OpinionExpressionDynamicsinSocialMediaChatGroups:An ......people’s daily life [4]. Unlike open social media platforms that produce outbursts of information, social media groupsprovide

Review ArticleOpinion Expression Dynamics in Social Media Chat Groups AnIntegratedQuasi-Experimental andAgent-BasedModel Approach

Siyuan Ma 1 and Hongzhong Zhang 2

1Department of Communication Michigan State University East Lansing MI USA2School of Journalism amp Communication Beijing Normal University Beijing China

Correspondence should be addressed to Hongzhong Zhang zhanghz9126com

Received 25 July 2020 Revised 17 September 2020 Accepted 28 December 2020 Published 9 January 2021

Academic Editor Hongshu Chen

Copyright copy 2021 Siyuan Ma and Hongzhong Zhang is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Social media chat groups such as WeChat andWhatsApp groups are widely applied in online communication is research hasconducted two studies to examine the individual level and collective levelrsquos opinion dynamics in those groups e opiniondynamic is driven by two variables peoplersquos perceived peer support and willingness of opinion expression e perceived peersupport influences the willingness of opinion expression and the willingness influences the dynamics of real opinion-expressionFirst the quasi-experimental study recruited twenty-five participants as the observation group and found that decreasingperceived peer support would significantly increase individualsrsquo expression willingness to protect hisher opinion To generalizethe individual level findings to a collective level the second study treated the social media chat groups as an undirected fully-connected social network and simulated peoplersquos opinion expression dynamics with an agent-based model e simulationindicated that (1) with the help of increased willingness of opinion expression the minority opinion supporters as a collective didnot fall silent but continue to express themselves and (2) increasing willingness of opinion expression would maintain theexistence of minority opinion but could not help the minority reverse to the majority

1 Introduction

Opinion discussions on social media have become increasinglydiversified when accompanied by the progress of media tech-nology diversification of personal interests and requirements ofgratification [1] is diversified feature boosts the formation ofsocial media chat groups (short for social media groups) such asWhatsApp groups WeChat groups and Interest groups inonline forums [2] Each social media group has regularmembers and focuses on some specific topics [3] By analyzingthe number of active users monthly social media groups havebecome increasingly popular and hold a broader influence onpeoplersquos daily life [4] Unlike open social media platforms thatproduce outbursts of information social media groups providean environment that allows a more in-depth discussion ofopinions which has a long-term impact on their users [5]

erefore the dynamic of opinion expression in social mediagroups is an essential topic and worth further study

An ideal media environment should not hinder theexpression of opinions especially minority opinionsAccording to Habermasrsquo public sphere theory [6] preservingspace for the exchange of opinions helps maintain politicallegitimacy social stability and protect the welfare of citizensUnfortunately it is hard for the mass media to provide anideal environment for opinions For instance opinions inmass media tended to grow more extreme [7 8] and theexpression of minority opinions tended to fall silent [9ndash11]However some recent studies proposed different findingsthat social media groups could provide a space for the ex-pression of opinion especially minority opinions (eg[12 13]) us researchers design two studies with thefollowing questions

HindawiComplexityVolume 2021 Article ID 2304754 14 pageshttpsdoiorg10115520212304754

(1) Quasi-experiment is individualsrsquo willingness ofopinion expression protected in social media groups(2) Agent-based model simulation how do individualsrsquowillingness of opinion expression trigger the collectivebehavior like the whole grouprsquos dynamics of opinionexpression

2 Related Work

21 Conflict Presumptions of Individual Opinion ExpressionWillingness Spiral of Silence versus Corrective ActionWillingness of opinion expression refers to individualsrsquoeagerness to share or post their opinions in public [14 15]is term is widely used as a dependent variable in com-munication and political science studies Previous studieshave long been concerned that perceived peer support affectsindividualsrsquo willingness of opinion expression Howevertheir primary two presumptions of that ldquoeffectrdquo are inconflict with each other

First the spiral of silence theory suggests that the de-crease of perceived peer support could lessen individualsrsquowillingness of opinion expression or even silence it becauseof peoplersquos fear of isolation [9 16 17] e spiral of silencetheory proposes that because individuals are afraid of beingisolated thus more perceived support will increase peoplersquoswillingness of opinion expression while less support willlessen the willingness [18 19] is theory was proposed inthe traditional mass media environmentus the perceivedsupport referred to support from mass media Researcherslater extended this support to peer relations and socialmedia Research by Oshagan [20] introduces the concept ofthe reference group which is used as a synonym of peer todescribe family members intimate partners colleagues andneighbors Studies use this concept for reference and pro-pose that reducing perceived peer support is even moreeffective than reducing mass media support when it tries tolessen individualsrsquo willingness of opinion expression[16 17 21]

On the contrary the corrective action hypothesis pro-poses that controversial issues will inspire people to speakout their thoughts to change othersrsquo perceptions of publicopinion [22] When people perceive news or comments onsocial media going biased against them they are concernedthat the public may be swayed in that direction Because ofthis fear people are motivated to take action to correctpublic opinion by speaking out even when their opinion is inthe minority [23] Similar findings are found both in thenews report and social media discussion situation peoplewho have received hostile news or received negative socialmedia comments on their opinion would like to speak out toprotect their opinion [24 25]

Evidence suggests that whether audiences are motivatedto keep silent or speak out depends on how they perceiveothersrsquo opinions [26] To deduct from the theory whenpeople feel the fear of isolation the decrease of perceivedpeer support will lessen the willingness of opinion expres-sion [27] However if people do not feel such fear theperceived peer support will not diminish or even increase thewillingness of opinion expression Nowadays people have

more peers on social media (although they may never meetoffline) comparing with the traditional mass media age andthey are more likely to find online peers who share the sameopinions [12 28 29] Because people are able to get psy-chological support conveniently from their online peersthey will not easily feel the fear of isolation [13] ereforeeven though individuals perceive they are the minorityrather than the majority their willingness of opinion ex-pression may not decline but even increase For instancesome studies found people who held the minority opiniondid not have much change in their willingness of opinionexpression while comparing with majority opinion [15 30]Besides some studies proposed that minority perceptionincreased individualsrsquo willingness of opinion expression[23ndash25 29]

To sum up the findings above there are conflictingconclusions between perceived peer support and willingnessof opinion expression Traditional mass media studies findthat a decrease of support will lessen individualsrsquo willingnessof opinion expression [9 16 17 20] However recent socialmedia studies have found that the perceived peer supportwill not decrease or even encourage this willingness (eg[29 30] In the current study social media groups created anunbiased fully-connected social network to help membersget in touch with each other more conveniently whichsuggests that people may not feel much fear of isolationerefore this research proposes the first research questionas follows

RQ1 Will the decrease of perceived peer support en-hance individualsrsquo willingness of opinion expression insocial media groups

e current research has conducted a quasi-experiment(study 1) to answer this question Details are presented laterin this article

