Are randomness of behavior and information flow important to opinion forming in organization?
AAre randomness of behavior and information flowimportant to opinion forming in organization?
Agnieszka Kowalska-Stycze´n ∗ , Krzysztof Malarz † Silesian University of Technology, Faculty of Organisation and Managementul. Roosevelta 26/28, 41-800 Zabrze, Poland AGH University of Science and Technology, Faculty of Physics and Applied Computer Scienceal. Mickiewicza 30, 30-059 Krak´ow, Poland
October 30, 2020
Abstract
We examine how the randomness of behavior and the flow of information between agents affectthe formation of opinions. Our main research involves the process of opinion evolution, opinionclusters formation and studying the probability of sustaining opinion. The results show thatopinion formation (clustering of opinion) is influenced by both flow of information between agents(interactions outside the closest neighbors) and randomness in adopting opinions.
Understanding what factors influence the formation of opinion in society is very important for manyaspects of an organization’s activities, including organizational behavior, organizational knowledgetransfer, leadership and many more. The basis of the proposed approach in this paper is to look at theorganization as a complex social system. This direction of research is more and more often seen as animportant element of management science (Kowalska-Stycze´n, 2018). To explain the specifications ofsocial systems (including organization) such as self-organization, order, chaos, complexity, the evolutionof mathematical theories must be extended (Ehsani et al., 2010). Such an extension of the theory is theusage of computer modeling, simulation, in particular agent-based modeling (Kowalska-Stycze´n, 2020).As emphasized by Acemoglu & Ozdaglar (2011), we acquire our beliefs and opinions through varioustypes of experiences, in particular through the process of ‘social learning’. As part of this process,people communicate with other people, they obtain information and they update their beliefs andopinions. The communication takes place with a subgroup of society consisting of friends, colleaguesand peers, co-workers and distant and close family members. Information obtained by a person froma particular partner on a social network is transferred to other members of that network. Dependingon the communication (information flow) in the social network, this information transfer may havea smaller or larger reach, the information may amount to more or less people. It should also benoted that in the formation of opinions, we often deal with unpredictability, as well as with irrationalprocessing of information (Sobkowicz, 2018; Stadelmann & Torgler, 2013).The purpose of this article is to study the formation of clusters of opinions (i.e. groups of peoplewith the same opinion). In a social network, individual opinions and interpersonal relationships alwaysinteract and evolve, leading to self-organization of clusters of opinions across the network (Zhang et al.,2013). Because it is very difficult to study social systems in terms of their complexity, researchers ∗ [email protected] † [email protected] a r X i v : . [ ec on . T H ] O c t ncreasingly use computer simulations. Therefore, in this article, we propose simulations carried outfor a model based on Latan´e (1981) theory of social impact, which takes into account both the differentflow of information between community members and the randomness of their behavior (noise). Thebasic assumption of Latan´e’s social impact theory is that people are members of a community andwithin that community they interact with each other. Social influence are all interactions betweenpeople (persuasion, joke, showing emotions, feelings, etc.). The theory of social influence is based onthree principles: social power, psychosocial law, and multiplication or division. The computer model used here has been formally described in the work by Ba´ncerowski & Malarz(2019). The model was also tested by Kowalska-Stycze´n & Malarz (2020) for two and three opinionsavailable in the system and initially randomly distributed among agents. The formation of opinionsin the community as a result of the flow of information and randomness of agents behavior wasinvestigated, and several phases in the behavior of the system (community) due to these parameterswere detected. In this paper, we focused on the relationship between the spatial distribution of opinionsand the probability of sustaining opinion by agents in opinion clusters.It should be noted that, the essence of social influence is not only exerting social influence, butalso succumbing to it. In the used model, this fact was taken into account by introducing the fol-lowing parameters: intensity of persuasion and intensity of support. These parameters determine theeffectiveness of which an individual may interact with or influence other individuals by changing orconfirming their opinions. These parameters are interpreted as