Majority rule dynamics between a double coalition and a third opinion: coalition profit models and majority coalition ties

Abstract

This article explores the opinion dynamics of a double coalition opinion against a third opinion under majority rule updates on odd fixed size connected groups. For this purpose, coalition benefit criteria and three opinion formation models which extend the 2-state majority rule model on lattices are introduced. The proposed models focus on the coalition profit of its constituent coalition opinions and cover the possible final scenarios from coalition alliance perspective: either minor opinion or major opinion is favored, or dynamics do not favor to any coalition opinion. Opinion exchanges take place on a torus embedded lattice network of a 3-state system having in consideration tie configurations and two rules to break them: either by random choice or leaving ties unaltered. Models were analyzed in the statistical mechanics spirit through Monte Carlo simulations without node replacement. Estimations for coalition benefits, the growth of coalition ties, and consensus probabilities are reported. The loss of coalition strengths due to coalition ties and its indecision is indicated. In particular, the logistic decay of consensus probability is due to the logistic adaptive growth of coalition ties. Scaling behaviors for consensus time and coalition ties in terms of network size are suggested. The results of numerical simulations are discussed in the context of social influence and social dynamics.

Keywords

Opinion dynamics majority rule models coalition dynamics majority ties social complexity adaptive behavior critical mass logistic functions Monte Carlo simulation

Get full access to this article

View all access options for this article.

References

Abrica-Jacinto

N. L.

Kurmyshev

Juarez

H. A.

(2017). Effects of the interaction between ideological affinity and psychological reaction of agents on the opinion dynamics in a relative agreement model. Journal of Artificial Societies and Social Simulation, 20(3), Article 3. https://doi.org/10.18564/jasss.3377

Axelrod

R. M.

Bennett

D. S.

(1993). A landscape theory of aggregation. British Journal of Political Science, 23(2), 211–233. https://doi.org/10.1017/S000712340000973X

Axtell

R. L.

(2000). Effects of interaction topology and activation regime in several multi-agent systems. In Moss

Davidsson

(Eds.), International workshop on multi-agent systems and agent based simulation (MABS 2000, Lecture notes in computer science, Vol. 1979, pp. 33–48). Springer. https://doi.org/10.1007/3-540-44561-7_3

Balankin

A. S.

Martínez Cruz

M. A.

Gayosso Martínez

Martínez-González

C. L.

Morales Ruiz

Patiño Ortiz

(2015). Effect of heterogeneity in initial geographic distribution on opinions’ competitiveness. Entropy, 17(5), 3160–3171. https://doi.org/10.3390/e17053160

Balankin

A. S.

Martínez Cruz

M. A.

Gayosso Martínez

Mena

Tobon

Patiño-Ortiz

Samayoa

(2017). Ising percolation in a three-state majority vote model. Physics Letters A, 381(5), 440–445. https://doi.org/10.1016/j.physleta.2016.12.001

Balankin

A. S.

Martínez Cruz

M. A.

Trejo Martínez

(2011). Effect of initial concentration and spatial heterogeneity of active agent distribution on opinion dynamics. Physica A, 390(21–22), 3876–3887. https://doi.org/10.1016/j.physa.2011.05.034

Ball

(2002). The physical modeling of society: A historical perspective. Physica A, 314, 1–14. https://doi.org/10.1016/S0378-4371(02)01042-7

Ball

(2004). The physical modeling of human social systems. ComPlexUs, 1, 190–206. https://doi.org/10.1159/000082449

Ball

(2005). Join the club, alliances in business and politics. In Ball

(Ed.), Critical mass: How one thing leads to another (pp. 272–295). Arrow Books.

10.

Bernardes

A. T.

Costa

U. M. S.

Araujo

A. D.

Stauffer

(2001). Damage spreading, coarsening dynamics and distribution of political votes in Sznajd model on square lattice. International Journal of Modern Physics C, 12(2), 159–167. https://doi.org/10.1142/S0129183101001584

11.

Bordogna

C. M.

Albano

V. E.

(2007). Statistical methods applied to the study of opinion formation models: A brief overview and results of a numerical study of a model based on the social impact theory. Journal of Physics: Condensed Matter, 19(6), Article 065144. https://doi.org/10.1088/0953-8984/19/6/065144

12.

Bostrom

(2003). Are you living in a computer simulation? Philosophical Quarterly, 53(211), 243–255. https://doi.org/10.1111/1467-9213.00309

13.

Boyce

W. E.

DiPrima

R. C.

(2009). Elementary differential equations and boundary value problems (9th ed.). John Wiley.

14.

Castellano

Fortunato

Loreto

(2009). Statistical physics of social dynamics. Reviews of Modern Physics, 81(2), 591–646. https://doi.org/10.1103/RevModPhys.81.591

15.

Cavallini

(1993). Fitting a logistic curve to data. The College Mathematics Journal, 24(3), 247–253. https://doi.org/10.2307/2686488

16.

