Public opinion evolution analysis model fusing network game and viewpoint dynamics and establishment method and application of public opinion evolution analysis model

Abstract

The invention discloses a public opinion evolution analysis model fusing network game and viewpoint dynamics and an establishment method and application thereof, and belongs to the technical field of social network analysis. According to the public opinion evolution analysis model, the social network game and the opinion dynamics theory are combined, a public opinion evolution mathematical model (POEM) is constructed according to related theories in social science while more comprehensive factors are considered, and scientific simulation of psychological activities of individuals in the public opinion propagation process is achieved; the two limitations of single behavior statistics in a traditional network game model and lack of behavior description in a viewpoint dynamics model are broken through; and the psychological trends and decision behaviors of the social individuals in the public opinion evolution process are described by using the uncertainty mathematical theory, and the influence of the individual propagation behaviors on the social public opinion evolution is described more accurately.

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 and opinion dynamics, and an establishment method and application thereof. Background Art

[0002] Public opinion management has always been an important issue in the field of public management. Among them, analyzing the evolution trend of public opinion based on social networks and mathematical models has become a hot topic in current research. It can provide important decision-making support for departments such as governments and enterprises that need to carry out public opinion management business, which is of great significance. In sociology, social network refers to the collection of social actors and their relationships. In other words, a social network is a collection of multiple points (social actors) and the lines between the points (the relationship between actors). As a mature analytical perspective, social network analysis can effectively express the relationship between social members. With the rise of the Internet, especially mobile social media, the ways of interaction between social individuals have become more diverse, and the influence of social media influencers on the attitudes of social individuals has become more complex, resulting in the social network presenting a diversified form. In the relevant research on public opinion management, social networks are often used to characterize the information communication relationship between social actors, which is the basis for the construction of relevant models for the evolution and management of public opinion. With the development of the Internet and the improvement of the public's education level, the unstable factors in social networks are increasing day by day, making the difficulty of public opinion management more and more significant.

[0003] The modeling of public opinion evolution based on social networks presents two typical schools, namely, the evolution analysis of group communication behavior based on network games and the evolution analysis of group opinion tendencies based on opinion dynamics. As a typical theory for multi-player game scenarios, network games have been widely used in games between researchers and corporate groups. In network game theory, players usually exist in the form of nodes and play games based on the relationships represented by network edges. The benefits generated by the game will affect the behavioral decisions of the players. The equilibrium state of the game evolution is analyzed by statistically analyzing the proportion of individual behaviors. The opinion dynamics model is mainly carried out in directed social networks. It often uses quantitative opinion tendency values ​​to represent the opinion tendencies of individuals and groups. Through network structure and different opinion update rules, the individual opinion tendency values ​​are updated in the dynamic evolution moment, thereby simulating the evolution trend of group opinions. It is not difficult to find that the public opinion evolution analysis based on network game theory mainly studies the equilibrium state of public opinion evolution by statistically analyzing the proportion of individuals taking certain behaviors, while the opinion dynamics theory mainly analyzes the trend of public opinion evolution by observing the group opinion attitude values ​​measured in numerical form. Although both theories can support the development of public opinion evolution analysis under certain conditions, they cannot directly depict the relationship between public opinion attitudes and individual communication behaviors, and can only reflect the trend of public opinion evolution from a single perspective. On the other hand, in related research in the field of communication studies, different scholars have proposed a wealth of public opinion management strategies, but the implementation effects of these strategies often need to be discovered from actual public opinion management operations. Therefore, modeling public opinion management strategies and discovering their effects through simulation experiments has also become an urgent problem to be solved 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, and 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 characterize 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 integrating network game 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 an individual chooses to express his or her opinions on 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] In the formula, p i Represents any node v i The influence value, PR i Represents node v i PageRank value, PR j Represents node v j The 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] In the formula, 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 The opinion value at the evolution time t uses the interval [0,1] to represent the individual opinion value range, max(o) = 1, min(o) = 0, o i (t)→1 represents that the individual has a 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 behavior 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 interactive satisfaction obtained through the game with neighbors, It means 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 an 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] In the formula, Represents individual v i For reachable neighbors v j The subjective probability of choosing strategy S1, strategy S1 is "expressing opinions"; the subjective probability of individuals choosing 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 three factors: 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 individual v i Determine the set of trusted neighbors among the neighbors who express their opinions in, Indicates that it points directly to node v i The neighbor set, N i Represents node v i The set of all neighbors of ;

