (e) to (h) are the proportions of the selected strategies S1 of the four networks ct, otc, wv and eec.

[0206] From the attached Figure 4 As can be seen in Figures (a)-(d), a higher level of τ leads to a higher polarity in the average opinion value in the evolutionary stable state, significantly different from the average opinion value at the initial moment. This trend is consistent across all four social network experiments, indicating that τ has a significant impact on the average opinion value in the evolutionary stable state. This phenomenon is not difficult to discern because a higher τ can lead to greater satisfaction in the process of opinion exchange. While increasing individuals' willingness to express opinions, it also increases their receptiveness to external opinions and the polarization effect of their opinions, leading to stronger opinion polarity.

[0207] From the attached Figure 4 As can be seen in Figures (e)-(h), a higher level of τ increases the probability of selecting the evolutionary stable state strategy S1. When the judgment threshold τ for similar opinions increases, individuals are more likely to achieve greater psychological satisfaction in the two-sided game. On the other hand, a higher τ strengthens the polarity of individual opinions and, consequently, increases their willingness to select S1.

[0208] 4. Comparative Experiment

[0209] 4.1 Comparative Experiment on the Effects of Different Public Opinion Management Strategies

[0210] Based on the parameters shown in Table 3, a comparative experiment was conducted on the effects of three different public opinion management strategies: information blocking, forced intervention, and gradual guidance. The specific results are shown in the attached figure. Figure 5 As shown; among them, from (a) to (d) are the average opinion values ​​of the four networks ct, otc, wv and eec, and from (e) to (h) are the proportions of S1 being selected for the four network strategies ct, otc, wv and eec.

[0211] From the attached Figure 5As shown in Figures (a)-(d), the information blockade strategy did not significantly affect the evolution of public opinion, with the average opinion value within the social network remaining nearly consistent with natural evolution. In contrast, the strategies of forced intervention and gradual guidance had a more pronounced impact on the average opinion value of individuals within the social network, with gradual guidance outperforming forced intervention in the CT and EEC datasets. In terms of its mechanism of action, information blockade only restricts the dissemination of the opinions of those holding negative views and does not inject positive opinions into the social network. The influence of individual media on the majority of the audience can cause the average opinion value to converge nearly to that of natural evolution, thus failing to effectively curb the trend of public opinion evolution. Compared to forced intervention, gradual guidance gradually injects more positive opinions that are more easily accepted by the audience into the social network, which makes it more effective than forced intervention under certain conditions. However, its effectiveness is also constrained by network structure and scale, which results in its performance being nearly identical to forced intervention in the OTC and WV datasets.

[0212] From the attached Figure 5 As can be seen from (e)-(h) of the results, in most cases, gradual guidance leads to an increase in the proportion of individuals adopting strategy S1 in the evolutionary stable state, while forced intervention generally leads to a decrease in the proportion of individuals adopting strategy S1 in the evolutionary stable state. Clearly, forced intervention, which directly and continuously releases extremely positive views within the social network, significantly inhibits the tendency of individuals with negative or neutral views to speak out. Gradual guidance, on the other hand, makes the audience more receptive to the authority's views, guiding their views towards positive evolution while better maintaining individuals' enthusiasm for expressing their own opinions. On the other hand, information blockade does not significantly affect the proportion of individuals adopting strategy S1 in the evolutionary stable state. This is because information blockade only suppresses the voices of authority figures with negative views, while the evolution of public opinion among other individuals still resembles natural evolution, resulting in a result that is close to natural evolution.