Chen

Redner

(2005a). Consensus formation in multi-state majority and plurality models. Journal of Physics A, 38(33), 7239–7252. https://doi.org/10.1088/0305-4470/38/33/003

17.

Chen

Redner

(2005b). Majority rule dynamics in finite dimensions. Physical Review E, 71(3), Article 036101. https://doi.org/10.1103/PhysRevE.71.036101

18.

Cialdini

R. B.

(2001). Influence: Science and practice (4th ed.). Allyn and Bacon.

19.

Costa Filho

R. N.

Almeida

M. P.

Andrade

J. S.

Jr. Moreira

J. E.

(1999). Scaling behavior in a proportional voting process. Physical Review E, 60(1), 1067–1068. https://doi.org/10.1103/PhysRevE.60.1067

20.

Dong

Zhan

Kou

Ding

Liang

(2018). A survey on the fusion process in opinion dynamics. Information Fusion, 43, 53–65. https://doi.org/10.1016/j.inffus.2017.11.009

21.

Emerson

(2016a). Majority rule in the West. In Emerson

(Ed.), From majority rule to inclusive politics (pp. 31–46). Springer. https://doi.org/10.1007/978-3-319-23500-4

22.

Emerson

(2016b). Majority rule: The right way may be wrong. In Emerson

(Ed.), From majority rule to inclusive politics (pp. 11–29). Springer. https://doi.org/10.1007/978-3-319-23500-4

23.

Figueredo

A. J.

Vázquez

Hagenah

G. H.

Schneider

S. M. R.

(2007). The K-factor, covitality, and personality: A psychometric test of life history theory. Human Nature, 18(1), 47–37. https://doi.org/10.1007/BF02820846

24.

Fokas

(2007). Growth functions, social diffusion, and social change. Review of Sociology, 13(1), 5–30. https://doi.org/10.1556/RevSoc.13.2007.1.1

25.

Folino

Medicino

Senatore

Spezzano

Straface

(2006). A model based on cellular automata for the parallel simulation of 3D unsaturated flow. Parallel Computing, 32, 357–376. https://doi:10.1016/j.parco.2006.06.003

26.

Fortunato

Castellano

(2007). Scaling and universality in proportional elections. Physical Review Letters, 99, Article 138701. https://doi.org/10.1103/PhysRevLett.99.138701

27.

Galam

(1999). Comment on “a landscape theory of aggregation.”British Journal of Political Science, 28(2), 411–412. https://www-jstor-org-443.web.bisu.edu.cn/stable/194312

28.

Galam

(2000). Real space renormalization group and totalitarian paradox of majority rule voting. Physica A, 285, 66–76. https://doi.org/10.1016/S0378-4371(00)00272-7

29.

Galam

(2002). Spontaneous coalition forming. Why some are stable? In Bandini

Chopard

Tomassini

(Eds.), Cellular automata (ACRI 2002, Lecture notes in computer science, Vol. 2493, pp. 1–9). Springer. https://doi.org/10.1007/3-540-45830-1_1

30.

Galam

(2004). The dynamics of minority opinions in democratic debate. Physica A, 336, 56–62. https://doi.org/10.1016/j.physa.2004.01.010

31.

Galam

(2008). Sociophysics: A review of Galam models. International Journal of Modern Physics C, 19(3), 1–17. https://doi.org/10.1142/S0129183108012297

32.

Galam

(2016). The Trump phenomenon, an explanation from sociophysics. Journal of Modern Physics B, 31(10), Article 1742015. https://doi.org/10.1142/S0217979217420152

33.

Goldsmith

E. B.

(2015). Introduction to social influence: Why it matters. In Xiao

J. J.

(Ed.), Social influence and sustainable consumption (International series on consumer science, pp. 3–22). Springer. https://doi.org/10.1007/978-3-319-20738-4

34.

Holyst

J. A.

Kacperski

Schweitzer

(2001). Social impact models of opinion dynamics. In Stauffer

(Ed.), Annual reviews of computational physics 1X (pp. 253–273). World Scientific. https://doi.org/10.1142/9789812811578_0005

35.

Kao

A. B.

Miller

Torney

Hartnett

Couzin

I. D.

(2014). Collective learning and optimal consensus decisions in social animal groups. PLOS Computational Biology, 10(8), Article e1003762. https://doi.org/10.1371/journal.pcbi.1003762

36.

Knuth

(1998). Random numbers. In The art of computer programming. Volume: 2: Seminumerical algorithms (3rd ed., pp. 1–193). Addison-Wesley.

37.

Kolbin

V. V.

(2003). Decision making and programming (1st ed.). World Scientific.

38.

Komorita

S. S.

Kravitz

D. A.

(1983). Coalition formation: A social psychological approach. In Paulus

P. B.

(Eds.), Basic group processes (Springer series in social psychology, pp. 179–203). Springer.

39.

Krapivsky

P. L.

Redner

(2003). Dynamics of majority rule in two-state interacting spins systems. Physical Review Letters, 90(23), Article 238701. https://doi.org/10.1103/PhysRevLett.90.238701

40.

Krügl

Fehler

Herrler

(2005). About the role of the environment in multi-agent simulations. In Weyns

Van Dyke Parunak

Michel

(Eds.), Environments for multi-agent systems (E4MAS 2004, Lecture notes in computer science, Vol. 3374, pp. 127–149). Springer.

41.

Locke

(1997a). Knowledge and probability. In Locke

(Ed.), An essay concerning human understanding (R. Woolhouse, Introduction and Redaction, pp. 467–635). Penguin Books. (Original work published in 1689)

42.

Locke

(1997b). Of ideas. In Locke

(Ed.), An essay concerning human understanding (R. Woolhouse, Introduction and Redaction, pp. 109–360). Penguin Books. (Original work published in 1689)

43.

Lyra

M. L.

Costa

U. M. S.

Costa Filho

R. N.

Andrade

J. S.

(2003). Generalized Zipf’s law in proportional voting processes. Europhysics Letters, 62, 131–137. https://doi.org/10.1209/epl/i2003-00371-6

44.

Mesterton-Gibbons

Gavrilets

Gravner

Akcay

(2011). Models of coalition or alliance formation. Journal of Theoretical Biology, 274(1), 187–204. https://doi.org/10.1016/j.jtbi.2010.12.031

45.

Meysam

Cioffi-Revilla

(2015). Activation regimes in opinion dynamics. Comparing asynchronous updating schemes. Journal of Artificial Societies and Social Simulation, 18(3), 1–12. https://doi.org/10.18564/jasss.2733

46.

Murnigham

J. K.

(1978). Models of coalition behavior: Game theoretic, social psychological, and political perspectives. Psychological Bulletin, 85(5), 1130–1153. https://doi.org/10.1037/0033-2909.85.5.1130.

47.

Nigel

Troitzsch

K. G.

(2012). Cellular automata. In Simulation for the social scientist. Open University Press; McGraw-Hill Education. http://www.modares.ac.ir/uploads/Agr.Oth.Lib.16.pdf

48.

Packard

N. H.

Wolfram

(1984). Two-dimensional cellular automata. Journal of Statistic Physics, 38, 901–406. https://doi.org/10.1007/BF01010423

49.

Reznick

Bryant

M. J.

Bashey

(2002). r- and K-Selection revisited: The role of population regulation in life-history evolution. Ecology, 83(2), 1509–1520. https://doi.org/10.2307/3071970

50.

Salazar

H. A.

Oerlemans

van Stroe-Biezen

(2012). Social Influence on sustainable consumption: Evidence from a behavioral experiment. International Journal of Consumer Studies, 37(2), 172–180. https://doi.org/10.1111/j.1470-6431.2012.01110.x

51.

Schelling

T. C.

(1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1(2), 143–186. https://doi.org/10.1080/0022250X.1971.9989794

52.

Sobkowicz

(2009). Modelling opinion formation with physics tools: Call for closer link with reality. Journal of Artificial Societies and Social Simulation, 12(1), Article 11. http://jasss.soc.surrey.ac.uk/12/1/11.html

53.

Stauffer

(2003). How to convince others? Monte Carlo simulations of the Sznajd model. In Gubernatis

J. E.

(Ed.), AIP conference proceedings on the Monte Carlo method in the physical sciences: Celebrating 50th anniversary of the metropolis algorithm (Vol. 690, pp. 147–155). https://doi.org/10.1063/1.1632125

54.

Stauffer

(2013). A biased review of sociophysics. Journal of Statistical Physics, 151(1–2), 9–20. https://doi.org/10.1007/s10955-012-0604-9

55.

Stauffer

Sousa

A. O.

De Oliviera

(2000). Generalization to square lattice of Sznajd sociophysics model. International Journal of Modern Physics C, 11(6), 1239–1245. https://doi.org/10.1142/S012918310000105X

56.

Taylor

Hewitt

Reeves

R. A.

Hobbs

S. H.

Lawless

W. F.

(2013). Group decision-making: Consensus rule versus majority rule. Procedia Technology, 9, 498–504. https://doi.org/10.1016/j.protcy.2013.12.055

57.

Ten Velden

F. S.

Beersma

De Dreu

C. K.

(2007). Majority and minority Influence in group negotiation: The moderating effects of social motivation and decision rules. Journal of Applied Psychology, 92(1), 259–268. https://doi.org/10.1037/0021-9010.92.1.259

58.

Troitzsch

K. G.

(2012). Simulating communication and interpretation as a means of interaction in human social systems. Simulation, 88(1), 7–17. https://doi.org/10.1177/0037549710386515

59.

Vandermeer

(2010). How populations grow: The exponential and logistic equations. Nature, Education Knowledge, 3(10), Article 15. https://www-nature-com-s.web.bisu.edu.cn/scitable/knowledge/library/how-populations-grow-the-exponential-and-logistic-13240157