Opinion formation in voting processes under bounded confidence

Sergei Yu. Pilyugin; M. C. Campi; Sergei Yu. Pilyugin; M. C. Campi

doi:10.3934/nhm.2019024

Networks and Heterogeneous Media

2019, Volume 14, Issue 3: 617-632. doi: 10.3934/nhm.2019024

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Opinion formation in voting processes under bounded confidence

Sergei Yu. Pilyugin ^{1
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M. C. Campi ^{2
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1.
St. Petersburg State University, Universitetskaya nab., 7-9, St.Petersburg, 199034, Russia
2.
Dipartimento di Ingegneria dell'Informazione, Università di Brescia, via Branze 38, 25123 Brescia, Italia

Received: 01 October 2018 Revised: 01 March 2019
90B10, 91D30, 91B12, 34D20, 15B51

In recent years, opinion dynamics has received an increasing attention and various models have been introduced and evaluated mainly by simulation. In this study, we introduce a model inspired by the so-called "bounded confidence" approach where voters engaged in an electoral decision with two options are influenced by individuals sharing an opinion similar to their own. This model allows one to capture salient features of the evolution of opinions and results in final clusters of voters. We provide a detailed study of the model, including a complete taxonomy of the equilibrium points and an analysis of their stability. The model highlights that the final electoral outcome depends on the level of interaction in the society, besides the initial opinion of each individual, so that a strongly interconnected society can reverse the electoral outcome as compared to a society with looser exchange.
- Opinion dynamics,
- voting processes,
- bounded confidence,
- dynamical systems,
- equilibrium points
Citation: Sergei Yu. Pilyugin, M. C. Campi. Opinion formation in voting processes under bounded confidence[J]. Networks and Heterogeneous Media, 2019, 14(3): 617-632. doi: 10.3934/nhm.2019024

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Abstract

In recent years, opinion dynamics has received an increasing attention and various models have been introduced and evaluated mainly by simulation. In this study, we introduce a model inspired by the so-called "bounded confidence" approach where voters engaged in an electoral decision with two options are influenced by individuals sharing an opinion similar to their own. This model allows one to capture salient features of the evolution of opinions and results in final clusters of voters. We provide a detailed study of the model, including a complete taxonomy of the equilibrium points and an analysis of their stability. The model highlights that the final electoral outcome depends on the level of interaction in the society, besides the initial opinion of each individual, so that a strongly interconnected society can reverse the electoral outcome as compared to a society with looser exchange.

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