Moreover some other variables also influence thewillingness of opinion expression First the spiral of silencetheory [9] proposes hardcore to describe the people who arewilling to express their opinions consistently regardless ofsocial pressure Studies have shown that if the hardcore isremoved minority opinion supportersrsquo willingness to ex-press will significantly decrease [31ndash33] Furthermore fearof authority lack of self-efficiency feeling the importance ofthe issue accessibility of different opinions and technicalconditions of communication could all influence personalopinion expression [13 33] In order to keep these variablesconsistent the quasi-experiment applies repeated mea-surements on each individual

22 Simulating theCollectiveOpinionExpressionDynamicsbythe Agent-Based Model According to Sawyerrsquos [34] mech-anism of emergence collective phenomena are collabora-tively created by individuals yet may not reducible toindividual action erefore to generalize individual-levelfindings to the collective behavior of opinion expression in asocial media chat group we need an agent-based model(ABM) to simulate the dynamics e ABM consists ofagents system space and external environment Agents have

2 Complexity

various attributes and are heterogeneous ABMrsquos rules act onthe agents rather than the process of action [35 36] Eachagent is autonomous and decides hisher behavior bylearning memories interacting with the neighbors or theexternal environment with the rules of behavior [37] Toapply ABM in the current research it will take into accountpeoplersquos initial opinion distribution in the social mediagroup the rules of opinion expression and the evolutionprocess After setting up rules new phenomena will emergefrom ABMrsquos simulation Previous ABMs of opinion dy-namics were originated from the Ising model e two spinstates of the Ising model corresponded to any relative set ofconcepts in social science such as the concepts of right orwrong and speaking out or silence In principle this modeldescribes all multibody systems with two possible states [38]Several representative evolutions of the Ising model areapplied to the research of public opinion such as the Votermodel Sznajd model Majority-rule model Krau-sendashHegselmann model and Deffuant model [39 40]

Although there were conflicting presumptions of theopinion expression willingness from individual-level studiesprevious simulation studies mainly bought the idea of thespiral of silence which proposed that less peer supportwould reduce the willingness and then also reduce or evensilence the opinion expression For instance the study as-sumed people who received external opinion pressure largerthan peer support would be less likely to speak out to protecttheir opinion As time progressed the minority opinionwould fall into silence in any kind of social network es-pecially when it was the BarabasindashAlbert scale-free network[41] Social bot studies also proposed that the spiral of silencetheory would lead agents to consensus opinion in a socialnetwork with some agents being silenced However ap-plying a small number of bots would easily shape the normsadopted by social media users and tip over the opinionclimate [42]

e current research has found that those proposedmodels can be improved from two perspectives First weshould analyze changes in opinion expression instead ofchanges of opinions Some studies did not pay much at-tention to the difference between opinion expression and theopinion itself From their assumption every change of anagent would be assumed as the change of opinion itselfwhich referred an individual would change his or heropinion after receiving some influence from an oppositeposition (eg [35 42 43]) However this assumption is notentirely consistent with the evidence According to the spiralof silence theory and echo-chamber effect the change ofopinion does not happen in such a straightforward way Onthe contrary the opinion expression is relatively easier tochange [44 45] Besides a silenced position does not nec-essarily mean the person has changed hisher idea Secondlywe should use behavioral data to support the design of ABMwhile previous studiesrsquo simulation did not have muchsupport from real behavioral data For instance Sohn andGeidner [46] did distinguish the opinion expression and theopinion itself interpreting the opinion dynamics moreaccurately However lacking real data intended that theirmodel needed more parameters to adjust and thus reduced

the validity [47] Besides previous models did not pay muchattention to the possibility that the spiral of silence may notexist in the social media environment us behavioral datacan help revise the rules of ABM

In order to improve the two perspectives of modelsimulation mentioned in the previous paragraph this studyhas planned to develop an agent-based model in study 2 thatis consistent with quasi-experimental findings us thecurrent research proposes as follows

RQ2 How do individualsrsquo change of opinion expres-sion willingness influence the whole grouprsquos dynamicsof real opinion-expression

In order to clarify the relationship between study 1 andstudy 2 we provide a workflow See Figure 1 formore details

3 Study 1 Quasi-Experiment in SocialMedia Group

31 Methods is study has designed a three-conditionquasi-experiment to explore the relationship between per-ceived peer support and willingness of opinion expressionfrom an individual level

311 Participants e quasi-experiment recruited 25 stu-dents from a North China university to form the observationgroup ose 25 participants all had the same opinionstowards three similar questions e quasi-experimentconsisted of three conditions that the observation group had(1) more members (2) evenly-matched members or (3)fewer members when compared with the opposite opiniongroup When the observation group members were morethan the opposite opinion group we named the observationgroup as a majority opinion condition when the memberswere balanced we named it as a balanced opinion conditionwhen the members were fewer than the opposite opiniongroup we named it as aminority opinion condition For eachcondition we asked those people to discuss one of the threequestions e opposite opinion group contained differentnumbers of people in different conditions and the currentstudy recruited volunteers to form the opposite opiniongroup Besides those volunteering opposite group memberswere not the object of analysis

312 Stimuli e stimuli in this quasi-experiment were theproportion of the observation group in the total participantsWhen the proportion was high (which referred to majorityopinion condition) we observed high perceived peer sup-port when the proportion was balanced (balanced opinioncondition) we observed medium perceived peer supportwhen the proportion was low (minority opinion condition)we observed low perceived peer support e manipulationcheck results are shown in the result part of study 1

e quasi-experimental conditions and participantsrsquoarrangements are shown in Table 1

Complexity 3

313 Procedure First the researchers designed a surveywith 15 questions and each of them had two oppositeopinions All the questions were about the campus life in thecollege to make sure the participants had enough experienceand background knowledge to discuss them A total of 127students from a North China University participated in thesurvey

Second 25 students who had the same opinion on threeof those questions were recruited to form the observationgroup e researcher announced that all participants whoshowed up in the experiment would be awarded the sameresearch credits in the course the credits were only related towhether they showed up in the experiment or not not re-lated to how active they behaved us even though theresearcher could know how many comments each personhad made in the discussion the participants would not feeltoo much pressure of expressing themselves Not beingactive does not impair their profits in this course

ird the researchers recruited volunteers who partic-ipated in the survey ey were assigned opinions that wereopposed to the observation group e researchers alsoprovided credible materials so that the opposite opiniongroup members had enough knowledge to discuss with theobservation group

Fourth the quasi-experiment manipulated the level ofperceived peer support by changing the different conditionsmentioned as follows majority opinion balanced opinionand minority opinion condition In each condition weorganized a group discussion which lasted approximately30minutes Discussion topics were the three questionsmentioned in the second step