[0213] 4.2 Comparative Experiments on Dynamic Models from Different Perspectives

[0214] Since the setting of individual strategy sets in POEM in the present invention does not reflect the individual's opinion tendency, this is different from the current paradigm in which individual strategy sets are set to express positive opinions, express negative opinions, express neutral opinions or remain silent in the study of public opinion evolution based on network games. Therefore, this simulation experiment will focus on comparing the public opinion evolution results driven by POEM and several typical opinion dynamics models. Four models, namely the HK model, the Degroot model, the IODM model and the MEPO model, were selected for comparison with the POEM proposed in the present invention. Since these models do not take into account the individual's public opinion dissemination behavior, this simulation experiment mainly compares the evolution of average opinion values ​​in different social networks driven by different models. In terms of parameter selection, the individual opinion confidence intervals in these comparison models are regarded as the approximate opinion judgment intervals in the present invention, and the numerical settings of the firmness factor in the original IODM text are followed. At the same time, in order to better compare the effects of different opinion dynamics models, the evolution time is extended to 400. The specific experimental results are shown in the attached figure. Figure 6 As shown, from (a) to (d) are the evolution trends of the average opinion values ​​of the four networks CT, OTC, WV and EEC.

[0215] From the attached Figure 6 As can be seen from the data, the MEPO model results in average opinion values ​​across different social networks remaining almost consistent with their initial state. This indicates that, given a slightly negative bias in group opinion, it fails to clearly capture the phenomenon of "opinion polarization," keeping group opinion at a nearly constant level. This suggests that the MEPO model tends to converge in its analysis and presentation of public opinion evolution across different social networks, but is less effective in capturing the diversity of public opinion changes across these networks.

[0216] The results driven by the Degroot model show a nearly linear relationship between average opinion value and evolution time. In experiments with the OTC dataset, the average opinion value showed an upward trend, indicating that opinion changes in social networks with high trust and high privacy are significantly influenced by public opinion evolution. This means that the Degroot model is significantly influenced by the structure and initial state of social networks, resulting in varying trends in public opinion evolution and potential risks beyond the actual evolution of public opinion.

[0217] In addition, from the attached Figure 6It can also be seen that the IODM and HK models lead to significant differences in the evolution of public opinion on different social networks. In experiments with the CT dataset, the IODM model failed to achieve a stable evolutionary state for the average opinion value, instead showing an upward and then downward trend. This demonstrates that in internet social media platforms like CT, the changes in public opinion evolution are reversible within a certain period of time. This may be influenced by the guidance of opinion leaders or by the evolution or reversal of the events themselves. In the OTC and EEC datasets, both the IODM and HK models lead to a certain degree of fluctuation in the average opinion value as it reaches a stable evolutionary state. Furthermore, it is clearly observed that the HK model causes relatively rapid changes in the average opinion value within a relatively short period of time after the initial evolution. In experiments with the WV dataset, both the IODM and HK models lead to rapid convergence of the average opinion value, maintaining it at a level significantly different from its initial state.

[0218] Obviously, without intervention, the evolution of average opinion values ​​is highly likely to fluctuate. However, in the real-world evolution of public opinion, the strengthening of group opinion polarity requires a certain amount of iteration and time to achieve, and is largely determined by the social influence of the public opinion event itself and the public attention it generates. If the public opinion event itself is only a small-scale emergency or a common occurrence, public attention will disappear quickly. In the wv dataset, the IODM and HK models cause the average opinion value to drop off sharply after the initial moment, which does not conform to the evolutionary trend of public opinion events in the real public opinion environment.

[0219] On the other hand, the observation Figure 6 As can be seen from the curves in Figure 2, the public opinion evolution model proposed in this invention reflects the trend of gradual polarization of group opinions in four different social networks, and also enables the average opinion value to reach a stable equilibrium state. It reflects the universal law of public opinion evolution in different social networks, namely the polarization and balance that group opinions may produce. This also proves that the model proposed in this invention can better depict the actual evolution of public opinion and has greater advantages than other public opinion evolution models.

