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Register a new userMulti-Winner Election Control via Social Influence
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Added by
Mohammad Abouei Mehrizi
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In an election, we are given a set of voters, each having a preference list over a set of candidates, that are distributed on a social network. We consider a scenario where voters may change their preference lists as a consequence of the messages received by their neighbors in a social network. Specifically, we consider a political campaign that spreads messages in a social network in support or against a given candidate and the spreading follows a dynamic model for information diffusion. When a message reaches a voter, this latter changes its preference list according to an update rule. The election control problem asks to find a bounded set of nodes to be the starter of a political campaign in support (constructive problem) or against (destructive problem) a given target candidate $c$, in such a way that the margin of victory of $c$ w.r.t. its most voted opponents is maximized. It has been shown that several variants of the problem can be solved within a constant factor approximation of the optimum, which shows that controlling elections by means of social networks is doable and constitutes a real problem for modern democracies. Most of the literature, however, focuses on the case of single-winner elections. In this paper, we define the election control problem in social networks for multi-winner elections with the aim of modeling parliamentarian elections. Differently from the single-winner case, we show that the multi-winner election control problem is NP-hard to approximate within any factor in both constructive and destructive cases. We then study a relaxation of the problem where votes are aggregated on the basis of parties (instead of single candidates), which is a variation of the so-called straight-party voting used in some real parliamentarian elections. We show that the latter problem remains NP-hard but can be approximated within a constant factor.
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The election control problem through social influence asks to find a set of nodes in a social network of voters to be the starters of a political campaign aiming at supporting a given target candidate. Voters reached by the campaign change their opinions on the candidates. The goal is to shape the diffusion of the campaign in such a way that the chances of victory of the target candidate are maximized. Previous work shows that the problem can be approximated within a constant factor in several models of information diffusion and voting systems, assuming that the controller, i.e., the external agent that starts the campaign, has full knowledge of the preferences of voters. However this information is not always available since some voters might not reveal it. Herein we relax this assumption by considering that each voter is associated with a probability distribution over the candidates. We propose two models in which, when an electoral campaign reaches a voter, this latter modifies its probability distribution according to the amount of influence it received from its neighbors in the network. We then study the election control problem through social influence on the new models: In the first model, under the Gap-ETH, election control cannot be approximated within a factor better than $1/n^{o(1)}$, where $n$ is the number of voters; in the second model, which is a slight relaxation of the first one, the problem admits a constant factor approximation algorithm.
Influence overlap is a universal phenomenon in influence spreading for social networks. In this paper, we argue that the redundant influence generated by influence overlap cause negative effect for maximizing spreading influence. Firstly, we present a theoretical method to calculate the influence overlap and record the redundant influence. Then in term of eliminating redundant influence, we present two algorithms, namely, Degree-Redundant-Influence (DRS) and Degree-Second-Neighborhood (DSN) for multiple spreaders identification. The experiments for four empirical social networks successfully verify the methods, and the spreaders selected by the DSN algorithm show smaller degree and k-core values.
Existing socio-psychological studies suggest that users of a social network form their opinions relying on the opinions of their neighbors. According to DeGroot opinion formation model, one value of particular importance is the asymptotic consensus value---the sum of user opinions weighted by the users eigenvector centralities. This value plays the role of an attractor for the opinions in the network and is a lucrative target for external influence. However, since any potentially malicious control of the opinion distribution in a social network is clearly undesirable, it is important to design methods to prevent the external attempts to strategically change the asymptotic consensus value. In this work, we assume that the adversary wants to maximize the asymptotic consensus value by altering the opinions of some users in a network; we, then, state DIVER---an NP-hard problem of disabling such external influence attempts by strategically adding a limited number of edges to the network. Relying on the theory of Markov chains, we provide perturbation analysis that shows how eigenvector centrality and, hence, DIVERs objective function change in response to an edges addition to the network. The latter leads to the design of a pseudo-linear-time heuristic for DIVER, whose computation relies on efficient estimation of mean first passage times in a Markov chain. We confirm our theoretical findings in experiments.
Online social networks are used to diffuse opinions and ideas among users, enabling a faster communication and a wider audience. The way in which opinions are conditioned by social interactions is usually called social influence. Social influence is extensively used during political campaigns to advertise and support candidates. Herein we consider the problem of exploiting social influence in a network of voters in order to change their opinion about a target candidate with the aim of increasing his chance to win/lose the election in a wide range of voting systems. We introduce the Linear Threshold Ranking, a natural and powerful extension of the well-established Linear Threshold Model, which describes the change of opinions taking into account the amount of exercised influence. We are able to maximize the score of a target candidate up to a factor of $1-1/e$ by showing submodularity. We exploit such property to provide a $frac{1}{3}(1-1/e)$-approximation algorithm for the constructive election control problem. Similarly, we get a $frac{1}{2}(1-1/e)$-approximation ratio in the destructive scenario. The algorithm can be used in arbitrary scoring rule voting systems, including plurality rule and borda count. Finally, we perform an experimental study on real-world networks, measuring Probability of Victory (PoV) and Margin of Victory (MoV) of the target candidate, to validate the model and to test the capability of the algorithm.
Influence competition finds its significance in many applications, such as marketing, politics and public events like COVID-19. Existing work tends to believe that the stronger influence will always win and dominate nearly the whole network, i.e., winner takes all. However, this finding somewhat contradicts with our common sense that many competing products are actually coexistent, e.g., Android vs. iOS. This contradiction naturally raises the question: will the winner take all? To answer this question, we make a comprehensive study into influence competition by identifying two factors frequently overlooked by prior art: (1) the incomplete observation of real diffusion networks; (2) the existence of information overload and its impact on user behaviors. To this end, we attempt to recover possible diffusion links based on user similarities, which are extracted by embedding users into a latent space. Following this, we further derive the condition under which users will be overloaded, and formulate the competing processes where users behaviors differ before and after information overload. By establishing the explicit expressions of competing dynamics, we disclose that information overload acts as the critical boundary line, before which the winner takes all phenomenon will definitively occur, whereas after information overload the share of influences gradually stabilizes and is jointly affected by their initial spreading conditions, influence powers and the advent of overload. Numerous experiments are conducted to validate our theoretical results where favorable agreement is found. Our work sheds light on the intrinsic driving forces behind real-world dynamics, thus providing useful insights into effective information engineering.
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