Finally researchers controlled experimental conditionsIn order to simulate the anonymous social media

circumstance each participant had a pseudoname epseudoname changed after each discussion In additionoffline communication was not allowed erefore an in-dividual of the observation group only knew that somepeople supported his or her opinion but could not match thepeople in the social media group to the offline is designalso helped to reduce the pressure of ldquoyou must speak outrdquofrom acquaintance friends

Because of participantsrsquo personal reasons three obser-vation group members did not participate in the firstcondition six members missed the second condition andfive members missed the third condition e current studyused an average interpolation method to handle the missingvalues

314 Measurement Perceived peer support and willingnessof opinion expression all need operational definitions In thisquasi-experimental design the two concepts aremeasured asfollows

(1) Perceived Peer Support In a social media group anindividualrsquos perceived peer support includes allcomments from the same-opinion people In tra-ditional mass media perceived peer support washard to quantify Researchers relied on self-report-ing asking how much the participant thought thatother commenters could support his or her opinionwith a Likert scale [14] In this quasi-experimentparticipants are not able to report their perceptionswhile participating in the discussion However allcomments in the social media group are recorded sothat we can use the real ldquoreceived peer supportrdquo torepresent the perceived support Some evidence in

Core question how do opinion dynamics work in social media chat groups

Study 1 quasi-experiment

Result individual level question answered

Updating ABM rules based on study 1

Study 2 agent-based model

Individual level unanswered question

perceived peer support opinion expression willingness +ndashCollective level unanswered question

Willingness dynamic of real opinion expression how

Figure 1 e workflow between study 1 and study 2

Table 1 Quasi-experimental participants arrangement

Condition Observation groupmembers

Opposite opinionmembers

Expected level of perceived peersupport

Majority opinion (more observation members) 64 (N 25) 36 (N 14) HighBalanced opinion (evenly-matched observationmembers) 53 (N 25) 47 (N 22) Medium

Minority opinion (fewer observation members) 39 (N 25) 61 (N 40) LowNote e majority opinion situation refers that observation group members are more than the opposite opinion group the balanced opinion situation refersthat observation group members are evenly-matched with the opposite opinion group the minority opinion situation refers that observation group membersare fewer than the opposite opinion group

4 Complexity

previous studies supported this operationalizationFor instance youngsters who got less support fromtheir partners would report less perceived peersupport and exhibited more psychosocial adjustmentproblems [48] and another psychological studyabout new mothers indicated that receiving more

peer support would increase the perceptions of beingtrusted accepted in the relationship [49] osestudies support that received peer support can be agood predictor of perceived support ereforeperceived peer support is measured as a ratio asfollows

perceived peer support the number of comments that an individual received from same opinion people

the number of all comments (1)

Note ldquothe number of all commentsrdquo should excludecomments made by this individual himherself

(2) Willingness of Opinion Expression Similar to theperceived peer support all comments in the groupdiscussion are recordederefore the willingness ofopinion expression is measured as the number ofcomments that an individual has posted during thediscussion

e current study created a workflow of doing study 1See Figure 2 for more details

32 Results e current study used a quasi-experiment tomeasure two variables and their relationships perceivedpeer support and willingness of opinion expression eresearch used individual-level repeated measurement

321 Manipulation Check e current study applied re-peated measurement F-test to examine whether changingthe situation of the majority opinion to a balanced opinionand aminority opinion wouldmanipulate the perceived peersupport or not

e result in Table 2 depicted that all different types of F-test concluded that the variation of the majority opinionbalanced opinion and minority opinion changed perceivedpeer support significantly

e current study made pairwise comparisons to ex-amine whether the direction of manipulation was correct ornot During the comparisons 1 represented the majorityopinion condition 2 represented the balanced opinioncondition 3 represented the minority opinion condition

is pairwise comparison in Table 3 concluded thatduring the process from the majority condition to a balancedcondition the perceived peer support decreased nonsig-nificantly during the process of the balanced to minoritycondition and from majority to minority the perceived peersupport decreased significantly In general it meant theperceived peer support was successfully decreased bychanging an opinion group from the majority condition to abalanced condition and then to a minority conditionerefore the manipulation was acceptable

322 Correlation Analysis Repeated measurement corre-lation analysis (Rmcorr) is a method specifically designed toanalyze the correlation between two variables under the

repeated measurement condition [50] is method isdesigned and efficiently reported within-group variance[50] Because the current study measured each individualthree times the Rmcorr would be an appropriate tool toanalyze the data A Rmcorr R-package was prepared tomeasure the correlations between perceived peer supportand willingness of opinion expression

e results in Table 4 showed that when the obser-vation group increased from the minority situation to abalanced situation then to a majority situation thecorrelation between perceived support and willingnesswas negative and significant (r minus0367 p 0008)According to the r and p value statistics indicated thatthe decrease of perceived peer support would significantlyincrease the willingness of opinion expression

Moreover the current study examined the relation-ship in two more concrete scenarios as follows (1) whenthe balanced opinion situation increased to the majorityopinion situation (2) when the minority opinion situa-tion increased to the balanced opinion situation

Results in Table 5 showed that when the observationgroup increased from the balanced situation to a majoritysituation the correlation between perceived support andwillingness was negative and nonsignificant (r minus0200p 0327) When the observation group increased fromthe minority situation to a balanced situation the cor-relation between perceived support and willingness wasnegative and significant (r minus0604 p 0001) Accordingto the r and p value statistics indicated that people in aminority opinion situation was more sensitive to thewillingness of opinion expression rather than people in amajority opinion situation

erefore the quasi-experiment concluded as (1) thedecrease of perceived peer support would increase thewillingness of opinion expression in a social media groupand (2) members in a minority opinion were moresensitive to the change of peer support When perceivedless peer support they were more willing to speak outrather than members in a majority opinion or vice versa

With the significant negative influence of perceivedpeer support towards the willingness of opinion ex-pression the research moved to a further step Wouldindividualsrsquo change of opinion expression willingnessinfluence a whole grouprsquos opinion expression dynamicsAn agent-based model was designed to answer thequestion in the next study of the current research

Complexity 5

4 Study 2 Opinion Expression Dynamics withAgent-Based Model Simulation

41Modeling Opinion Expression Dynamics of a SocialMediaGroup is study has designed an ABM to simulate theopinion expression process and observe the collective levelrsquosemergent phenomena of two conflict opinion clustersrsquogambling Specific operations and conclusions are detailedin the following sections

411 Basic Rules of the ABM Combined quasi-experimentconclusions with previous theories (eg corrective action)which mentioned opinion expression and the study hassummarized three basic rules to design the ABM

(1) Once the opinions are determined it is difficult toreverse them e only factor that can change is thewillingness of opinion expression not the opinionitself

(2) When people perceived their peer support is de-creasing they are more willing to speak out eperceived peer support of onersquos opinion is measured

by the same ratio in the quasi-experiment that equalsto

P(support) the number of comments that an individual received from the same opinion cluster


Table 4 e repeated measurement correlation between perceivedpeer support and willingness of opinion expression

Item Resultr (correlation) minus0367lowastlowastlowastdegrees of freedom 49p value 0008lowastlowastlowastplt 0001

Table 5 e repeated measurement correlation under balan-ced⟶majority condition and minority⟶ balanced condition

Balanced⟶majority Minority⟶ balancedItem Result Resultr (correlation) minus0200 minus0604lowastlowastlowastdegrees offreedom 24 24

p value 0327 0001lowastlowastlowastp lt 0001

Minority opinion situation

Observation group Opposite opinion groupMore members than

Observation groupNearly equal members

Observation groupFewer members than

Majority opinion situation

Balanced opinion situation

=

=

=

High perceived peersupport

Medium perceivedpeer support

Low perceived peersupport

Manipulation check

Willingness ofopinion expression



Testing correlation

Opposite opinion group


Figure 2 e workflow of study 1

Table 2 e significant test of manipulating the level of perceived peer support

Source Measurement Mean square F Sig

Perceived peer support

Spherical distribution hypothesis 0124 10489 0000GreenhousendashGeisser 0171 10489 0001

Huynh-Feldt 0162 10489 0001Lower limit 0248 10489 0004

Note Spherical distribution hypothesis GreenhousendashGeisser Huynh-Feldt and lower limit refer to different measurement methods

Table 3 Pairwise comparison of manipulating the level of perceived peer support

Measurement Opinion proportion Mean difference SE Sig b

Perceived peer support1⟶ 2 minus0055 0042 06211⟶ 3 minus0152lowastlowastlowast 0031 00002⟶ 3 minus0097lowastlowast 0025 0003

Note e significance level of the mean difference is 005 the adjusted multiple comparison method is Bonferroni lowastlowastplt 001 lowastlowastlowastplt 0001

6 Complexity

(3) Minority opinion cluster members are more sensi-tive to the change of perceived peer support whilecomparing with the majority

412 Agents and Initial Assigned Parameters in the ABMe study defined that all the agents were contained in thesame chat group Each agent represented a person in thegroup and those agents could freely communicate with eachother In other words this social media chat group wasdefined as an undirected and fully-connected social networkis network was separated into two opinion clustersnamed A and B e two clusters had conflict opinions(assigned as opinion 1 or minus1) towards each other For eachagent in one cluster it also had an initial percentage ofopinion expression willingness which was randomlyassigned by numbers ranging from 0 to 100 which issimilar to Gaussian distribution

P(willingness) randomnumber[0 1] (3)

0 represented that the agent did not have any will-ingness of opinion expression while 100 represented thatthe agent must speak out when it was given a chance eparameter cannot exceed 1 or below 0 at any time during thesimulation When it exceeds 1 or below 0 it will be countedjust as 1 or 0 To be specific the code set random number ofP(willingness) based on Gaussian distribution with μ 05and σ 1 if the random number of an agent exceeded 1 orbelow 0 the code would randomly assign a new number tothis agent until it fell into the range of [0 1] us the finaldistribution of P(willingness) is an approximately Gaussiandistribution but with higher kurtosis is is an acceptableassumption because social science discipline usually assumes

human behavior concepts following Gaussian distributionFor instance Chun and Leersquos paper [14] used structuralequation modeling (SEM) to analyze the relationship ofperceived peer support and willingness to speak out whilethe basic presumption of SEM is the two variables followGaussian distribution

To sum up the social media group was defined as a fullyconnected network and had two competing opinion clustersA and B For each agent in any cluster it was assigned as anopinion and a percentage of opinion expression willingnesse assigned opinion could not change in the ABM but thepercentage of willingness could change over time

413 Round of Speaking e discussion in a real socialmedia group could be conducted alternately by two conflictopinion clusters and formed a flowing stream of statementsIn the ABM the current study simulated the dynamics bydefining round of speaking e whole discussion processwas segmented by several rounds of speaking In each roundwe randomly picked up several agents and asked if theychose to speak e percentage of opinion expressionwillingness (which was defined in 412) was used here todetermine whether the agent chose to speak or not After oneround of speaking we moved to the next round

414 Modeling Perceived Peer Support e current studyexplicitly defined two types of perceived peer support efirst one was p(initial support) which represented the initialperceived peer support e p(initial support) was oper-ationalized as

P(initial support) the number of statements in the first15 rounds fromone opinion cluster(eg opinionA)

the number of all statements in the first15 rounds (4)

e second one was p(later support) which representedthe perceived peer support in the later one round ofspeaking e p(later support) was operationalized as

P(later support) the number of statements in one round fromone opinion cluster(eg opinionA)

the number of all statements in one round (5)

When the agents in one opinion cluster found theirP(later support) was less than P(initial support) that meantthey perceived less peer support or vice versa

415 Modeling Willingness of Opinion ExpressionAccording to the basic rules when agents perceive less peersupport (than before) they will increase the willingness ofopinion expression On the contrary when they perceivemore peer support they will decrease the willingness ofopinion expression Besides minority opinion agents change

their willingness broader than majority opinion agents ecurrent study defined the changing percentage of willingnessas p for minority agents and the changing percentage ofwillingness as q for majority agents pwas larger than qif there were onemajority and oneminority opinion clustersOn a special occasion p was equaled to q if the twoopinion clusters had the same number of agents

416 e Procedure of ABM Simulation Using the basicrules and parameters let the agents work as follows

Complexity 7

Step 1 Assumed that there was a social media group of100 agents some belong to opinion cluster A and somebelong to BStep 2 Randomly assigned initial P(willingness) to eachagent with a similar Gaussian distribution For in-stance suppose A was the majority opinion and B wasthe minority opinion Ai(1 30) meant an agent incluster A was assigned to opinion 1 and P(willing-ness) 30 possibility to speak out when given achance Bj(minus1 50) meant an agent in cluster B wasassigned to an opposite opinion minus1 and P(willing-ness) 50 possibility to speak out when given achanceStep 3 Set 100 rounds of speaking and in each roundwe randomly selected N 10 agents Whether the tenagents chose to speak or not were depended on theirpercentage of opinion expression willingness For in-stance if Ai(1 30) was one of the 10 agents selected inone round it would have a 30 possibility to speak outin that round Here the 100 rounds of speaking areused to simulate a real discussion time of a topic Eventhough it is possible that after several thousands ofdiscussion rounds later the majority and minoritysituations are switched it is less possible to have such along-lasting discussion in the real worldStep 4 e simulation ran 15 rounds first then cal-culated p(initial support) of opinion A and opinion BStep 5 Starting from round 16 for each round if oneopinion clusterrsquos perceived peer support changedcomparing with the total first 15 rounds we had foursituations

A e opinion cluster was the minority and the peersupport decreased ose agents would increase theiropinion expression willingness by p For instance ifcluster B found

P(later support)ltP(initial support)

thenBj(t + 1) minus1 50lowast(1 + p)( 1113857(6)