[0031] S302: Combined individual v i Current views on individual v i The influence of neighbors who express opinions, determine the update rules of individual opinions, and build 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 value of the view 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 the value of v at time t i The set of neighbors who expressed their 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 previous 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, 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, compulsory 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, constructs a mathematical model based on relevant theories in social sciences while considering more comprehensive factors, and realizes the scientific simulation of the psychological activities of individuals in the process of public opinion dissemination. Simulation experiments show that the public public opinion evolution model proposed in the present invention is more scientific and reasonable in describing the general laws of public opinion evolution. From the perspective of actual 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, which 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 public opinion.

[0042] 2. At the method level, the model proposed by this invention innovates the application mode of combining network game model with complex network dynamics model, and realizes the simulation of psychological activities based on uncertain mathematical model. On the basis of providing a scientific and powerful public opinion evolution analysis method, it further models and analyzes the effect of public opinion management strategy, which has strong practical value and can provide theoretical reference for related research in the fields of group decision-making, public management, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a 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)Simulation result diagram of the impact on evolution results.

[0045] Figure 3 This is a simulation result diagram of 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 of 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] Embodiment 1:

[0051] Embodiment 1 provides a method for establishing a public opinion evolution analysis model integrating network game 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 including 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, the present invention adopts a directed network to represent the social network. Use N i Represents node v i The set of all neighbors of Indicates that it points directly 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 individual's tendency to hold 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 individual's opinion value range, and o is set i (t)→1 represents that the individual has a 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 individual's position in information dissemination, that is, the individual's position in the social network, which is closely related to the structure of the social network. In the present 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] In the formula, 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 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 will have more trust in the opinions and attitudes of authorities under the influence of security psychology and recognition psychology, 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 authority, 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 the present invention, the problem model Γ of 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 the present invention, the metric "satisfaction" is defined and regarded as the benefit generated by the game behavior. Satisfaction refers to the measure of the psychological benefits caused by different behavioral interactions during the game 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] Since the information communication relationship between individuals in a social network is directional, not all individuals can effectively express their opinions to their neighbors. This means that when an individual chooses S1, the expression of such opinions will be "invalid" if the individual can only receive information from neighbors but cannot effectively spread opinions to neighbors. Therefore, the present invention defines the following two judgment rules for this feature:

[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 in the case of one-way connection and two-way connection is shown. The solid 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 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 "contrary opinions". i and its neighbors v j Taking the viewpoint value at the time t of evolution as an example, assuming that the viewpoint approximation threshold is τ, then when o j (t)∈[o i (t)-τ,o i (t)+τ], it is believed that the two views are similar. At the time, I thought the two views were contradictory.

[0071] The similarity and deviation of opinions between individuals are the direct motivations that affect satisfaction. This invention will analyze from the perspectives of the game between homogeneous individuals (no difference in individual influence) and the game between heterogeneous individuals (differences 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 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] Assumption 1: When any individual receives similar opinions from neighbors, the absolute value of the positive increment of his satisfaction will be much smaller than the absolute value of the negative increment of his satisfaction when he receives the opposite opinions from neighbors. This also means that a and b satisfy the relationship |a|<<|b|, a>0, b<0.

[0073] In another case, when an individual expresses his or her views to a neighbor unilaterally, the individual may have two perceptions: one is that the neighbor "accepts" his or her views, which in turn increases his or her satisfaction; the other is that the individual's own views are "ignored" by the neighbor, which results in a negative decrease in satisfaction. However, the formation of these two perceptions is not certain, and depends on many factors such as the personality and intention of different individuals, and the impact on individual satisfaction is relatively slight. Therefore, c represents the absolute value of this impact. In the present invention, the two perceptions of an individual in this case are randomly represented.

[0074] Under the condition that there are large differences in influence between individuals, the scope of information dissemination of high-influence 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 era of social media, 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 will be less than the impact of interpersonal communication. Define that when an authority observes similar opinions expressed by the audience, the positive increment of satisfaction obtained by the authority is f, and when the authority observes opposite opinions expressed by the audience, the negative increment of satisfaction obtained is g. Similarly, let the positive increment of satisfaction of the audience when obtaining similar opinions of the authority be d, and the negative increment of satisfaction when obtaining opposite opinions of 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 opinions, while the audience will attach importance to the influence of the authority's opinions.

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

[0077] Let's further consider the situation where there is a one-way expression of opinions between individuals with different influence. In fact, the difference in influence creates a "gap" between the audience and the authority, which makes them less sensitive to the satisfaction impact of the two perceptions of "acquiescence" and "ignorance" of their neighbors. Suppose that when opinions are expressed one-way between the authority and the audience, the absolute value of the impact on the satisfaction of the individual expressing the opinion is h, then: h<c.

[0078] Based on the above analysis, under different bilateral game scenarios, the relationship of the impact on individual satisfaction is shown in formula (4), and the meaning of various parameters is 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 the game, the interaction of similar views will produce a "mutual recognition" effect, which will increase the satisfaction of both parties. On the contrary, the interaction of opposite 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 increment of the two is shown in the following formula (6).

[0089]

[0090] In this case, v j Received v i The influence of the two opinions on satisfaction is determined by the similarity of their opinions. i From the perspective of neighbors j No response, which means v i Maybe you think v j "Default" to his own point of view, or he may think 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 to measure the two possible perceptions. The same is true for other combinations in situation B.

[0091] Case C:

[0092] Case C is simpler than cases A and B. At this time, the individual and his neighbors remain silent and do not interact with each other. The increment of satisfaction of both parties 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] Situation 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,j 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 remains silent, the game payoffs of both parties are as shown in formula (9).

[0099]

[0100] In another case v i Next, individual v i For the authority individuals who remain silent, v j is the audience neighbor who expressed the opinion, then v i and v j The benefits can be expressed by the above formulas (8) and (9) respectively.

[0101] Case F:

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

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

[0104] The benefit of an individual at an evolutionary moment is not just the sum of the benefits of the bilateral game with all neighbors, but also includes the "group pressure" formed by the opinions of the neighbor group 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 your opinion and share your experience with v i A set of neighbors with similar opinions satisfies the relationship: Therefore, among all the external opinions received by an individual at time t, the proportion of opinions similar to it 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] Formula (12) shows that the satisfaction obtained by an individual through opinion interaction is composed of the cumulative impact of all bilateral games on satisfaction and the impact of external cognitive pressure. Among them, m represents the impact of group cognitive pressure on individual satisfaction. Compared with bilateral games between individuals, the impact of group cognitive pressure is stronger, so |m|>>|e|, m>0.

[0111] In a general complex network game model, the benefits of the players at the current evolution moment only depend on the game results at the current moment, and only affect the strategy choice at the next moment. However, in the problem of public opinion evolution, individuals have a certain "memory" of satisfaction, a "sensory" factor, which makes historical benefits also affect individual 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 perceptual benefits during the evolution process. When γ→1, individuals The greater the proportion of the individual's previous satisfaction in the current income, the stronger the memory of historical satisfaction. When γ→0, the individual pays more attention to recent income and despises previous income. Real satisfaction is the actual income of any individual at a certain evolutionary moment. It measures the psychological satisfaction obtained by individuals due to gaming behavior during the process of public opinion dissemination and is the main motivation for individuals to engage in gaming.

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

[0117] In the current complex network game research, the difference in income between individuals is usually used as a single influencing factor for strategy selection according to the Fermi rule, which is reasonable in certain scenarios. In the present invention, the satisfaction of individual opinion dissemination is one of the motivations for the generation of their game behavior. In the problem of public opinion evolution, the factors affecting individual strategy selection are not limited to this. Therefore, in the present invention, these influencing factors will be specifically analyzed and a decision-making model for individual bilateral games will be constructed. At the same time, the behavior of any individual in a social network to express opinions is essentially determined by a "chaotic" psychological effect, which depends not only on the deterministic factors that can be observed, but also on factors such as individual personality and psychological state, and there is significant uncertainty. The probability of strategy selection is essentially a probability with strong subjectivity, which is difficult to measure by general probability statistics methods. In view of this feature, the present invention draws on the idea of ​​fuzzy comprehensive decision-making theory and regards the individual decision-making process as the optimization process of the "scheme", that is, the process of the individual judging 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 prompt individuals to express their opinions more frequently. Since x1 does not strictly belong to the interval [0,1], the idea of ​​membership function in fuzzy comprehensive evaluation is borrowed to 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 difference in influence be x2=p i -p j , which is the difference in influence between an individual and its reachable neighbors. i The influence of j When i will tend to v j Select S1, otherwise there is no tendency to select S1. This characteristic can be characterized by the Relu function. Therefore, the tendency coefficient μ of the individual to select S1 caused by the difference in influence 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 that 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 polarity of 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 caused by the polarity of opinion. In the actual evolution of public opinion, individuals who hold strong emotions about a public opinion event are more inclined 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, the increment Δx3 of the polarity of opinions has a close positive correlation with the increment of their tendency to express their opinions, that is, as the polarity of opinions increases, the membership of strategy S1 is more sensitive to the polarity of opinions, so: Obviously, according to formula (16), we know that: x3∈[0,1], so we can simplify the representation of this property 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 the individual to choose 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 is more reasonable 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 individual bilateral games, the strategy choice of an individual can be regarded as a "subjective probability" caused by the strategy "evaluation". This probability characterizes the individual's strategy decision-making process. The elements in the fuzzy evaluation vector are normalized to 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 the present invention. The model accurately simulates the psychological factors that affect the 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, that is, a public opinion evolution analysis model, is constructed to determine the individual v i The view value.

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

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

[0139] The selective contact 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 or close to their existing positions, views, and attitudes, and avoid those that are contrary to their existing views. According to 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 views are not blindly influenced by all of their neighbors, but tend to selectively accept the views of neighbors that are similar to their own; the second is the influence of neighbors. An individual's confidence in his or her neighbors' views does not entirely depend on the similarity of their views, but also depends on the influence of the neighbors, and individuals will have more trust in the views 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 confidence that the difference in opinion between an individual and any previous neighbor leads the individual to regard the neighbor as a “trustworthy neighbor”. Similarly, the influence confidence function ψ can be constructed p (x5) represents the degree of trust that an individual regards his predecessor as a credible neighbor due to the influence of the individual's predecessor. 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 previous 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 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 opinion difference trust function 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 derivatives and second-order derivatives of the two belief functions have the following characteristics:

[0142]

[0143] Based on the characteristics shown in equation (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 equations (23) and (24) below.

[0144]

[0145] In the credibility 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 the present invention, considering the characteristics of the reliability function, we assume 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 predecessor neighbor. If this predecessor 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 predecessor neighbor, because there is a large difference between their views; on the contrary, when the influence of this predecessor 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 the 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 that they will occur simultaneously. for

[0146]

[0147] Among them, "∧" means taking the smaller operation. Obviously, This satisfies the range of reliability. Therefore, when judging the individual v i The predecessor neighbor v j Is it v i When the trusted neighbor of When v j Treated as v i 's trusted neighbors.

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

[0149] In the actual interaction of opinions, there is such a phenomenon: more similar opinions will make individuals stick to their initial opinions, while fewer similar opinions will increase individuals' doubts about themselves, causing them to give up their initial opinions. In order to describe this phenomenon, the present invention defines α i (t) is the sensitivity factor of the individual 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 opinion. 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 similar opinions, the individual v i The sensitivity factor α at the 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 timing of the impact, the change of individual self-cognition often depends on the external influence. 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 satisfied, which 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] When When individual opinions cannot be influenced by the outside world, On this basis, we further consider the internal driving force of individual opinions. The 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 reason, 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] Embodiment 2:

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

[0163] In the context of crisis events, the purpose of public opinion management is to suppress and reverse the evolution of the public's views on major public opinion events, such as the public's negative views on the government's response measures in the event of a major disaster, to prevent bad public opinion from causing harm to the normal social order, and thus improve the society's crisis response capabilities. This invention proposes three strategies: information blocking, compulsory intervention, and gradual guidance for social network authorities.

