Convergence of Opinion Diffusion is PSPACE-Complete

Chistikov, Dmitry; Lisowski, Grzegorz; Paterson, Mike; Turrini, Paolo

doi:10.1609/aaai.v34i05.6197

Cited by 16 publications

(32 citation statements)

References 24 publications

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“…Which rules converge to a stable state? (Section 4) While some works consider convergence of diffusion processes under simultaneous updates of the agents [18,26,11], we focus on sequential updates. For the case of only two opinions a standard update rule is to follow the (strict) majority of the neighbours' opinions.…”

Section: Rulementioning

confidence: 99%

Single-Peaked Opinion Updates

Bredereck¹,

George²,

Israel³

et al. 2022

Preprint

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We consider opinion diffusion for undirected networks with sequential updates when the opinions of the agents are single-peaked preference rankings. Our starting point is the study of preserving single-peakedness. We identify voting rules that, when given a single-peaked profile, output at least one ranking that is single peaked w.r.t. a singlepeaked axis of the input. For such voting rules we show convergence to a stable state of the diffusion process that uses the voting rule as the agents' update rule. Further, we establish an efficient algorithm that maximises the spread of extreme opinions.

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Section: Rulementioning

confidence: 99%

Single-Peaked Opinion Updates

Bredereck¹,

George²,

Israel³

et al. 2022

Preprint

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“…It was proven in [27] that periodicity is always one or two. Recently, it was shown in [15] and [52] that it is PSPACE-complete to decide whether the periodicity is one or not for a given coloring of a directed graph. Regarding the stabilization time, Fogelman, Goles, and Weisbuch [21] showed that it is bounded by O n 2 .…”

Section: Related Workmentioning

confidence: 99%

“…Particularly, the majority-based models, where each node chooses the most frequent color among its neighbors, have received a substantial amount of attention, cf. [15]. This imitating behavior can be explained in several ways: an agent that sees a majority agreeing on an opinion might think that her neighbors have access to some information unknown to her and hence they have made the better choice; also agents can directly benefit from adopting the same behavior as their friends (e.g., prices going down).…”

Section: Introductionmentioning

confidence: 99%

Majority Opinion Diffusion in Social Networks: An Adversarial Approach

Zehmakan¹

2020

Preprint

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We introduce and study a novel majority-based opinion diffusion model. Consider a graph G, 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.

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“…In other words, when voters update their preferences looking at their connections, it is the strategic positioning of a party's electorate that matters, rather than the initial majority (what they call information gerrymandering). Undoubtedly, a metric that allows us to forego the equilibrium computation of a highly complex system is an important practical tool, significantly simplifying the analysis of the opinion diffusion dynamics, a notoriously complex problem [16,17,18]. Moreover, it allows for a further understanding of the effects of manipulation, for example through the strategical placements of bots or zealots to alter the network dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…Research on this has been both empirical [34] and theoretical [35,36,10] (see overviews [37,38]), including attempts to find influential nodes in the social graph [39]. Computational models of opinion diffusion have looked at the fixedpoint properties of the graph dynamics, in connection with consensus formation [17] and its complexity [18]. An important stream of research has looked at how to control opinion diffusion by external intervention, for example through bribery [13], false-name attacks [40] or information control [11], and we see our results as introducing effective heuristics for outcome prediction in those frameworks.…”

Section: Introductionmentioning

confidence: 99%

Predicting Voting Outcomes in the Presence of Communities, Echo Chambers and Multiple Parties

Bara¹,

Lev²,

Turrini³

2022

Preprint

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When individuals interact in a social network their opinions can change, at times quite significantly, as a result of social influence. In elections, for example, while they might initially support one candidate, what their friends say may lead them to support another. But how do opinions settle in a social network, as a result of social influence?A recently proposed graph-theoretic metric, the influence gap, has shown to be a reliable predictor of the effect of social influence in two-party elections, albeit only tested on regular and scale-free graphs. Here, we investigate whether the influence gap is able to predict the outcome of multi-party elections on networks exhibiting community structure, i.e., made of highly interconnected components, and therefore more resembling of real-world interaction. To encode communities we build on the classical model of caveman graphs, which we extend to a richer graph family that displays different levels of homophily, i.e., how much connections and opinions are intertwined.Our contribution is three-fold. First, we study the predictive power of the influence gap in the presence of communities. We show that when there is no

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Convergence of Opinion Diffusion is PSPACE-Complete

Cited by 16 publications

References 24 publications

Single-Peaked Opinion Updates

Single-Peaked Opinion Updates

Majority Opinion Diffusion in Social Networks: An Adversarial Approach

Predicting Voting Outcomes in the Presence of Communities, Echo Chambers and Multiple Parties

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