B e opinion cluster was the majority and the peersupport decreased ose agents would increase theiropinion expression willingness by q For instance ifcluster A found


thenAi(t + 1) 1 30lowast(1 + q)( 1113857(7)

C e opinion cluster was the minority and the peersupport increased ose agents would decrease theiropinion expression willingness by p For instance ifcluster B found

P(later support)gtP(initial support)

thenBj(t + 1) minus1 50lowast(1 minus p)( 1113857(8)

D e opinion cluster was the majority and the peersupport increased ose agents would decrease theiropinion expression willingness by q For instance ifcluster A found


then Ai(t + 1) 1 30lowast(1 minus q)( 1113857(9)

Once determined an opinion people in the group wouldnot change their views e most extreme possibility was theopinion remained unchanged but the percentage of opinionexpression willingness was 0 or 100

is study used a C++ program to run the ABM

42 Results ree key parameters were needed to adjust inthe ABM as follows the percentage of opinion expressionwillingness p and q and the number of agents in twoopinion clusters a and 100minus a is simulation set severallevels of each parameter When a 10 20 30 and 40 (p q) (5 25) (10 5) (15 75) and (20 10)When a 50 (p q) (5 5) (10 10) (15 15)and (20 20) erefore this simulation had 5 lowast 4 20 indifferent situationse ABM in each situation ran 100 timesand took the average to construct the curve of two clustersrsquoopinion expression

421 Model Analysis When Two Opinions Were BalancedTo simulate the situation that two opinions were balancedthis research assigned two opposite opinions A and B andeach of them had 50 agents eir initial willingness ofopinion expression was a randomly assigned normal dis-tribution before the simulation Following the rules men-tioned above the ABM drew the opinion expressionpercentage of opinion A e opinion expression percentagewas operationalized as

P(expression) the number of statements in one round fromone opinion cluster(eg opinionA)


Note that the opinion expression percentage is countedby statements made by agents which is different from thewillingness of opinion expression in peoplersquos minds If at aspecific time point the opinion expression percentage of

cluster A equaled to 50 that meant opinion cluster Aagents made 50 of the statements in the discussion

From Figure 3 the current study concluded that the twoequally balanced opinions antagonized one another and

8 Complexity

were always fluctuating up and down around 50 Differentvalues of the parameter p (5 10 and 15) shared similartrends However when the parameter p gets larger to 20the opinion expression percentage of opinion A couldfluctuate to 60 at the end of 100 rounds of speaking whichis more unstable than small p values

422 Model Analysis When the Social Media Group WasDivided into Two Opinions One Majority and One MinorityTo simulate the situation that two opinions had oneminorityand another majority this research assigned two oppositeopinions A and B with four situations A 10 B 90A 20 B 80 A 30 B 70 A 40 B 60 Each agentrsquosinitial willingness of opinion expression was a proportionthat was randomly assigned with normal distribution beforethe simulation Following the rules mentioned above thesimulation ran 100 times in each situation and then drew theopinion expression percentage on the minoritymajorityopinion discussion in Figure 4

In Figure 4 the blue thick line referred to the minorityopinion the red thin line referred to the majority opinionFrom the figure the current study indicated that the twoopinions antagonized one another and the minority opinionspoke out more than expected For instance the minorityopinion members constituted 10 of the population while

constituted 15ndash25 in opinion expression at the end of 100rounds of speaking Different values of parameter p sharedthe same trends Besides the increasing range of minorityopinion was enhanced by parameter p

However with the increasing members of the minorityopinion the opinion expression percentage became closer tothe percentage of the population For instance in Figure 5when the minority population increased from 10 to 40 theexpression percentage did not increase continuously above40 but fluctuated around 40 instead Different values ofparameter p shared the same trends

Figures 6 and 7 show the simulation results when A 20and 30 eir opinion dynamics fluctuated less than theposition in Figure 4 but more than the position in Figure 5

To sum up according to the rules of ABM the minorityopinionrsquos expression percentage behaved better than thepercentage of the total population when the opinion hadvery few supporters For instance when A 10 and B 90the opinion expression percentage could be around 15ndash25 for clusterA but only 75ndash85 for cluster Be largerthe number of parameters p and q the more unstable thetrend would be However we could not find enough supportthat the minority opinion could be reversed to be the ma-jority opinion As the number of minority opinion membersincreased the superiority of opinion expression graduallydeclined

y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opinion expression gaming (A = 50 B = 50 p = 5 q = 5)O

pini

on ex

pres

sion

perc

enta

ge

Opinion expression gaming (A = 50 B = 50 p = 15 q = 15)

02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 3E ndash 05x + 0490902

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918

Opinion cluster AOpinion cluster BTrend line for cluster A




Figure 3 Balanced opinion situation (A 50 and B 50) Note Opinion expression percentage with A (minority cluster) blue thick lineand B (majority cluster) red thin line Round of speaking represents time because each discussion allows 100 rounds of speaking All theresults were shown in the average score of 100 timesrsquo simulation

Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage





Figure 4 Minoritymajority opinion expression (For example A 10 B 90) Note Opinion expression percentage with A (minoritycluster) blue thick line and B (majority cluster) red thin line Round of speaking represents time because each discussion allows 100rounds of speaking All the results were shown in the average score of 100 timesrsquo simulation

y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11

5 Conclusion and Discussion

e current research concluded that the minority opinionmembers were more sensitive to the change of peer supportthan the majority opinionmembers Notably an individualrsquoswillingness of opinion expression could be encouraged whilethe perceived peer support decreased which was signifi-cantly different from the traditional spiral of silence studiesas well as the simulation studies One potential explanationof this finding is the fear of isolation is the premise of thespiral of silence [27] while people tend to find peers in socialmedia groups so they may not feel enough isolated even ifthey receive less support Besides the studies of correctiveaction and hostile media have proposed that when peoplefeel their opinions are unfairly suppressed they will feelmore indignation and then protecting their opinions ratherthan perceiving fear [51 52] us less support in socialmedia groups can encourage the willingness of opinionexpression

New phenomena emerged during the simulation ofopinion expression dynamics in the social media group esimulation model based on the quasi-experimental resultsshowed that the increase of the willingness of opinion ex-pression on an individual level could encourage the realopinion expression and prevent the whole cluster of mi-nority opinion from falling into silence at means it isquite difficult to achieve complete suppression of oneopinion in social media groups However findings alsoindicate that enhancing willingness of opinion expression isnot a panacea for the minority opinion members to demandgreater influence Because results showed that the minorityrsquosopinion expression percentage could only behave relativelybetter than the minority opinion supportersrsquo populationpercentage then floated up and down Reaching the finalone-side win or reversing the minority opinion to themajority may both need time and luck which is hard toachieve in real life

e current research findings have practical implica-tions First people should be vigilant if some specific interestgroups intend to manipulate their willingness of opinionexpression Because it can help seek greater influence notmatching their capacity and then mislead the public opinionto be more beneficial to themselves Second those whosupport a minority opinion should have the confidence tosurvive in social media groups ird it is probably notnecessary for majority opinion members to pursue acomplete suppression of opinions on the contrary it isnecessary to acknowledge that most changes of pluralisticpublic opinions are ordinary and respectful Finally socialmedia chat groups are widely existed nowadays but aredifferent from those open social media platforms ereforemore researches are encouraged to study further about thecause effect and mechanism of opinion dynamics in socialmedia groups

