Effect of undecided agents on an opinion-forming model
aa r X i v : . [ phy s i c s . s o c - ph ] J a n Effect of undecided agents on anopinion-forming model
Ver´onica Calder´on, Wilfredo Cano, Victor H. Blanco
Carrera de F´ısica y Energ´ıas Alternativas, UPEA, El Alto, Bolivia
January 26, 2021
Abstract
We study the effect of undecided agents within a population in anopinion-forming dynamic, varying the number of undecided agents fordifferent proportions of populations in a complete opinion-exchangenetwork. The result is that the dynamic depends on the number ofundecided agents, with 10% of the undecided population potentiallyaffecting the change in consensus and then becoming linear with anegative slope. keywords , Social Systems Dynamics, Collective Phenomenon, Ran-dom Processes, Non-Equilibrium Transition Phases, ComputationalSimulations
The dynamics of opinion on is studied with different models, several shownin [1, 7, 4], with different dynamics of opinion formation. From the resultsobtained in [2] in the model used, and showing the scale behavior in thefigures: (1) for the average opinion, (2) its variance and (3) third moment,where is. he dynamics of the project have been scaled up, and its exponents1merge: caracterısticos. It has been observed that in different situations priorto an election, a certain number of agents have a choice of the moment, theirdecision not depending on a memory from which they extract their final de-cision, but if these agents during the course can influence other agents duringthe dynamics [5, 6]. Now we wish to see the effect of undecided agents who,without a preference for choice, develop their choice without the influenceof other agents, but whose decision is totally random, nevertheless, on theirway to choosing their preference of the moment. To observe what is effecton a decision of the group. Based on three possible choices, if they influenceothers but being undecided they change their influence in their moment. alsothe variance and the binder: With their respective scale exponents for eachmagnitude. Now it is tried to use the model in a situation already agreed toobserve the effect of the undecided agents in that decision. the variance and o pprobability of undecided vs. opinion"100q20c305t02A" u 1:2"300q20c305t02A" u 1:2"600q20c305t02A" u 1:2"100q20c305t03A" u 1:2"300q20c305t03A" u 1:2"600q20c305t03A" u 1:2"100q20c305t04A" u 1:2"300q20c305t04A" u 1:2"600q20c305t04A" u 1:2"100q20c305t05A" u 1:2"300q20c305t05A" u 1:2"600q20c305t05A" u 1:2"100q20c305t06A" u 1:2"300q20c305t06A" u 1:2"600q20c305t06A" u 1:2"100q20c305t07A" u 1:2"300q20c305t07A" u 1:2"600q20c305t07A" u 1:2"100q20c305t08A" u 1:2"300q20c305t08A" u 1:2"600q20c305t08A" u 1:2"100q20c305t09A" u 1:2"300q20c305t09A" u 1:2"600q20c305t09A" u 1:2 Figure 1: The figure shows agents interacting among themselves obtainingsome consensus and observing some fixed points depending on the populationof the system, note that the results were scaled.the binder too: With their respective scale exponents for each magnitude.Now it is tried to use the model in a situation already agreed to observe theeffect of the undecided agents in that decision. With their respective scaleexponents for each magnitude. 2 v a r i an c e pvariance scale"100q20c305t03A" u (($1)-A)*100**(1/v):(($3)*100**(-g/v))"300q20c305t03A" u (($1)-A)*300**(1/v):(($3)*300**(-g/v))"900q20c305t03A" u (($1)-A)*900**(1/v):(($3)*900**(-g/v)) 0 1 2 3 4 5 6 7 8 9 10-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 v a r i an c e pvariance scale"100q20c305t03A" u (($1)-A)*100**(1/v):(($3)*100**(-g/v))"300q20c305t03A" u (($1)-A)*300**(1/v):(($3)*300**(-g/v))"900q20c305t03A" u (($1)-A)*900**(1/v):(($3)*900**(-g/v)) Figure 2: The figure shows the variance of the agents interacting in theopinion system, note that the results were scaled -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 ob i n pscale binder"100q20c305t03A" u (($1)-A)*100**(1/v):4"300q20c305t03A" u (($1)-A)*300**(1/v):4"900q20c305t03A" u (($1)-A)*900**(1/v):4-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-0.1 -0.05 0 0.05 0.1 ob i n pscale binder"100q20c305t03A" u (($1)-A)*100**(1/v):4"300q20c305t03A" u (($1)-A)*300**(1/v):4"900q20c305t03A" u (($1)-A)*900**(1/v):4 Figure 3: The figure shows the binder for the system, note that the resultswere scaled.
