Balancing spreads of influence in a social network

The personalization of our news consumption on social media has a tendency to reinforce our pre-existing beliefs instead of balancing our opinions. To tackle this issue, Garimella et al. (NIPS’17) modeled the spread of these viewpoints, also called campaigns, using the independent cascade model introduced by Kempe, Kleinberg and Tardos (KDD’03) and studied an optimization problem that aims to balance information exposure when two opposing campaigns propagate in a network. This paper investigates a natural generalization of this optimization problem in which μ different campaigns propagate in the network and we aim to maximize the expected number of nodes that are reached by at least ν or none of the campaigns, where μ ≥ ν ≥ 2. Following Garimella et al., despite this general setting, we also investigate a simplified one, in which campaigns propagate in a correlated manner. While for the simplified setting, we show that the problem can be approximated within a constant factor for any constant μ and ν, for the general setting, we give reductions leading to several approximation hardness results when ν ≥ 3. For instance, assuming the gap exponential time hypothesis to hold, we obtain that the problem cannot be approximated within a factor of n−g(n) for any g(n) = o(1) where n is the number of nodes in the network. We complement our hardness results with an Ω(n−1/2)-approximation algorithm for the general setting when ν = 3 and μ is arbitrary

Balancing spreads of influence in a social network

The personalization of our news consumption on social media has a tendency to reinforce our pre-existing beliefs instead of balancing our opinions. This finding is a concern for the health of our democracies which rely on an access to information providing diverse viewpoints. To tackle this issue from a computational perspective, Garimella et al. (NIPS'17) modeled the spread of these viewpoints, also called campaigns, using the well-known independent cascade model and studied an optimization problem that aims at balancing information exposure in a social network when two opposing campaigns propagate in the network. The objective in their $NP$-hard optimization problem is to maximize the number of people that are exposed to either both or none of the viewpoints. For two different settings, one corresponding to a model where campaigns spread in a correlated manner, and a second one, where the two campaigns spread in a heterogeneous manner, they provide constant ratio approximation algorithms. In this paper, we investigate a more general formulation of this problem. That is, we assume that $\mu$ different campaigns propagate in a social network and we aim to maximize the number of people that are exposed to either $\nu$ or none of the campaigns, where $\mu\ge\nu\ge2$. We provide dedicated approximation algorithms for both the correlated and heterogeneous settings. Interestingly, for the heterogeneous setting with $\nu\ge 3$, we give a reduction leading to several approximation hardness results. Maybe most importantly, we obtain that the problem cannot be approximated within a factor of $n^{-g(n)}$ for any $g(n)=o(1)$ assuming Gap-ETH, denoting with $n$ the number of nodes in the social network. For $\nu \ge 4$, there is no $n^{-\epsilon}$-approximation algorithm if a certain class of one-way functions exists, where $\epsilon > 0$ is a given constant which depends on $\nu$

Information is not a Virus, and Other Consequences of Human Cognitive Limits

The many decisions people make about what to pay attention to online shape the spread of information in online social networks. Due to the constraints of available time and cognitive resources, the ease of discovery strongly impacts how people allocate their attention to social media content. As a consequence, the position of information in an individual's social feed, as well as explicit social signals about its popularity, determine whether it will be seen, and the likelihood that it will be shared with followers. Accounting for these cognitive limits simplifies mechanics of information diffusion in online social networks and explains puzzling empirical observations: (i) information generally fails to spread in social media and (ii) highly connected people are less likely to re-share information. Studies of information diffusion on different social media platforms reviewed here suggest that the interplay between human cognitive limits and network structure differentiates the spread of information from other social contagions, such as the spread of a virus through a population.Comment: accepted for publication in Future Interne

Modelling diffusion of innovations in a social network

A new simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information agents decide whether to upgrade their level or not balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.Comment: 4 pages, 5 figures. Final version accepted in PR

Hipsters on Networks: How a Small Group of Individuals Can Lead to an Anti-Establishment Majority

The spread of opinions, memes, diseases, and "alternative facts" in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread. In this paper, we explore how \textit{anti-establishment} nodes (e.g., \textit{hipsters}) influence the spreading dynamics of two competing products. We consider a model in which spreading follows a deterministic rule for updating node states (which describe which product has been adopted) in which an adjustable fraction $p_{\rm Hip}$ of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two. The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted. We simulate our model on both synthetic and real networks, and we show that the hipsters have a major effect on the final fraction of people who adopt each product: even when only one of the two products exists at the beginning of the simulations, a very small fraction of hipsters in a network can still cause the other product to eventually become the more popular one. To account for this behavior, we construct an approximation for the steady-state adoption fraction on $k$-regular trees in the limit of few hipsters. Additionally, our simulations demonstrate that a time delay $\tau$ in the knowledge of the product distribution in a population, as compared to immediate knowledge of product adoption among nearest neighbors, can have a large effect on the final distribution of product adoptions. Our simple model and analysis may help shed light on the road to success for anti-establishment choices in elections, as such success can arise rather generically in our model from a small number of anti-establishment individuals and ordinary processes of social influence on normal individuals.Comment: Extensively revised, with much new analysis and numerics The abstract on arXiv is a shortened version of the full abstract because of space limit

Scenarios for the development of smart grids in the UK: synthesis report

‘Smart grid’ is a catch-all term for the smart options that could transform the ways society produces, delivers and consumes energy, and potentially the way we conceive of these services. Delivering energy more intelligently will be fundamental to decarbonising the UK electricity system at least possible cost, while maintaining security and reliability of supply. Smarter energy delivery is expected to allow the integration of more low carbon technologies and to be much more cost effective than traditional methods, as well as contributing to economic growth by opening up new business and innovation opportunities. Innovating new options for energy system management could lead to cost savings of up to £10bn, even if low carbon technologies do not emerge. This saving will be much higher if UK renewable energy targets are achieved. Building on extensive expert feedback and input, this report describes four smart grid scenarios which consider how the UK’s electricity system might develop to 2050. The scenarios outline how political decisions, as well as those made in regulation, finance, technology, consumer and social behaviour, market design or response, might affect the decisions of other actors and limit or allow the availability of future options. The project aims to explore the degree of uncertainty around the current direction of the electricity system and the complex interactions of a whole host of factors that may lead to any one of a wide range of outcomes. Our addition to this discussion will help decision makers to understand the implications of possible actions and better plan for the future, whilst recognising that it may take any one of a number of forms