Here are some limitations of the current research Firstin order to maintain a good external validity of the resultsthe quasi-experiment tries to simulate a real environmentof a social media chat group and uses behavioral data tooperationalize psychological concepts However it does

not test the difference between intention and behaviorsuch as perceived peer support and received peer supportwillingness to speak out and the actual speak out Wewould suggest future studies to come up with a betterdesign to measure the intensions Second the quasi-ex-periment needs more participants in the observation groupand the percentage changes of the observational groupbetween the majority balance and minority situationsneed to be controlled more strictly ird we do not haveenough empirical data to support that peoplersquos willingnessof opinion expression is normally distributed but the re-searchers assume that it is in the agent-based modelAlthough it is a relatively common assumption that humanbehavior is following Gaussian distribution it could havepossibilities and may cause bias in the simulationerefore researchers plan to do further studies focusingon exploring more theoretically-supported communicationstrategies to simulate the collective level phenomenon anddesign more rigorous experiments to test the individuallevel presumptions

Data Availability

e quasi-experimental data used to support the findings ofthis study are available from the corresponding author uponrequest e agent-based model codes are included withinthe supplementary information file

Conflicts of Interest

e authors declare that they have no conflicts of interest

Supplementary Materials

e supplementary file includes codes of conducting theagent-based model (Supplementary Materials)

References

[1] M Jing and C Zang ldquoOn the information flow modedemassification communication and the influence of massmedia over the social cohesion under the age of mediaconvergencerdquo Journalism amp Communication vol 5 pp 34ndash42 2011

[2] Y Chen ldquoComparison of communication mechanism be-tween micro-blog andWeChat under different identityrdquo PressCircles vol 3 pp 54ndash57 2015

[3] G M Yu ldquoSome ideas about the future development of themedia industryrdquo News Front vol 1 2014

[4] K N Hampton I Shin andW Lu ldquoSocial media and politicaldiscussion when online presence silences offline conversa-tionrdquo Information Communication amp Society vol 20 no 7pp 1090ndash1107 2017

[5] Z A Zhang and K R Shu ldquoResearch on the public opinion ofWeChat relationship network and ecological characteristicsrdquoShanghai Journalism Review vol 20 no 6 pp 29ndash37 2016

[6] J Habermas e Structural Transformation of the PublicSphere Xue Lin Publishing House Shanghai China 1962

[7] D Goldie M Linick H Jabbar and C Lubienski ldquoUsingbibliometric and social media analyses to explore the ldquoechochamberrdquo hypothesisrdquo Educational Policy vol 28 no 2pp 281ndash305 2014

12 Complexity

[8] G H Guo ldquoOn the ldquogroup polarizationrdquo tendency of the mainbody of network public opinionrdquo Journal of Social Science ofHunan Normal University vol 6 pp 110ndash113 2004

[9] E Noelle-Neuman e Spiral of Silence Public Opinion-OurSocial Skin Peking University Press Bejing China 1974

[10] D A Scheufele and P Moy ldquoTwenty-five years of the spiral ofsilence a conceptual review and empirical outlookrdquo Inter-national Journal of Public Opinion Research vol 12 pp 3ndash282000

[11] L Willnat WP Lee and B H Detenber ldquoIndividual-levelpredictors of public outspokenness a test of the spiral ofsilence theory in Singaporerdquo International Journal of PublicOpinion Research vol 14 no 4 pp 391ndash412 2002

[12] M J Lee and J W Chun ldquoReading othersrsquo comments andpublic opinion poll results on social media social judgmentand spiral of empowermentrdquo Computers in Human Behaviorvol 65 pp 479ndash487 2016

[13] G Neubaum and N C Kramer ldquoOpinion climates in socialmedia blending mass and interpersonal communicationrdquoHuman Communication Research vol 43 no 4 pp 464ndash4762017

[14] J W Chun andM J Lee ldquoWhen does individualsrsquo willingnessto speak out increase on social media Perceived socialsupport and perceived powercontrolrdquo Computers in HumanBehavior vol 74 pp 120ndash129 2017

[15] T Zerback and N Fawzi ldquoCan online exemplars trigger aspiral of silence Examining the effects of exemplar opinionson perceptions of public opinion and speaking outrdquo NewMedia amp Society vol 19 no 7 pp 1034ndash1051 2017

[16] A F Hayes ldquoExploring the forms of self-censorship on thespiral of silence and the use of opinion expression avoidancestrategiesrdquo Journal of Communication vol 57 no 4pp 785ndash802 2007

[17] P Moy D Domke and K Stamm ldquoe spiral of silence andpublic opinion on affirmative actionrdquo Journalism amp MassCommunication Quarterly vol 78 no 1 pp 7ndash25 2001

[18] E Katz ldquoPublicity and pluralistic ignorance notes on ldquothespiral of silencerdquordquo in Public Opinion and Social Change ForElisabeth Noelle-Neumann H Baier Kepplinger andK Reumann Eds pp 28ndash38 Westdeutscher Verlag Wies-baden Germany 1981

[19] E Wartella C Whitney Mass Communication ReviewYearbook Sage Vol 4 Beverley Hills CA USA 1983

[20] H Oshagan ldquoReference group influence on opinion ex-pressionrdquo International Journal of Public Opinion Researchvol 8 no 4 pp 335ndash354 1996

[21] C J Glynn A F Hayes and J Shanahan ldquoPerceived supportfor onersquos opinions and willingness to speak out a meta-analysis of survey studies on the ldquospiral of silencerdquordquo PublicOpinion Quarterly vol 61 no 3 pp 452ndash463 1997

[22] W P Davison ldquoe third-person effect in communicationrdquoPublic Opinion Quarterly vol 47 no 1 pp 1ndash15 1983

[23] H Rojas ldquoldquoCorrectiverdquo actions in the public sphere howperceptions of media and media effects shape political be-haviorsrdquo International Journal of Public Opinion Researchvol 22 no 3 pp 343ndash363 2010

[24] M Duncan and D Coppini ldquoParty v e People testingcorrective action and supportive engagement in a partisanpolitical contextrdquo Journal of Information Technology amp Pol-itics vol 16 no 3 pp 265ndash289 2019

[25] M Duncan A Pelled D Wise et al ldquoStaying silent andspeaking out in online comment sections the influence ofspiral of silence and corrective action in reaction to newsrdquoComputers in Human Behavior vol 102 pp 192ndash205 2020