[0164] Information blocking: Information blocking is a common way of public opinion management. It prevents the spread of negative information by controlling the authority figures with negative attitudes in social networks. The specific method 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 on its successor to 0 and keep it.

[0167] Information blocking is a low-cost and easy-to-implement method of public opinion management. Public opinion management departments can use social platforms to block opinion leaders who spread negative opinions in the short term, thus curbing the spread of negative opinions to a certain extent. However, since information blocking does not deliver positive information to social networks, its actual effect 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. Get the set L of all authorities.

[0170] Step 2: Opinion control. For individuals in L, their opinion values ​​are continuously controlled to be max(o) during the continuous evolution process, and the probability value of their expressing their opinion values ​​to subsequent neighbors is set to 1, that is, they always release biased positive opinions to guide the audience during the continuous evolution process.

[0171] The compulsory intervention strategy can rely on extreme speech to guide the audience's views in social networks. Compared with information blockade, the control of authority requires more judicial, economic, and technical means, and the cost of implementation is relatively high. However, compared with information blockade, it is gentler, the audience is more receptive to the policy, and it can change the evolution trend of group views by sending positive information to social networks. It is suitable for application in the network media environment under Internet technology.

[0172] Gradual guidance: Experimental studies on crisis communication have shown that benign interaction and effective communication have an important 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 kind of benign communication is called gradual guidance. As an effective public opinion management strategy, the main principle of gradual guidance is to influence the authority in a continuous and permeating manner 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 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. Get the authority set T.

[0174] Step 2: Conduct guidance. For each authority, add σ to its existing opinion value and set the probability of expressing its opinion to the 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 with forced intervention, gradual guidance adopts a softer, slower, and more gradual approach to public opinion management, which can change the audience's opinions in an effective and understandable way. However, gradual guidance will cost a lot of public opinion monitoring and analysis costs, and requires dynamic adjustments to the opinions of authorities.

[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 the 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 It is the parameter index mainly observed in the present 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 the 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 network of who trusts whom, where people use Bitcoin to trade 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, who are users with 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. About 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 a person has sent at least one email to another person, there is an edge between the two in the network. The network also contains links between members of the institution and people outside the institution.

[0186] These social networks are extracted from real social relations and represent the information connection between people. These networks all mark the direction of information dissemination between individuals in the form of directed edges, and the average degree of nodes in the network is at different levels. The specific network parameters are shown in Table 2. This means that through these networks, it is possible to verify the implementation effects of various public opinion management strategies under different scales of connection density.

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

[0188]

[0189] 2. Parameter settings

[0190] For each parameter involved in the public opinion evolution model and management strategy, reasonable settings are made in combination with the characteristics of actual public opinion management. The specific parameter values ​​are shown in Table 3. At the same time, in order to facilitate intuitive comparison, the evolution time is set to 100 in this simulation experiment.

[0191] In the consideration of the benefits of bilateral game behavior between individuals, the numerical value is set according to the analyzed properties. At the same time, this simulation experiment simplifies the sensitivity factor of individuals to external opinions and sets the α of all individuals at the initial moment. i (0) is set to 0.5, which means that individuals consider external opinions to be equally important as their own opinions 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, so 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 the present invention that may affect the evolution results. These parameters include: the sensitivity factor α of individuals 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 among individuals at the initial moment, and randomly generates the initial opinion value of individuals in the interval of (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 and the proportion of strategy S1 selected at each moment in these 30 experiments 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 of ct, otc, wv and eec, and from (e) to (h) are the proportions of S1 being selected among the four network strategies of 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 (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 (0) is larger, the external opinions have a greater impact on the individual, 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, and also in the experiments of the wv dataset and the ct dataset to a certain extent. This is due to the higher αi (0) 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 Effect of λ on evolution results