follows: • intensity of persuasion: the larger 0 ≤ p i ≤ • intensity of support: the larger 0 ≤ s i ≤ i .In the simulations presented in the next section, random values of p i and s i for each agent wereassumed. As in previous works, we take into account two parameters of the model: information flowin the community and random behavior (noise). The varied flow of information in the community wasexpressed in the model by the parameter α (this parameter talks about the influence of close or distantneighbors in the community). Small values (e.g. α = 1 or 2) mean good communication betweenagents and good access to information (an exchange of information with a large number of agents inthe network takes place). The larger values of α , the weaker the communication between the groupsof agents (the exchange of information takes place only in the closest neighborhood, e.g. α = 6).The randomness of agents’ behavior is expressed by the parameter T (social temperature). If T = 0,then a lack of randomness is observed, and the agent adopts an opinion that has the most influenceon him/her. As T increases, more and more often opinions that do not have the greatest impact onagents are chosen.To sum up, in the used computer model: • The society is represented by agents occupying the nodes of the square lattice. Each networknode corresponds to one person. • Every agent i has one among K available opinions and, moreover, it is characterized by twoparameters: intensity of persuasion ( p i ) and intensity of support ( s i ). We assume random valuesof these parameters for all agents. • Each agent is influenced by all other agents. The strength of this influence decreases with in-creasing distance between them. Additionally, in order to reduce the impact of distant neighbors,the parameter α was introduced, which appears as a constant in the distance scaling function.2 The randomness of human behavior is reflected by T parameter, which characterize the entiresystem. • The simulations are carried out on square lattice of linear size L = 41 with open boundaryconditions. Let us start presentation of the results by showing the spatial distribution of opinions for K = 2 (twopossible opinion), for α = 2, 3, 6 (various levels of flow of information) and for T = 0, 1, 3, 5 (variouslevels of noise, i.e. various levels of randomness in the opinion adopting). As can be seen in Figure 1,both α and social temperature T have influence on opinion formation and polarization in the groups(self-organization of opinion clusters).For α = 2 (and α = 1) the consensus takes place (all agents accept one of two opinions), except ofsingle cases for large T values. The higher α , the less interactions unit has outside the closest neighborsgroup, which leads to lower polarization of opinions (there are more and more clusters, i.e. groupsof agents with the same opinions). In addition, small clusters are able to survive, although they aresurrounded by large clusters of agents with different opinion. An analogous situation occurs when the T parameter is increased. With larger T , there is more heterogeneity in the areas where actors withopposite opinions occur and the division into clusters is less pronounced (less polarization of opinionsin the groups). An increase of the social temperature T often results in the emergence of small clustersof agents with a minority of opinion. In general, the increase of T and causes that more clusters areformed, and the polarization of opinions in groups is weaker. For Figure 1 discussed in the previous Section, corresponding heat-maps have been created (see Fig-ure 2). Each agent is assigned to one point in the network with a certain color. This color depends onthe probability that agent will sustain his/her opinion. The colors change from yellow (high probabilityof sustaining opinion) to black (low probability of sustaining opinion). We do not show heat-maps for T = 0, because the probability of sustaining the opinion has then only two values: either 0—the agentwill change his/her opinions or 1—the agent will sustain his/her opinion. The smallest probability ofsustaining the opinion occurs for agents on the outskirts of clusters—compare Figure 2 to Figure 1. Inaddition, this probability is higher in large clusters than in small ones. This likelihood also decreaseswith the increase of T (more and more darker colors in the agents’ network). This probability is ofcourse affected by T and α . The higher T , the less probability of sustaining the opinion (less yellow),which is especially visible for α = 6 in the Figure 2i and Figure 2l. The chances of sustaining thecurrent opinion of agents also decrease with the rise of α (there is more and more darker color). Tosum up, the greater the randomness of behavior and the smaller the flow of information (i.e. greater α ), the less yellow color in the heat-maps is observed (a lower probability of sustaining opinion inthe entire lattice of agents), which is particularly evident in Figure 2i ( T = 3) and Figures 2k and 2l( T = 5). Analyzing the results in the previous Section, the clustering of opinions is influenced by both thelevel of randomness in agents’ decisions ( T ) and the influence coming from close or distant neighbors( α ). For clusters detection, the Hoshen & Kopelman (1976) algorithm has been applied. In Hoshen–Kopelman algorithm each agent is labelled in such way, that agent with the same opinions and in the3 a) α = 2, T = 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (b) α = 3, T = 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (c) α = 6, T = 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (d) α = 2, T = 1
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (e) α = 3, T = 1
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (f) α = 6, T = 1
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (g) α = 2, T = 2
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (h) α = 3, T = 2
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (i) α = 6, T = 2
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (j) α = 2, T = 3
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (k) α = 3, T = 3
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ (l) α = 6, T = 3
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 x y ξ Figure 1: Spatial distribution of opinions for K = 2 opinions for various α and various social temper-atures ( T ) after t = 100 time steps of the system evolution (red and green mean different opinions). L = 41. 4 a) α = 2, T = 1
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (b) α = 3, T = 1
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (c) α = 6, T = 1
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (d) α = 2, T = 2
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (e) α = 3, T = 2
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (f) α = 6, T = 2
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (g) α = 2, T = 3
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (h) α = 3, T = 3
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (i) α = 6, T = 3
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (j) α = 2, T = 5
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (k) α = 3, T = 5
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P (l) α = 6, T = 5
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 x y P Figure 2: Spatial distribution of probabilities of sustaining opinion for K = 2 opinions, social temper-ature T and for various values of α after t = 100 time steps of the system evolution. L = 41.5able 1: The relative size of the largest cluster S max /L for L = 41. α = 1 2 3 6 T = 0 100% 94% 54% 34%1 100% 100% 83% 57%2 100% 99% 92% 62%3 100% 99% 92% 24%4 100% 99% 90% 15%5 100% 100% 85% 12%same cluster have identical labels. The algorithm in this paper was used for a square lattice with vonNeumann neighborhoods (with the nearest neighbours interactions).In Table 1, the relative size S max /L of the largest cluster after t = 1000 simulations time stepsfor different values of T and for K = 2 has been shown. These results coincide with Figure 1. In allcases, for α = 1, the largest cluster fills the entire lattice in 100% (i.e. there is a consensus in opinion).It should be noted that this is a situation in which most agents in the lattice influence the opinion ofthe selected agent (the flow of information between agents is very good). For α = 2, the influence ofother agents in the lattice is still greater than the influence of the closest neighborhood. The size ofthe maximum cluster then fluctuates around 100% of the network size (i.e. one large cluster with oneopinion). In general, for any size of T , the size of the largest cluster of opinions decreases with theincrease of α .In order to get a better look at the clustering of opinions, the average number of small and largeclusters after thousand time steps for hundred simulations was also studied (see Figure 3). We assumedthat small clusters contain no more than five agents sharing the same opinion ( S ≤ T ) often results in the formation of small clusters of opposing opinions (as canbe seen in the Figure 1). The number of clusters increases with an increase of α , i.e. the smaller theinfluence of all agents in the network on the selected agent, the more difficult is appearing the opinionsclustering. In general, the number of clusters increases with T , but for α = 3 and α = 6 and for T = 1,the number of clusters is lower than for T = 0. First of all, the probability of a new cluster forming(with opposite opinion) inside another cluster is still very small. Secondly, the probability of changingopinions is greater at the clusters borders than inside the cluster. If the adjacent clusters have differentsizes, then the probability of changing the agent’s opinion in a smaller cluster is greater than in thelarger one. This situation leads to the disappearance of small clusters, or in general to a reductionin number of clusters. We can see similar phenomena in terms of the number of small clusters (seeFigure 3). The number of small clusters increases with T (of course, apart from low T values and for α > In this article, we used a cellular automaton model in which the theories of Latan´e’s social influencewere implemented. We studied how the social temperature (randomness of human behavior) and theflow of information in society influenced the clustering of opinion. To achieve this goal, the spatialdistribution of opinions, probability of sustaining opinion and the number of clusters were studied.First, the spatial distribution of opinions after 100 steps of simulation was analyzed. The simulationsshowed how clusters of opinion are formed depending on the flow of information in the agents’ network,as well as after considering the randomness in forming the opinion. Consensus (one large cluster) waspossible for K = 2 (two opinions) for low values α ( α = 1, 2), when agents formed their opinionsalso contacting more distant agents (that is, when the flow of information was good in the wholecommunity). 6 a) α = 1 T S ≤ S > (b) α = 2 T S ≤ S > (c) α = 3 T S ≤ S > (d) α = 6 T S ≤ S > Figure 3: Histogram of cluster sizes S for various values of the temperature T and parameter α . L = 41.Generally, the greater the α and T , the more clusters, i.e. groups of agents with the same opinions(less polarization of opinions in the groups). Of course, it should be noted that the appearance ofnoise in the system ( T = 1) slightly orders the system in relation to the situation when T = 0 (lack ofrandomness). This is in accordance with other studies (Ren et al., 2007; Biondo et al., 2013; Shirado& Christakis, 2017; Kowalska-Stycze´n & Malarz, 2020), in which a low noise level has brought orderto the system. With the formation of opinion clusters, the probability of sustaining opinion is closelyrelated. This probability is greater within the clusters than at their borders and it is larger in thelarger clusters (Figure 2). This leads to the disappearance of small clusters, and thus to reduction ofthe number of clusters.The formulation of opinions is also described by the number and size of clusters of opinion. Theclustering of opinions is influenced by both the level of randomness in agents’ decisions and the influencecoming from neighbors. Generally, the size of the largest cluster of opinions decreases with the increaseof α . This, of course, corresponds with the spatial distribution of opinions (see Figure 1). Furthermore,the number of clusters increases with α , i.e. the smaller the influence of all agents in the network onthe selected agent, the more difficult it is for forming clusters of opinions. An interesting phenomenonoccurs in the case of analysis of the impact of T (for T > α (when information7able 2: The impact of both T and α on the formation and spread of opinions.Impact on for T > α Spatial distribution of opinions The greater the T , there aremore and more clusters The greater the α , there aremore and more clustersProbability of sustaining opinion The higher T , the less prob-ability of sustaining the opin-ion The higher α , the chances ofsustaining the current opin-ion of agents decreaseClustering of opinions The number of clusters in-creases with T The number of clusters in-creases with α . The size ofthe largest cluster decreaseswith the increase of α Summary Generally randomness (irra-tionality) hinders polariza-tion of opinions in groups The better the flow of infor-mation in the community, theeasier it is to form and spreadopinions, which can also leadto consensusflow is very good), the result of the simulation is a consensus, as in most sociophysical models of socialdynamics (Castellano et al., 2009). For large values of α (when opinions are consulted only in theclose neighborhood), the polarization of opinions is weak and there are many small groups of agentswith the same opinion. In addition, the presence of many small clusters causes a lower probability ofsustaining opinion for individual agents, i.e. they change their opinions more often.As mentioned earlier, the better the flow of information in the community, the better the opinionspreads and the more often there is consensus and polarization of opinions. Also, Bj¨orkman et al.(2004) and Tsai (2002) emphasize that good communication and wide interaction channels favor theexchange of knowledge and information. In organization, good spread of opinions and informationis particularly important in the case of organizational change, organizational culture and knowledgetransfer. Managers should therefore ensure good information flow between members of the organizationby creating both formal information flow channels and informal communication networks. Moreover,they should make sure that the number of members in the organization who act in a random andunpredictable manner is small, because the more randomness in the organizational behavior, the lesschance of polarization of opinions and consensus appearing. References
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