[26] Y Tsfati N J Stroud and A Chotiner ldquoExposure to ideo-logical news and perceived opinion climate testing the mediaeffects component of spiral-of-silence in a fragmented medialandscaperdquoe International Journal of PressPolitics vol 19no 1 pp 3ndash23 2014

[27] P J Shoemaker M Breen and M Stamper ldquoFear of socialisolation testing an assumption from the spiral of silencerdquoIrish Communication Review vol 8 pp 65ndash78 2000

[28] N Pang S S Ho A M R Zhang J S W Ko W X Low andK S Y Tan ldquoCan spiral of silence and civility predict clickspeech on Facebookrdquo Computers in Human Behavior vol 64pp 898ndash905 2016

[29] G W Yun S-Y Park and S Lee ldquoInside the spiral hostilemedia minority perception and willingness to speak out on aweblogrdquo Computers in Human Behavior vol 62 pp 236ndash2432016

[30] C Wells K J Cramer M W Wagner et al ldquoWhen we stoptalking politics the maintenance and closing of conversationin contentious timesrdquo Journal of Communication vol 67no 1 pp 131ndash157 2017

[31] C J Glynn and J M McLeod ldquoImplication of the spiral ofsilence theory for communication and public opinion re-searchrdquo in Political Communication Yearbook D R SandersL L Kaid and D Nimmo Eds pp 43ndash65 Southern IllinoisUniversity Press Carbondale IL USA 1984

[32] D G Mcdonald C J Glynn S-H Kim and R E Ostmanldquoe spiral of silence in the 1948 presidential electionrdquoCommunication Research vol 28 no 2 pp 139ndash155 2001

[33] L Willnat ldquoMass media and political outspokenness in HongKong linking the third-person effect and the spiral of silencerdquoInternational Journal of Public Opinion Research vol 8 no 2pp 187ndash212 1996

[34] R K Sawyer ldquoe mechanisms of emergencerdquo Philosophy ofthe Social Sciences vol 34 no 2 pp 260ndash282 2004

[35] M Pineda and G M Buendıa ldquoMass media and heteroge-neous bounds of confidence in continuous opinion dynam-icsrdquo Physica A Statistical Mechanics and Its Applicationsvol 420 pp 73ndash84 2015

[36] W B Wang ldquoe present situation and prospect of the re-search on evolutionary game theoryrdquo Statistics and Decisionvol 25 no 3 pp 158ndash161 2009

[37] N Jung E S Cho J H Choi and J W Lee ldquoAgent-basedmodels in social physicsrdquo Journal of the Korean PhysicalSociety vol 72 pp 1272ndash1280 2018

[38] Z-D Zhang ldquoConjectures on the exact solution of three-dimensional (3D) simple orthorhombic Ising latticesrdquo Phil-osophical Magazine vol 87 no 34 pp 5309ndash5419 2007

[39] F W S Lima ldquoree-state majority-vote model on squarelatticerdquo Physica A Statistical Mechanics and Its Applicationsvol 391 no 4 pp 1753ndash1758 2012

[40] Y J Liu Q Li and W Y Niu ldquoA summary of the model ofpublic opinion dynamicsrdquoManagement Review vol 25 no 1pp 167ndash176 2013

[41] Y Wu Y-J Du X-Y Li and X-L Chen ldquoExploring thespiral of silence in adjustable social networksrdquo InternationalJournal of Modern Physics C vol 26 no 11 Article ID1550125 2015

[42] B Ross L Pilz B Cabrera F Brachten G Neubaum andS Stieglitz ldquoAre social bots a real threat An agent-basedmodel of the spiral of silence to analyse the impact of ma-nipulative actors in social networksrdquo European Journal ofInformation Systems vol 28 no 4 pp 394ndash412 2019

[43] L Deng Y Liu and F Xiong ldquoAn opinion diffusion modelwith clustered early adoptersrdquo Physica A Statistical

Complexity 13

Mechanics and Its Applications vol 392 no 17 pp 3546ndash3554 2013

[44] A Boutyline and R Willer ldquoe social structure of politicalecho chambers variation in ideological homophily in onlinenetworksrdquo Political Psychology vol 38 no 3 pp 551ndash5692017

[45] D Trilling M van Klingeren and Y Tsfati ldquoSelective ex-posure political polarization and possible mediators evi-dence from e Netherlandsrdquo International Journal of PublicOpinion Research vol 29 pp edw003ndash213 2017

[46] D Sohn and N Geidner ldquoCollective dynamics of the spiral ofsilence the role of ego-network sizerdquo International Journal ofPublic Opinion Research vol 28 no 1 pp 25ndash45 2015

[47] J J H Zhu Y Huang and X Zhang ldquoDialogue on com-putational communication research origins theoriesmethods and research questionsrdquo Communication amp Societyvol 44 pp 1ndash24 2018

[48] P L East L E Hess and R M Lerner ldquoPeer social supportand adjustment of early adolescent peer groupsrdquo e Journalof Early Adolescence vol 7 no 2 pp 153ndash163 1987

[49] C-L Dennis ldquoPostpartum depression peer support maternalperceptions from a randomized controlled trialrdquo Interna-tional Journal of Nursing Studies vol 47 no 5 pp 560ndash5682010

[50] J Z Bakdash and L R Marusich ldquoRepeated measures cor-relationrdquo Frontiers in Psychology vol 8 p 456 2017

[51] C S Carver ldquoNegative affects deriving from the behavioralapproach systemrdquo Emotion vol 4 no 1 pp 3ndash22 2004

[52] H Hwang Z Pan and Y Sun ldquoInfluence of hostile mediaperception on willingness to engage in discursive activities anexamination of mediating role of media indignationrdquo MediaPsychology vol 11 no 1 pp 76ndash97 2008

14 Complexity

(1) Quasi-experiment is individualsrsquo willingness ofopinion expression protected in social media groups(2) Agent-based model simulation how do individualsrsquowillingness of opinion expression trigger the collectivebehavior like the whole grouprsquos dynamics of opinionexpression

2 Related Work

21 Conflict Presumptions of Individual Opinion ExpressionWillingness Spiral of Silence versus Corrective ActionWillingness of opinion expression refers to individualsrsquoeagerness to share or post their opinions in public [14 15]is term is widely used as a dependent variable in com-munication and political science studies Previous studieshave long been concerned that perceived peer support affectsindividualsrsquo willingness of opinion expression Howevertheir primary two presumptions of that ldquoeffectrdquo are inconflict with each other