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

[0202] From the attached Figure 3 As can be seen from (a)-(d) in the experiments of the OTC and EEC datasets, the increase in the polarization coefficient λ will lead to an increase in the gap between the average opinion value in the stable state of evolution and the average opinion value in the initial state, resulting in a greater polarity of the average opinion in the social network. In the experiments of the WV and CT datasets, the polarization coefficient did not have a significant effect on the evolution results of the average opinion value. This means that different network structures are sensitive to different levels of λ. On the other hand, since the increase in λ will increase the polarization of individual opinions, individuals with stronger opinion polarity will receive more similar opinions as the evolutionary moment progresses, and their willingness to express their opinions will increase; while individuals with weaker opinion polarity will receive more contradictory opinions, which will reduce their willingness to speak out.

[0203] From the attached Figure 3 It can be seen from (e)-(h) that different levels of λ lead to different convergence trends in the proportion of S1 being selected in different social networks, which is due to the differences in different social networks. However, the influence of λ on the evolutionary equilibrium state is relatively small, indicating that in the public opinion evolution model proposed in this invention, the individual's strategic choice is highly robust to λ under different 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 was set at: τ = 0.2, τ = 0.3 and τ = 0.4. The average results of 30 simulation experiments in different social networks are shown in Figure 2. Figure 4As shown. Among them, from (a) to (d) are the average opinion values ​​of the four networks of ct, otc, wv and eec, and from (e) to (h) are the proportions of S1 selected by the four network strategies of ct, otc, wv and eec.

[0206] From the attached Figure 4 As can be seen from (a)-(d), a higher level of τ will make the average opinion value in the evolutionary stable state have a higher polarity, which is significantly different from the average opinion value at the initial moment. This trend is consistent in the experiments of the four social networks, indicating that τ has a significant impact on the average opinion value in the evolutionary stable state. It is not difficult to find that the reason for this phenomenon is that a higher τ can prompt individuals to have higher satisfaction in the process of opinion interaction, which increases the individual's willingness to express opinions and increases the individual's acceptance of external opinions and the polarization effect of individual opinions, thereby causing stronger opinion polarity.

[0207] From the attached Figure 4 As can be seen from (e)-(h) of Figure 1, a higher level of τ will increase the proportion of evolutionary stable state strategy S1 being selected. When the judgment threshold τ of similar opinions increases, individuals will be more likely to obtain greater psychological satisfaction in bilateral games. On the other hand, a higher τ will strengthen the polarity of individual opinions and also enhance the individual's willingness to choose S1.

[0208] 4. Comparative Experiment

[0209] 4.1 Experimental comparison of 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, compulsory 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 of ct, otc, wv and eec, and from (e) to (h) are the proportions of S1 selected by the four network strategies of ct, otc, wv and eec.

[0211] From the attached Figure 5As can be seen from (a)-(d) of the data, the information blockade strategy has no significant impact on the results of public opinion evolution, and the average opinion value in the social network is almost the same as that in natural evolution. In contrast, the two strategies of compulsory intervention and gradual guidance have a more obvious impact on the average opinion value of individuals in the social network, and the performance of gradual guidance in the CT dataset and the EEC dataset is better than that of compulsory intervention. From the perspective of the working principle, information blockade only limits the spread of the opinions of the authority holding negative opinions, and does not send positive opinions to the social network. Under the influence of individual media, the majority of the audience can make the convergence of the average opinion value almost consistent with natural evolution, so it cannot effectively curb the trend of public opinion evolution. Compared with compulsory intervention, gradual guidance gradually sends positive opinions that are easier for the audience to accept to the social network, which makes it show a better management effect than compulsory intervention under certain conditions, but its effect is also restricted by the network structure and scale. This restriction makes its effect on the OTC dataset and the WV dataset almost the same as that of compulsory intervention.

[0212] From the attached Figure 5 It can be seen from (e)-(h) that in most cases, the gradual guidance method will increase the proportion of individuals who choose strategy S1 in the evolutionary stable state, while the compulsory intervention method will generally lead to a decrease in the proportion of individuals who choose strategy S1 in the evolutionary stable state. Obviously, compulsory intervention, which directly releases extremely positive views in the social network, will significantly inhibit the tendency of individuals with negative or neutral views to choose to speak out, while the gradual guidance method will make the audience more receptive to the views of the authority, and while guiding their views to evolve positively, it can better maintain the enthusiasm of individuals to express their own views. On the other hand, information blockade does not have a significant impact on the proportion of individuals who choose strategy S1 in the evolutionary stable state. This is because information blockade only suppresses the voice channels of authorities with negative views, but the evolution of public opinion among other individuals is still similar to natural evolution, so the results it leads to are close to the same as 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 public opinion evolution research 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 to compare 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 the average opinion value 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 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 It can be seen that the MEPO model causes the average opinion value in different social networks to almost always remain consistent with the initial state, which means that under the premise that the group's opinion is slightly biased towards the negative, it fails to clearly reflect the "opinion polarization" phenomenon, making the group's opinion almost remain at a constant level. This shows that the MEPO model has convergence in the analysis and presentation of the evolution of public opinion in different social networks, which is not conducive to showing the differences in the changes of public opinion in different social networks.

[0216] Observing the results driven by the Degroot model, there is an approximately linear relationship between the average opinion value and the evolution time, and in the experiment of the OTC data set, the average opinion value shows an upward trend, indicating that opinion changes in social networks with high trust and high privacy are greatly affected by public opinion evolution. This means that the Degroot model is relatively significantly affected by the structure and initial state of the social network, and there are certain differences in the public opinion evolution trends driven by it, and there may be unknown risks beyond the actual public opinion evolution situation.

[0217] In addition, from the attached Figure 6It can also be seen that the IODM and HK models lead to significant differences in the results of public opinion evolution on different social networks. In the experiment of the ct dataset, IODM failed to make the average opinion value reach an evolutionary stable state, showing a trend of "first rising and then falling", which reflects that in Internet social media such as ct, the opinion changes in the evolution of public opinion are reversible within a certain period of time, which may be affected by the point guidance of opinion leaders in public opinion, or by the evolution or reversal of the event itself. In the otc dataset and the eec dataset, both IODM and HK models make the average opinion value have a certain "fluctuation" trend in the process of reaching the evolutionary stable state. At the same time, it can also be clearly observed that the HK model causes the average opinion value to show relatively rapid changes in a short period of time after the evolution begins. In the experiment of the wv dataset, both IODM and HK models lead to the rapid convergence of the average opinion value and maintain it at a level that is very different from the initial state.

[0218] Obviously, without intervention, the evolution of the average opinion value is very likely to fluctuate, but in the actual evolution of public opinion, the enhancement of the polarity of group opinions requires a certain amount of time and iteration, and is largely determined by the social influence of the public opinion event itself and the public attention it arouses. If the public opinion event itself is only an emergency event in a small range, or an ordinary event that occurs frequently, then the public's attention to this event will disappear in a short time. In the wv data set, the IODM and HK models cause the average opinion value to drop precipitously after the initial moment, and the result does not conform to the opinion evolution trend of public opinion events in the actual public opinion environment.

[0219] On the other hand, the observation Figure 6 From the curve shape in , we can see that the public opinion evolution model proposed in the present invention reflects the trend of gradual polarization of group opinions in four different forms of social networks, and also enables the average opinion value to reach a stable equilibrium state. It reflects the general law of public opinion evolution in different social networks, that is, the polarization and balance that group opinions may produce. This also proves that the model proposed in the present 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 in line 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 finance, public security, etc., the universal social values ​​of the public 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, namely, compulsory intervention and gradual guidance, have better effects than single information blocking, and under certain conditions, gradual guidance may show significantly better effects than compulsory intervention (such as the attached Figure 5 (d) shows the result). At the same time, it can be observed through the present invention that the proportion of strategy S1 selected generally has a trend of "first decreasing and then increasing" in the evolution process under different social networks. This is because in the early stage of evolution, among the opinions received by individuals, some opinions that contradict them have a greater negative impact on their satisfaction, which in turn leads to a weakening of the willingness of individuals to express their opinions. As the evolution time increases, the opinions of most individuals in the social network tend to be similar, and the satisfaction of individuals increases due to obtaining more similar opinions, which in turn enhances the willingness of individuals to express their opinions.

[0221] In fact, in the process of public opinion dissemination, when group opinions tend to be neutral, individuals often tend to "wait and see" when they first receive some opinions with strong polarity, but their opinions and attitudes may change in this process. As individuals perceive more opinions with distinct cognitive attitudes during the evolution process, their opinions will gradually become more polarized, and they will be more inclined to speak out in order to gain more social recognition. For example, the Italian Renzi Cabinet (Renzicabinet) government formulated and implemented two policies in 2014-2015: the "jobs act" labor market reform and the "labuonascuola" school reform, which caused heated discussions on the Internet social media. Through the study of relevant cases of this event, the data on Twitter were analyzed using aggregated sentiment analysis technology, and it was found that the evolution of public opinion on the Internet social media is cyclical, and the spread of polarized opinions will promote the intensity of public discussion on hot issues. This real case also further confirms the rationality 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 for 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 an approximate average degree and have a large difference in node scale. In different numerical settings and simulation experiments, the evolution of its 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 specific social network characteristics, so as to better avoid the waste of management costs.

[0223] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for establishing a public opinion evolution analysis model that integrates network game theory and opinion dynamics, characterized in that: 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 his or her opinions on 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.

2. The method for establishing a public opinion evolution analysis model integrating network game and opinion dynamics according to claim 1 is characterized by: The individual influence difference model described in step S1 is expressed as In the formula, p i Represents any node v i The influence value, PR i Represents node v i PageRank value, PR j Represents node v j The 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.

3. The method for establishing a public opinion evolution analysis model integrating network game 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 Γ={G,{δ i (t)|v i ∈V},{π ij (t)|v i ∈V,v j ∈N i },{o i (t)|v i ∈V}} In the formula, 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, with neighbor individual v j 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 The opinion value at the evolution time t uses the interval [0,1] to represent the individual opinion value range, max(o) = 1, min(o) = 0, o i (t)→1 represents that the individual has a 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 behavior strategies.

4. The method for establishing a public opinion evolution analysis model integrating network game 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 game 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 interactive satisfaction obtained through the game with neighbors, It means that at the time t-1 of evolution, individual v i The interaction satisfaction obtained through the game with neighbors, and is a Boolean variable used to judge the external cognitive pressure on an individual, and m represents the impact of group cognitive pressure on individual satisfaction; 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.

6. The method for establishing a public opinion evolution analysis model integrating network game and opinion dynamics according to claim 5 is characterized in that: The bilateral game decision model described in step S204 is expressed as In the formula, Represents individual v i For reachable neighbors v j The subjective probability of choosing strategy S1, strategy S1 is "expressing opinions"; the subjective probability of individuals choosing 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 °R=[Score1 Score2],W B =[w1,w2,w3] is the fuzzy weight vector considering three factors: 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. The method for establishing a public opinion evolution analysis model integrating network game and opinion dynamics according to claim 6 is characterized in that: The specific operation of step S3 includes 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 that it points directly to node v i The neighbor set, N i Represents node v i The set of all neighbors of ; S302: Combined individual v i Current views on individual v i The influence of neighbors who express opinions, determine the update rules of individual opinions, and build 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 of i (t) is expressed as 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 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 the value of v at time t i The set of neighbors who expressed their 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 previous 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, expressed as is the polarization coefficient; when hour, 8. A public opinion evolution analysis model established using the establishment method described in any one of claims 1-7.

9. Application of the public opinion evolution analysis model as described in claim 8 in formulating public opinion management strategies.

10. The use according to claim 9, characterized in that: The public opinion management strategies include information blocking, compulsory intervention and gradual guidance.

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