The Model and Analysis of Conformity in Opinion Formation

Transcription

1 roceedings of the 7th WSEAS International Conference on Simulation, Modelling and Otimization, Beijing, China, Setember 5-7, The Model and Analysis of Conformity in Oinion Formation ZHANG LI, LIU YUN School of Electronics and Information Engineering Beijing Jiaotong University Beijing, China Abstract: - The formation of ublic oinion has been focused by many scholars recently; a lot of models have been roosed to verify the rocess of formation. Many models have noticed that individuals can exchange their oinions and many scholars make their own rule of how individuals change their oinions. After year 2000, some classic models and their variants outut some useful result, but there is no aer talk about grou size and its influence. This aer resents a model from the social sychology oints of view. The model considers both arts (ositive oinions and negative oinions) of some connected eole. We simulated the formation rocess using the roosed model, results show that the model is useful for exlaining how grou/herd mentality causes revalence and how conformity lead to balance. Key words: - oinion formation; grou size; conformity; comuter simulation; Introduction Oinion is a belief or conclusion held by individuals, these individuals may have confidence about their oinion, but in most times, there is no ositive knowledge or roof to suort this. ublic oinion is oinion held by some eole. Consensus is oinion held by all of the eole, but in most cases, olarization and fragmentation are more usually. ublic oinion is made u of four arts basically which are Oinions, Individuals, Media and Toics. Oinions are held with Toics which could be olitics, economics, and culture. Which kind of soft drink will you choose, Coke Cola or esi? This is a question, and this is also a toic which could result in an endless debate. Question like choosing a movie from two or more and choosing colors of clothing are also toics which could easily roduce many kinds of oinions. Oinions are held by Individuals which may have big differences. eole are difference-men and women, higher education level and less education level, wealth eole and oor eole, eole live in downtown and eole live in country, extremist and moderatist. Sonsored by a National Science Foundation grant ( ). Without any ositive knowledge or roof, one could easily make his/her decision. And without any strong evidence, one could easily change his/her original oinion. Oinions are transformed by Media which could be broadcasting, television, newsaers, books, newsgrous, blogs, mails/ s and individuals. As new technology develos, more and more kinds of media join in. No matter what kinds of media are revailing, no matte what kinds of media are strongly controlled, both authority messages and rumors can find their land and survived well. In recent years, there have been a lot of interests in the fields of formation of ublic and the oinion dynamics in hysics. The methods used by hysicist are different with classical mass communication scholars. hysicist make a new interdiscilinary subject called sociohysics which mainly focused on exlain the social henomena with their skills in hysics [-5]. Ref [, 3] focus mainly oinion dynamics which give many interesting results and conclusions. The most oular model in oinion dynamics is Sznajd model which resented by K Sznajd-Weron, and

2 roceedings of the 7th WSEAS International Conference on Simulation, Modelling and Otimization, Beijing, China, Setember 5-7, J Sznajd at 2000 [6].Sznajd model is develoed from Ising sin model and has been tested with Monte Carlo simulations in a closed and one dimension community. In the resented model, individuals are described by interacting articles, with only two attitudes: A (ositive) or B (negative).stauffer et al generalization Sznajd model to a square lattice [7]. Hegselmann and Krause invested various models and bounded confidence of continuous oinion dynamics [8]. In this aer, we roosed a model of oinion formation takes into account the conformity of individuals and the effect of grou size in changing individuals oinions. The remainder of this aer is organized as follows: Section introduce the model and the suorting materials. Section 2 describes the simulation analysis of the roosed model in oinion formation. Section 3 is the conclusion and views the future work in this field. Fig. The roortion of conformity assengers vs. Grou size Suose a community as a L L square lattice with each individual I in one grid. Every individual I has his/her own oinion S i, S i can be ositive(+) or negative(-). Each individual has eight neighbors, these neighbors has their own oinions. Fig. 2 shows the osition of one s neighbors. 2 The Model The model roosed in this aer takes into account conformity of social sychology field. Conformity is the rocess by which eole's beliefs or behaviors are influenced by others. eole can be influenced via subtle, even unconscious rocesses, or by direct and overt eer ressure. This aer only focused on the oinion changes by an unforced way. Conformity is a social behavior which could haen in a grou. One of the factors could affect conformity is grou size. In Asch s famous conformity exeriment, a high roortion (32%) conformed to the erroneous majority view of the others in the room when there were at least three confederates resent, even when the erroneous ones make obvious mistakes [9]. The model is mainly insired by Milgram et al [0]. Milgram and his colleague found that if one erson stood in a Manhattan street gazing at a sixth floor window, 20% of edestrians looked u; if five eole stood gazing 80% of eole looked u. Fig. shows this using the data from Milgram [0]. Fig. 2 The osition of Neighbors Consider about the marginal grid in the square lattice, just like the grid labeled with number 3 in Fig. 2. In this model, we suosed that the marginal grids connect with the grid in the corresonding edge which means the righter grid of grid 3 is grid and the uer grid of grid 3 is grid 8. Obviously, the right uer grid of grid 3 is grid 6. In each ste, individuals try to make their decisions. They mainly focus their neighbors choice. Here we simlify the Milgram s data to the below: 0.6 xx, {0,, 2,3, 4} y = 0.8, x {5, 6, 7,8} () Suose that y is the conformity robability of individuals to follow their neighbors oinion according to their grou size, x is the grou size. Everyone has his initial oinion in this model, ositive or negative, so there are two kinds of transformation, from ositive to negative and from negative to ositive. The equations below are the robability of the two way transformation.