First the spiral of silence theory suggests that the de-crease of perceived peer support could lessen individualsrsquowillingness of opinion expression or even silence it becauseof peoplersquos fear of isolation [9 16 17] e spiral of silencetheory proposes that because individuals are afraid of beingisolated thus more perceived support will increase peoplersquoswillingness of opinion expression while less support willlessen the willingness [18 19] is theory was proposed inthe traditional mass media environmentus the perceivedsupport referred to support from mass media Researcherslater extended this support to peer relations and socialmedia Research by Oshagan [20] introduces the concept ofthe reference group which is used as a synonym of peer todescribe family members intimate partners colleagues andneighbors Studies use this concept for reference and pro-pose that reducing perceived peer support is even moreeffective than reducing mass media support when it tries tolessen individualsrsquo willingness of opinion expression[16 17 21]

On the contrary the corrective action hypothesis pro-poses that controversial issues will inspire people to speakout their thoughts to change othersrsquo perceptions of publicopinion [22] When people perceive news or comments onsocial media going biased against them they are concernedthat the public may be swayed in that direction Because ofthis fear people are motivated to take action to correctpublic opinion by speaking out even when their opinion is inthe minority [23] Similar findings are found both in thenews report and social media discussion situation peoplewho have received hostile news or received negative socialmedia comments on their opinion would like to speak out toprotect their opinion [24 25]

Evidence suggests that whether audiences are motivatedto keep silent or speak out depends on how they perceiveothersrsquo opinions [26] To deduct from the theory whenpeople feel the fear of isolation the decrease of perceivedpeer support will lessen the willingness of opinion expres-sion [27] However if people do not feel such fear theperceived peer support will not diminish or even increase thewillingness of opinion expression Nowadays people have

more peers on social media (although they may never meetoffline) comparing with the traditional mass media age andthey are more likely to find online peers who share the sameopinions [12 28 29] Because people are able to get psy-chological support conveniently from their online peersthey will not easily feel the fear of isolation [13] ereforeeven though individuals perceive they are the minorityrather than the majority their willingness of opinion ex-pression may not decline but even increase For instancesome studies found people who held the minority opiniondid not have much change in their willingness of opinionexpression while comparing with majority opinion [15 30]Besides some studies proposed that minority perceptionincreased individualsrsquo willingness of opinion expression[23ndash25 29]

To sum up the findings above there are conflictingconclusions between perceived peer support and willingnessof opinion expression Traditional mass media studies findthat a decrease of support will lessen individualsrsquo willingnessof opinion expression [9 16 17 20] However recent socialmedia studies have found that the perceived peer supportwill not decrease or even encourage this willingness (eg[29 30] In the current study social media groups created anunbiased fully-connected social network to help membersget in touch with each other more conveniently whichsuggests that people may not feel much fear of isolationerefore this research proposes the first research questionas follows

RQ1 Will the decrease of perceived peer support en-hance individualsrsquo willingness of opinion expression insocial media groups

e current research has conducted a quasi-experiment(study 1) to answer this question Details are presented laterin this article

Moreover some other variables also influence thewillingness of opinion expression First the spiral of silencetheory [9] proposes hardcore to describe the people who arewilling to express their opinions consistently regardless ofsocial pressure Studies have shown that if the hardcore isremoved minority opinion supportersrsquo willingness to ex-press will significantly decrease [31ndash33] Furthermore fearof authority lack of self-efficiency feeling the importance ofthe issue accessibility of different opinions and technicalconditions of communication could all influence personalopinion expression [13 33] In order to keep these variablesconsistent the quasi-experiment applies repeated mea-surements on each individual

22 Simulating theCollectiveOpinionExpressionDynamicsbythe Agent-Based Model According to Sawyerrsquos [34] mech-anism of emergence collective phenomena are collabora-tively created by individuals yet may not reducible toindividual action erefore to generalize individual-levelfindings to the collective behavior of opinion expression in asocial media chat group we need an agent-based model(ABM) to simulate the dynamics e ABM consists ofagents system space and external environment Agents have

2 Complexity













Complexity 3

























4 Complexity




















Complexity 5




















=

=

=




Manipulation check




Testing correlation














6 Complexity


















Complexity 7







thenAi(t + 1) 1 30lowast(1 + q)( 1113857(7)
















8 Complexity








y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


pini

on ex

pres

sion

perc

enta

ge


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking



03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918






Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity













Complexity 3

























4 Complexity




















Complexity 5




















=

=

=




Manipulation check




Testing correlation














6 Complexity


















Complexity 7







thenAi(t + 1) 1 30lowast(1 + q)( 1113857(7)
















8 Complexity








y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


pini

on ex

pres

sion

perc

enta

ge


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking



03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918






Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity

























4 Complexity




















Complexity 5




















=

=

=




Manipulation check




Testing correlation














6 Complexity


















Complexity 7







thenAi(t + 1) 1 30lowast(1 + q)( 1113857(7)
















8 Complexity








y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


pini

on ex

pres

sion

perc

enta

ge


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking



03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918






Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity




















Complexity 5




















=

=

=




Manipulation check




Testing correlation














6 Complexity


















Complexity 7







thenAi(t + 1) 1 30lowast(1 + q)( 1113857(7)
















8 Complexity








y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


pini

on ex

pres

sion

perc

enta

ge


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking



03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918






Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity




















=

=

=




Manipulation check




Testing correlation














6 Complexity


















Complexity 7







thenAi(t + 1) 1 30lowast(1 + q)( 1113857(7)
















8 Complexity








y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


pini

on ex

pres

sion

perc

enta

ge


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking



03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918






Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity


















Complexity 7







thenAi(t + 1) 1 30lowast(1 + q)( 1113857(7)
















8 Complexity








y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


pini

on ex

pres

sion

perc

enta

ge


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking



03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918






Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity







thenAi(t + 1) 1 30lowast(1 + q)( 1113857(7)
















8 Complexity








y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


pini

on ex

pres

sion

perc

enta

ge


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking



03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918






Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity








y = 1E ndash 04x + 0497602

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


pini

on ex

pres

sion

perc

enta

ge


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00002x + 049951 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking



03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = 00011x + 04918






Complexity 9

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity

y = 00005x + 010180

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 01060

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00013x + 009730

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00015x + 009630

01020304050607

10908

0

01

005

02

015

025

04

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage






y = 1E ndash 05x + 0409902

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage


1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


y = ndash 00002x + 0423402

03

04

05

06

07

08

Opi

nion

expr

essio

n pe

rcen

tage


02

03

04

05

06

07

08

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking

Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00006x + 04092






10 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity

y = 00002x + 020080

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 020050

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00003x + 020210

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00007x + 018720

01020304050607

10908

01

02

015

025

04

045

035

03

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage










y = 00003x + 030190

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = 00001x + 029830

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage

y = ndash 00002x + 030550

01020304050607

0908

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100

Round of speaking


Opi

nion

expr

essio

n pe

rcen

tage


Complexity 11







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity







Data Availability






References








12 Complexity





































Complexity 13











14 Complexity





































Complexity 13











14 Complexity











14 Complexity

Documents

OpinionExpressionDynamicsinSocialMediaChatGroups:An ......people’s daily life [4]. Unlike open social media platforms that produce outbursts of information, social media groupsprovide