Reasoning about Consensus when Opinions Diffuse through Majority Dynamics

@inproceedings{Auletta2018ReasoningAC,
  title={Reasoning about Consensus when Opinions Diffuse through Majority Dynamics},
  author={Vincenzo Auletta and Diodato Ferraioli and Gianluigi Greco},
  booktitle={IJCAI},
  year={2018}
}
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 matter of the graph given at hand, there always exists a group formed by a half of the agents that can annihilate the opposite opinion. Instead, the influence… 

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References

SHOWING 1-10 OF 42 REFERENCES
Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks
TLDR
It is proved that for networks that are sparse and expansive, the population will converge to the correct opinion with high probability, and on the other hand, it is shown that there exist networks for which consensus is unlikely, or for which declarations converge on the incorrect opinion with positive probability.
Minority Becomes Majority in Social Networks
TLDR
The case in which agents express preferences over two alternatives and model social pressure with the majority dynamics is considered: at each step an agent is selected and its preference is replaced by the majority of the preferences of her neighbors.
Manipulating Opinion Diffusion in Social Networks
TLDR
Several ways of manipulating the majority opinion in a stable outcome are considered, such as bribing agents, adding/deleting links, and changing the order of updates, and the computational complexity of the associated problems is investigated.
Propositional Opinion Diffusion
TLDR
A formal model of opinion diffusion and formation is presented which combines notions from social network analysis together with concepts and techniques from judgment aggregation and merging to study the propagation of individual opinions in a multiagent system linked by an influence network.
Majority dynamics and aggregation of information in social networks
TLDR
A family of examples in which interaction prevents efficient aggregation of information, and a condition on the social network which ensures that aggregation occurs, is constructed, which shows that if the initial population is sufficiently biased towards a particular alternative then that alternative will eventually become the unanimous preference of the entire population.
Strategic Disclosure of Opinions on a Social Network: (Extended Abstract)
TLDR
It is shown that games of influence provide a simple abstraction to explore the effects of the trust network structure on the agents' behaviour, by considering solution concepts from game-theory such as Nash equilibrium, weak dominance and winning strategies.
Social Pressure in Opinion Games
TLDR
It is proved that for clique social networks, the dynamics always converges to consensus if the social pressure is high enough, and bounds are polynomial in the number of players provided that the pressure grows sufficiently fast.
Stability in Binary Opinion Diffusion
TLDR
Stabilization of the process of diffusion of binary opinions on networks is studied in terms of neighborhood structures, and how the monotone \(\mu \)-calculus can express relevant properties of them is shown.
Pairwise Diffusion of Preference Rankings in Social Networks
TLDR
This work introduces a model of preference diffusion in which agents in a social network update their preferences based on those of their influencers in the network, and considers both a synchronous and an asynchronous variant of this model.
Group Reasoning in Social Environments
TLDR
A thoroughly computational complexity analysis is conducted on the problem of deciding the existence of stable outcomes and the convergence of Nash dynamics consisting of sequences of best response updates is studied, too.
...
1
2
3
4
5
...