3 roceedings of the 7th WSEAS International Conference on Simulation, Modelling and Otimization, Beijing, China, Setember 5-7, ( + ) ( + ) = = ( ) + ( + ) ( ) ( + ) + ( + ) ( ) (2) (3) Equation 2 is the robability of individuals changing their oinion to negative with initial oinion ositive. Equation 3 is in reverse. (+) is conformity robability of the grou with ositive oinion, (+) is conformity robability of the grou with negative oinion The following equation is obvious. ( + ) ( + ) + = (4) Equation 4 ensures that the whole robability of a individual changing his/her original oinion and stick with his/her initial attitude is. Take a individual with initial ositive oinion for examle, (+ -) is the robability of changing, (- +) is the robability of keeing. The following seudo code defines the whole rocess of oinion formation. Table seudo code of oinion formation rocess.initialize the L L square lattice 2.Assign individuals with oinions in desired distribution 3. The formation of oinion. stecount 0 while (stecount < finalste) for i = b L for j = to L if (S i = ositive) comute (+ -) change oinion with (+ -) else comute (- +) change oinion with (- +) end if next next stecount++; end while 3 Simulation analysis Using a comuter with Intel entium IV.4G, 52MB DDR, we simulate the roosed model for more than 000 times with each time 0000 stes of evolution. The following reresentative figure is one of the simulation with one initial ste, two intermediate stes and a final ste. Fig. 3 Examles of simulation rocess In Fig. 3, black oints reresent individuals with ositive attitude and white oints reresent individuals with negative attitude. Suose the initial roortion of individuals with ositive attitude to individuals with negative attitude is init. We have simulated with init from 9/ to /9 which means the roortion of ositive individuals decrease for 0% in each ste and negative ones increase for 0%. The global difference of oinions is a imortant indicator in the oinion formation rocess, suosed that m is the global difference, we define m as the following. L L Si L i= m= L (5) The following figure is the statistical result of all the

4 roceedings of the 7th WSEAS International Conference on Simulation, Modelling and Otimization, Beijing, China, Setember 5-7, simulations running for the roosed model. Fig. 5 arameters of grow curves Fig. 5 shows the fitting arameters including a, b and c. It is obvious that arameters a and c are almost the same excet the secial curve 5N5. arameters b of all these curves connected with each other combine an almost straight line with sloe equals The sloe indicates the grow seed of all growing curves which could be useful for redicting the trends of oinion formation. 4 Conclusion and future work Fig. 4 The global oinions difference Label of curves in Fig. 4 is formatted like *N*. take 9N for examle, 9N means that init is 9/. Fig. 4 shows that it is hard to achieve dominance for one kind of oinion in our model. All kinds of initial distribution of ositive oinions and negative oinions will return to the balance line of m = 0. More the initial difference is, sharer the initial arts of curves are. The curve with init equals 5/5 is a secial one which has only fluctuations. In order to understand the relationshi between init and curves, we make nonlinear curve fit of all these grow curves including N9, 2N8, 3N7, 4N6 and 5N5. The fitting function is as below. x y = a b c (6) Conformity is a common henomenon in social life, grou size is one of the factors will affect individuals conformity behavior. Famous social sychologist study conformity itself, this aer concerns the effect of conformity in oinion formation. It can be roved that conformity will lead to oinion balance in a closed, edge connected, 2D square lattice and 8-neighbour community. Different initial distributions of ositive attitude ones and negative attitude ones are simulated, the statistical result of global difference is comuted. Though interesting conclusion is gotten, there are still many variants which can be made to the original model. Future work can be the followings:. Not all of the individuals will be affected by others which means there are some of the stubborn ones whom can not be easily ersuaded. It can be a future work to deal with different roortion of stubborn ones. 2. The real relationshi between individuals in our society is a comlex network. Some individuals have little friends who will affect them, others may have more. 3. There is no global or mass media who can affect big arts of individuals as external force in the roosed model. Such kind of influences should be considered and added in the simulation model in the future. References: [] Stauffer D. Sociohysics Simulations[J]. Comuting

5 roceedings of the 7th WSEAS International Conference on Simulation, Modelling and Otimization, Beijing, China, Setember 5-7, In Science & Engineering. 2003, 5(3): [2] Schulze C, Stauffer D. Sociohysics Simulations I: Language Cometition[C] [3] Stauffer D. Sociohysics Simulations II: Oinion Dynamics[C] [4] Zekri L, Stauffer D. Sociohysics Simulations III: Retirement Demograhy[C] [5] Stauffer D. Sociohysics Simulations IV: Hierarchies of Bonabeau et al.[c] [6] Sznajd-weron K, SznajdJózef. Oinion Evolution in Closed Community[J]. International Journal of Modern hysics C. 2000, (06): [7] Stauffer D, Sousa A O, De Oliveira S M. Generalization to Square Lattice of Sznajd Sociohysics Model[J]. International Journal Of Modern hysics C. 2000, (06): [8] Hegselmann R, Krause U. Oinion Dynamics and Bounded Confidence Models, Analysis and Simulation[J]. Journal of Artificial Societies and Social Simulation. 2002, 5(3). [9] Asch S E. Effects of Grou ressure Uon the Modification and Distortion of Judgements[J]. Grous, Leadershi, and Men. 95: [0] Milgram S, Bickman L, Berkowitz L. Note on the drawing ower of crowds of different size[j]. Journal of ersonality and Social sychology. 969, 3: