6 research outputs found
Convergence of Opinion Diffusion is PSPACE-complete
We analyse opinion diffusion in social networks, where a finite set of
individuals is connected in a directed graph and each simultaneously changes
their opinion to that of the majority of their influencers. We study the
algorithmic properties of the fixed-point behaviour of such networks, showing
that the problem of establishing whether individuals converge to stable
opinions is PSPACE-complete
Election Manipulation on Social Networks: Seeding, Edge Removal, Edge Addition
We focus on the election manipulation problem through social influence, where
a manipulator exploits a social network to make her most preferred candidate
win an election. Influence is due to information in favor of and/or against one
or multiple candidates, sent by seeds and spreading through the network
according to the independent cascade model. We provide a comprehensive study of
the election control problem, investigating two forms of manipulations: seeding
to buy influencers given a social network, and removing or adding edges in the
social network given the seeds and the information sent. In particular, we
study a wide range of cases distinguishing for the number of candidates or the
kind of information spread over the network. Our main result is positive for
democracy, and it shows that the election manipulation problem is not
affordable in the worst-case except for trivial classes of instances, even when
one accepts to approximate the margin of victory. In the case of seeding, we
also show that the manipulation is hard even if the graph is a line and that a
large class of algorithms, including most of the approaches recently adopted
for social-influence problems, fail to compute a bounded approximation even on
elementary networks, as undirected graphs with every node having a degree at
most two or directed trees. In the case of edge removal or addition, our
hardness results also apply to the basic case of social influence
maximization/minimization. In contrast, the hardness of election manipulation
holds even when the manipulator has an unlimited budget, being allowed to
remove or add an arbitrary number of edges.Comment: arXiv admin note: text overlap with arXiv:1902.0377
Reasoning about consensus when opinions diffuse through majority dynamics
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 the majority of 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 underlying graph, there is always a group formed by a half of the agents that can annihilate the opposite opinion. Instead, the influence power of minorities depends on certain features of the given graph, which are NP-hard to be identified. Deciding whether the two opinions can coexist in some stable configuration is NP-hard, too
Majority Opinion Diffusion in Social Networks: An Adversarial Approach
We introduce and study a novel majority-based opinion diffusion model.
Consider a graph , which represents a social network. Assume that initially
a subset of nodes, called seed nodes or early adopters, are colored either
black or white, which correspond to positive or negative opinion regarding a
consumer product or a technological innovation. Then, in each round an
uncolored node, which is adjacent to at least one colored node, chooses the
most frequent color among its neighbors.
Consider a marketing campaign which advertises a product of poor quality and
its ultimate goal is that more than half of the population believe in the
quality of the product at the end of the opinion diffusion process. We focus on
three types of attackers which can select the seed nodes in a deterministic or
random fashion and manipulate almost half of them to adopt a positive opinion
toward the product (that is, to choose black color). We say that an attacker
succeeds if a majority of nodes are black at the end of the process. Our main
purpose is to characterize classes of graphs where an attacker cannot succeed.
In particular, we prove that if the maximum degree of the underlying graph is
not too large or if it has strong expansion properties, then it is fairly
resilient to such attacks.
Furthermore, we prove tight bounds on the stabilization time of the process
(that is, the number of rounds it needs to end) in both settings of choosing
the seed nodes deterministically and randomly. We also provide several hardness
results for some optimization problems regarding stabilization time and choice
of seed nodes.Comment: To appear in AAAI 202