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Election control through social influence with voters’ uncertainty

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Abstract

The problem of election control through social influence consists in finding a set of nodes in a social network of voters to be the starters of a political campaign aimed at supporting a particular target candidate. The voters reached by the campaign change their views on the candidates. The goal is to model the spread of the campaign in such a way as to maximize the chances of winning for the target candidate. Herein, differently from previous work, we consider that each voter is associated with a probability distribution over the candidates modeling the likelihood of the voter to vote for each candidate. In a first model we propose, we prove that, under the Gap-ETH, the problem cannot be approximated to within a factor better than \(1/n^{o(1)}\), where n is the number of voters. In a second model, which is a slight relaxation of the first one, the problem instead admits a constant-factor approximation algorithm. Finally, we present simulations on both synthetic and real networks, comparing the results of our algorithm with those obtained by a standard greedy algorithm for Influence Maximization.

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Notes

  1. https://en.wikipedia.org/wiki/Facebook-Cambridge_Analytica_data_scandal (page retrieved on 08/07/2021).

  2. The assumption is used in the approximation results, since Influence Maximization problem with exponential (or exponentially small) weights on nodes is an open problem (Kempe et al. 2015, footnote 3, page 119). However, the assumption is realistic: Current techniques to estimate such parameters generate values linear in the number of messages shared by a node.

  3. It is still an open question how well the value of \(\sigma _w(S)\) can be approximated for an influence model with arbitrary node weights [Kempe et al. (2015), footnote 3, page 119].

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Authors and Affiliations

  1. Gran Sasso Science Institute, L’Aquila, Italy

    Mohammad Abouei Mehrizi

  2. Missouri University of Science and Technology, Rolla, USA

    Federico Corò

  3. Paris-Lodron-Universität Salzburg, Salzburg, Austria

    Emilio Cruciani

  4. Gran Sasso Science Institute, L’Aquila, Italy

    Gianlorenzo D’Angelo

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  1. Mohammad Abouei Mehrizi
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  2. Federico Corò
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  3. Emilio Cruciani
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  4. Gianlorenzo D’Angelo
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Correspondence to Federico Corò.

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Abouei Mehrizi, M., Corò, F., Cruciani, E. et al. Election control through social influence with voters’ uncertainty. J Comb Optim 44, 635–669 (2022). https://doi.org/10.1007/s10878-022-00852-3

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