Abstract
Social network science and social interaction science is an interesting and steadily growing field of research in current time. Social network influences the lives of millions, and therefore the propagation of influence in such a network deserves study. In this paper, we have studied voting in a Watts-Strogatz small-world network for two parties. In our model, each node has an initial bias towards one of the parties (or can be neutral) and are influenced by their neighbours to vote for a particular party. We show via simulation that (i) for linear of logarithmic voting function, the small-scale variation is minimum, but the majority of the nodes tend to align towards one of the parties in the long term, (ii) for periodic voting function, the small-scale variations are sharp and oscillating, but in the long term the number of voters in each party roughly remains the same, (iii) the degree of the graph does not seem to have a strong influence on the result, and (iv) networks with higher small-world probability tend to resist the alignment of voters towards a particular party for a longer time as compared to networks with lower small-world probability. This majority voting model seems to efficiently capture the potential behaviour of voters on small-world network over a campaigning period.
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References
Glauber, R.J.: Time-dependent statistics of the Ising model. J. Math. Phys. 4(2), 294–307 (1963). https://doi.org/10.1063/1.1703954
Cicera, M.V.A., Lima, F.W.S.: Majority-vote model in one-dimensional on directed small-world networks. Phys. Astron. Int. J. 2(6) (2018). https://doi.org/10.15406/paij.2018.02.00140
Luz, E.M.S., Lima, F.W.S.: Majority vote on a directed small world network. Int. J. Mod. Phys. C 18(08), 1251–1261 (2007). https://doi.org/10.1142/s0129183107011297
Tullock, G.: Problems of majority voting. J. Polit. Econ. 67(6), 571–579 (1959). https://doi.org/10.1086/258244
Amarla, L.A.N., Scala, A., Barthelemy, M., Stanley, H.E.: Classes of small-world networks. Proc. Nat. Acad. Sci. 97(21), 11149–11152 (2000). https://doi.org/10.1073/pnas.200327197
Barrat, A., Weigt, M.: On the properties of small-world network models. Europ. Phys. J. B 13(3), 547–560 (2000). https://doi.org/10.1007/s100510050067
Erdos, P., Renyi, A.: On the evolution of random graphs. The Structure and Dynamics of Networks (1960). https://doi.org/10.1515/9781400841356.38
Watts, D.J., Strogatz, S.H.: Collective dynamics of small world networks. Nature 393(6684), 440–442 (1998). https://doi.org/10.1038/30918
Gudgin, G., Taylor, P.J.: Electoral bias and the distribution of party voters. Trans. Inst. Br. Geogr. 63, 53 (1974). https://doi.org/10.2307/621532
Gardenfors, P.: Positionalist voting functions. Theory Decis. 4(1), 1–24 (1973). https://doi.org/10.1007/bf00133396
Parhami, B.: Voting algorithms. IEEE Trans. Reliab. 43(4), 617–629 (1994). https://doi.org/10.1109/24.370218
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Ray, S., Chatterjee, K., Majumdar, R., Ganguly, D. (2021). Voting in Watts-Strogatz Small-World Network. In: Bhattacharjee, D., Kole, D.K., Dey, N., Basu, S., Plewczynski, D. (eds) Proceedings of International Conference on Frontiers in Computing and Systems. Advances in Intelligent Systems and Computing, vol 1255. Springer, Singapore. https://doi.org/10.1007/978-981-15-7834-2_31
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DOI: https://doi.org/10.1007/978-981-15-7834-2_31
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