Similar al modelo utilizado en [2] ahora se le asocia una fracci´on de lapoblaci´on como vol´atil en diferentes proporciones a la din´amica utilizada,con las siguientes consideraciones: 3
A pair of i, j agents are randomly selected. • If i is a volatile agent, it will choose its next opinion randomly fromthe two possible options. • On the other hand if it is a non-volunteer agent it will interact with itsopinion for the time t + 1 with the following rule: o i ( t + 1) = [ o i ( t ) + µ ij o j ( t )] i, j = 1 , ..., N . For o i normal individuals. Undecided agents are given by thefunction:: o i ( t + 1) = rnd [ − ,
1] (1)With rnd random function between the two options for undecided agents,that no matter who they interact with, their answer is always random.The proportion of undecided agents varies and they are allowed to interactfor different amounts of populations. O = * N N X i =1 o i + (2)Where < . > denotes an average configuration disorder, it is sensitive tothe balance condition between extreme views. Note that O plays the role of’magnetic spin’. Results were obtained for different populations. The follow-ing figure shows how the consensus varies with the introduction of undecidedagents in the figure (4) taking a population of 600 agents and varying theprobability that these agents are undecided agents. As the case has aleatori-cal variables, we will not consider more than the average for the analysis. Itcan be observed that the fewer undecided agents there are, the more consen-sus there is in the group and the more group decisions decrease, the greaterthe probability that there are more undecided agents.Here we will analyze a case, the case of continuous opinions, since it wasdemonstrated that the different cases of discreet opinions, discreet and con-tinuous, are obtained similar tendency ([2]), where it is observed that the4 o popinion vs probability of undecided agents for N=600"600q20c305t02A" u 1:2"600q20c305t03A" u 1:2"600q20c305t04A" u 1:2"600q20c305t05A" u 1:2"600q20c305t06A" u 1:2"600q20c305t07A" u 1:2"600q20c305t08A" u 1:2"600q20c305t09A" u 1:2 Figure 4: The figure shows the opinion of the group varying the number ofundecided agents of probability from 0 . . o pprobability of undecided vs. opinion"100q20c305t00A" u 1:2"300q20c305t00A" u 1:2"600q20c305t00A" u 1:2"100q20c305t0025A" u 1:2"300q20c305t0025A" u 1:2"600q20c305t0025A" u 1:2"100q20c305t005A" u 1:2"300q20c305t005A" u 1:2"600q20c305t005A" u 1:2"100q20c305t0075A" u 1:2"300q20c305t0075A" u 1:2"600q20c305t0075A" u 1:2"100q20c305t01A" u 1:2"300q20c305t01A" u 1:2"600q20c305t01A" u 1:2"100q20c305t02A" u 1:2"300q20c305t02A" u 1:2"600q20c305t02A" u 1:2"100q20c305t03A" u 1:2"300q20c305t03A" u 1:2"600q20c305t03A" u 1:2 "100q20c305t04A" u 1:2"300q20c305t04A" u 1:2"600q20c305t04A" u 1:2"100q20c305t05A" u 1:2"300q20c305t05A" u 1:2"600q20c305t05A" u 1:2"100q20c305t06A" u 1:2"300q20c305t06A" u 1:2"600q20c305t06A" u 1:2"100q20c305t07A" u 1:2"300q20c305t07A" u 1:2"600q20c305t07A" u 1:2"100q20c305t08A" u 1:2"300q20c305t08A" u 1:2"600q20c305t08A" u 1:2"100q20c305t09A" u 1:2"300q20c305t09A" u 1:2"600q20c305t09A" u 1:2"100q20c305t1A" u 1:2"300q20c305t1A" u 1:2"600q20c305t1A" u 1:2 Figure 5: The figure shows how the consensus is for different numbers ofundecided agents converging to a point independent of population size.5s observed that there is a point of inflection through which the different pop-ulations pass, this point will delimit us what we call disorder of the electionagainst the order of the same one and the different probabilities of obtainingundecided agents are varied.Elaborating a regression to the system obtained from the transitions fromorder to disorder, we obtain: De la figura (6) se obtiene dos tendencias di-Figure 6: The figure shows how consensus for different numbers of undecidedagents is the probability of having undecided agents vs. consensus.vididas por la probabilidad de agentes indecisos del 0 .
1, donde se obtiene:From the figure (6) two trends are obtained divided by the probability ofundecided agents of 0 .
1, where it is obtained: f ( x ) = 0 . x . for x ∈ [0 , .
1] (3)Where f ( x ) represents the consensus reached and x the different proportionsof undecided agents that form a relationship for the region between 0 to 0 . .
1, the consensus behaves linearly with the trend: f ( x ) = − . x + 0 .
403 for x ∈ [0 . ,
1] (4)6igure 7: Tendencia potencial de la caida del concenso entre 0 a 0.1 deprobabilidad de tener agentes indecisos.Figure 8: Potential trend of falling consensus between 0 and 0 . .
035 of the undecidedpopulation, the consensus is affected to half of the total population.For the region greater than 0 . R = 0 .
96, this image shows the borderbetween order with disorder caused by undecided agents. It can be seen thatundecided agents cause a greater effect on the consensus of the populationwhen they are less than 10% of the population. This consensus reaches 30%of the population when practically the entire population is undecided, anextreme case that would appear to be a society with information comingonly from its interactions.
The influence of volatile decision agents, shows that the 10% of the undecidedagents cause more influence in the consensus that while more the undecidedagents increase. For a few undecided agents, the effect is greater, obeyinga potential fall f ( x ) = 0 . x . causing decisions to move away from unan-imous consensus. For higher values of undecided agents, the trend of thisrelationship behaves with a slope: − .
129 continues.Undecided agents can cause a change in the trend of the consensus as theyincrease, for this 3.5% of undecided agents of the total population is enoughto decrease the initial consensus by half, which represents as a practice thatcausing doubts in the population can cause a turn of the trend of the con-sensus.