Reasoning about Consensus when Opinions Diffuse through Majority Dynamics

IJCAI, pp. 49-55, 2018.

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Keywords:
social networksocial pressurebinary opinioncomputational social choicemajority dynamicMore(1+)
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In the paper we addressed a number of questions related to whether consensus can be achieved in settings where opinions of the agents are affected by social influence phenomena

Abstract:

Opinion diffusion is studied on social graphs where agents hold binary opinions and where social pressure leads them to conform to the opinion manifested by their neighbors. Within this setting, questions related to whether a minority/majority can spread the opinion it supports to all the other agents are considered.It is shown that, no m...More

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Introduction
  • Each of them holds an opinion on her ideal choice.
  • They are neither strategic [Osborne and Rubinstein, 1994; Gottlob et al, 2005] nor inclined to use voting rules or other mechanisms to find an agreement [Brandt et al, 2016; Endriss, 2017].
  • The authors ask: Would be they capable to reach a consensus for some/all profiles of their initial opinions? Can a minority have enough social “power” to influence all other agents? Is it any easier for a majority to guide convergence towards consensus?
Highlights
  • We know that, at a certain point, they will exchange their viewpoints and each of them will be affected by a social pressure leading to adapt her opinion to the one manifested by the majority of her friends
  • We show that the answer is positive on any social graph and for any given value of α≥1/2
  • We show that the answer to the question depends on the structure of the social graph and, more interestingly, recognizing such graphs is NP-hard
  • In the paper we addressed a number of questions related to whether consensus can be achieved in settings where opinions of the agents are affected by social influence phenomena
  • We have shown that a configuration always exists for which the opinion of the majority diffuse to all the agents
Conclusion
  • In the paper the authors addressed a number of questions related to whether consensus can be achieved in settings where opinions of the agents are affected by social influence phenomena.
  • The authors have shown that a configuration always exists for which the opinion of the majority diffuse to all the agents.
  • The authors exhibited hardness results for spreading the opinion of the minority and for checking the existence of “plural” configurations.
  • An interesting avenue for further research is to identify special classes of graphs where it is easy to answer similar questions, by looking at structural and topological restrictions
Summary
  • Introduction:

    Each of them holds an opinion on her ideal choice.
  • They are neither strategic [Osborne and Rubinstein, 1994; Gottlob et al, 2005] nor inclined to use voting rules or other mechanisms to find an agreement [Brandt et al, 2016; Endriss, 2017].
  • The authors ask: Would be they capable to reach a consensus for some/all profiles of their initial opinions? Can a minority have enough social “power” to influence all other agents? Is it any easier for a majority to guide convergence towards consensus?
  • Conclusion:

    In the paper the authors addressed a number of questions related to whether consensus can be achieved in settings where opinions of the agents are affected by social influence phenomena.
  • The authors have shown that a configuration always exists for which the opinion of the majority diffuse to all the agents.
  • The authors exhibited hardness results for spreading the opinion of the minority and for checking the existence of “plural” configurations.
  • An interesting avenue for further research is to identify special classes of graphs where it is easy to answer similar questions, by looking at structural and topological restrictions
Funding
  • Vincenzo Auletta and Diodato Ferraioli were supported by “GNCS–INdAM”
  • Gianluigi Greco was partially supported by Regione Calabria under POR project “Explora Process”
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