[0220] In summary, for the evolution trend of the average opinion value, numerical simulation experiments show that the individual's sensitivity factor α to external opinions at the initial moment is i(0), the polarization coefficient λ of individual opinions and the judgment threshold τ of approximate opinions can all affect the results of public opinion evolution under certain conditions, and they are positively correlated with the polarity of the average opinion value in the stable state of evolution. This phenomenon is consistent with the logic of the model design of the present invention. In fact, when facing public opinion events on different topics, how to choose reasonable parameters is also a problem worth studying. For example, when studying the impact of public opinion events of the types of finance, public security, etc., the universal social values ​​of the people will make them less sensitive to external opinions (i.e., α i On the other hand, the comparative experiment of different strategies shows that the two management strategies of delivering expected opinions to social networks, forced intervention and gradual guidance, have better effects than single information blocking, and under certain conditions, gradual guidance may show significantly better effects than forced intervention (such as the attached Figure 5 (d) shows the results). At the same time, the present invention can also be observed that the proportion of strategy S1 selected generally shows a trend of "first decreasing and then increasing" during the evolution process in different social networks. This is because in the early stage of evolution, some opinions that contradict the opinions received by individuals have a greater negative impact on their satisfaction, which in turn leads to a weakening of the individuals' willingness to express their opinions. As the evolution time increases, the opinions of most individuals in the social network tend to be similar. As individuals obtain more similar opinions, their satisfaction increases, which in turn strengthens their willingness to express their opinions.

[0221] In fact, during the process of public opinion dissemination, when group opinion tends to be neutral, individuals often tend to "wait and see" when initially exposed to highly polarized viewpoints. However, their opinions and attitudes can change during this process. As individuals perceive more distinct viewpoints, their opinions become increasingly polarized, and they are more inclined to speak out in the hope of gaining greater social recognition. For example, the Italian Renzi government formulated and implemented two policies in 2014-2015: the "Jobs Act" labor market reform and the "Labuonascuola" school reform, which sparked heated discussions on social media. A case study of these events, using aggregated sentiment analysis techniques to analyze Twitter data, found that the evolution of public opinion on social media exhibits cyclical patterns, and that the spread of polarized viewpoints can fuel heated public discussion on hot issues. This real-world example further reinforces the validity of POEM.

[0222] On the other hand, the comparative experimental results of different opinion dynamics models show that the public opinion evolution model proposed by the present invention can show an approximate average opinion value evolution form in different social networks, reflecting its robustness to different social networks. By observing the results of numerical simulation experiments and comparative experiments, it can also be found that the scale of the social network also has a more significant impact on the results of public opinion evolution. Especially in the CT data set and the WV data set, the two data sets have similar average degrees and have large differences in node scale. In different numerical settings and simulation experiments, the evolution of the average opinion value is relatively stable, which also means that when the node scale in the social network is small and large, the evolution trend of opinion attitudes is relatively weak in sensitivity to different initial states and public opinion management strategies. Therefore, the scale and structure of the social network also determine the effect of public opinion evolution to a large extent. In actual public opinion management, it is also necessary to select appropriate management strategies based on the specific characteristics of the social network to better avoid the waste of management costs.

[0223] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for establishing a public opinion evolution analysis model that integrates network gaming and opinion dynamics, characterized by: The following steps are involved: S1: Construct a model of individual influence differences in the process of public opinion dissemination; S2: Based on the individual influence difference model, a decision-making model of individual bilateral behavior game based on social network game is constructed to determine individual behavior strategies, including expressing opinions and keeping silent; S3: Based on the individual behavior strategy selection results in step S2, when an individual chooses to express an opinion on a reachable neighbor, an improved opinion dynamics model based on individual behavior, that is, a public opinion evolution analysis model, is constructed to determine the individual's opinion value; The specific operations of step S3 include the following steps: S301: Based on uncertainty theory, from the perspective of individual v i Determine the set of trusted neighbors among the neighbors who express their opinions, where Indicates direct access to node v i The neighbor set of Represents node v i The set of all neighbors of ; S302: Combine individual v i Current views on individual v i The influence of neighbors who express opinions, determining the update rules of individual opinions, and constructing an improved opinion dynamics model based on individual behavior: when When , the update rule of individual opinions is Then at time t, individual v i The view value o i (t) is expressed as in, Represents individual v i The set of trusted neighbors at time t of evolution; Represents individual v i At the evolution time t, the opinion value after being affected by the outside world, α i (t) represents individual v i The sensitivity factor at the evolution time t, and Represents individual v i The ratio of the number of credible neighbors to the number of neighbors who can influence their opinions at time t, Indicates that at time t, i The set of neighbors who express opinions, β i ∈[0,1] represents individual v i The change threshold of the sensitivity factor; Δo ji (t) represents individual v i With the former neighbor v j The difference in opinion values ​​at time t; ω ij represents the influence weight of neighbors’ opinions; φ i (t) represents the polarization increment when individual opinions become polarized, which is expressed as λ∈(0,max(o)) is the polarization coefficient; when hour, 2. The method for establishing a public opinion evolution analysis model integrating network gaming and opinion dynamics according to claim 1 is characterized by: The individual influence difference model described in step S1 is expressed as Where p i Represents any node v i The influence value, PR i Represents node v i PageRank value, PR j Represents node v j PageRank value, v j For individual v i Neighbors, Represents the set of nodes in the social network, and n represents the number of nodes.

3. The method for establishing a public opinion evolution analysis model integrating network gaming and opinion dynamics according to claim 2 is characterized in that: The specific operation of step S2 includes the following steps: S201: Construct a problem model of individual behavior game, specifically Where, represents a social network consisting of n nodes and m edges, ε={e1,e2,…,e ι } represents the edge set in the social network; For individual v i The strategy vector at the evolution time t, δ ij (t)∈{S1,S2} represents individual v i At the evolution time t, for individual v j The strategies adopted, S1 and S2 represent the two strategic options of expressing opinions and keeping silent respectively; π ij (t) represents individual v i At the evolution time t, the neighbor individual v j The psychological benefits gained from gaming, Represents node v i The set of all neighbors of i (t) represents the node v i At the moment of evolution t, the opinion value is expressed in the interval [0,1], with max(o)=1, min(o)=0, and o i (t)→1 represents the individual's positive attitude towards public opinion, o i (t)→0 means that the individual has a negative attitude towards public opinion; S202: Determine the payoffs of a bilateral game between individuals; S203: Determine the update rule of individual benefits; S204: Construct a decision-making model for individual bilateral games and determine individual behavioral strategies.

4. The method for establishing a public opinion evolution analysis model integrating network gaming and opinion dynamics according to claim 3 is characterized by: The benefits of the bilateral game between individuals in step S202 include benefits between homogeneous individuals and benefits between heterogeneous individuals. Homogeneous individuals include audience-audience and authority-authority, and heterogeneous individuals include audience-authority.

5. The method for establishing a public opinion evolution analysis model integrating network gaming and opinion dynamics according to claim 4 is characterized by: In step S203, individual v is used i The true satisfaction Π at the evolution time t i (t) represents the actual benefit of the individual at a certain evolutionary moment, then Π i (t) is expressed as Among them, γ∈(0,1) is the memory sensitivity coefficient, Indicates that at the time t of evolution, individual v i The interaction satisfaction obtained through the game with neighbors, Indicates that at the time t-1 of evolution, individual v i The interaction satisfaction obtained through the game with neighbors, and i (t)∈{-1,0,1} is a Boolean variable used to judge the external cognitive pressure on the individual, and m represents the impact of group cognitive pressure on individual satisfaction; r i N (t) represents the proportion of all external opinions received by an individual at time t to opinions similar to his / hers, and ξ∈[0.5,1] is the group pressure threshold, which is used to judge the impact of group pressure on individual satisfaction.

6. The method for establishing a public opinion evolution analysis model integrating network gaming and opinion dynamics according to claim 5 is characterized in that: The bilateral game decision model described in step S204 is expressed as Where, Represents individual v i For reachable neighbors v j The subjective probability of selecting strategy S1, strategy S1 is "expressing opinions"; the subjective probability of individuals selecting strategy S2 is Strategy S2 is "remain silent"; the fuzzy evaluation vector of the individual on strategies S1 and S2 measured by Score1 and Score2 is W B =[w1,w2,w3] is the fuzzy weight vector considering the three factors of individual satisfaction, influence difference and individual opinion polarity. R represents the fuzzy relationship matrix of the individual for strategies S1 and S2. Among them, x1=P i (t-1); x2=p i -p j ; u i (x i )=1-μ i (x i )i=s,p,po.

7. A public opinion evolution analysis system established using the establishment method described in any one of claims 1-6.

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