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Manipulating an election in social networks through link addition

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Abstract

We investigate the effects of the social influence in determining the behavior of agents in a social network in the context of an election. In particular, we concentrate our attention on how the structure of a social network can be manipulated in order to determine the outcome of an election. We consider an election with m candidates and n voters, each one with her own ranking on the candidates. Voters are part of a social network and the information that each voter has about the election is limited to what her friends are voting. We consider an iterative elective process where, at each round, each voter decides her vote strategically, based on what her neighbors voted in the previous round and her ranking. Thus, a voter may decide to vote for a candidate different from her favorite to avoid the election of a candidate she dislikes. Following Sina et al. (Adapting the social network to affect elections. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, pp 705–713, 2015) we investigate how a central organization that knows rankings of all the voters and can manipulate the structure of the social network can determine the outcome of the election by creating new connections among voters. Our main result is an algorithm that, under mild conditions on the social network topology and on the voters’ rankings, is able to compute a limited number of links to be added to the social network in order to make our designed candidate the winner of the election. Our results can be seen as another indication that who controls social media can have a great influence on our lives by strategically determining what information we are exposed to.

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Notes

  1. Here, in order to make simpler our analysis, we present a basic version of our algorithm, in which we do not constrain the order in which nodes are processed to make them vote for candidate w at round 1. Anyway, we may include here the different optimizations introduced in Sina et al. (2015), with the goal to minimize both the number of nodes processed in this phase and the number of links that have been added. For example, one may prefer to process nodes with a low degree first (since they need less links to be “influenced”), or one may prefer to process node that are supporters of the candidate different from w that is currently winning the election (since, this reduce the gap between w and the current winner by two units and not just one).

  2. Many models are known in literature for dealing with this kind of players: the mutation model (Kandori et al. 1993), the mistake model (Kandori and Rob 1995; Young 1993), the logit update rule (Blume 1993) and its corresponding equilibria concepts, quantal response equilibrium (McKelvey and Palfrey 1995), and logit equilibrium (Auletta et al. 2016b).

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Acknowledgements

The funding has been received form Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni with Grant No. Progetti di Ricerca 2019; Ministero dell’Istruzione, dell’Universitá e della Ricerca with Grant no. PRIN 2017 Project ALGADIMAR “Algorithms, Games, and Digital Markets”.

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  1. Università degli Studi di Salerno, Fisciano, Italy

    Vincenzo Auletta, Diodato Ferraioli & Vincenzo Savarese

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  1. Vincenzo Auletta
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  2. Diodato Ferraioli
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  3. Vincenzo Savarese
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Correspondence to Diodato Ferraioli.

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An extended abstract of the work appeared as Auletta et al. (2019c).

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Auletta, V., Ferraioli, D. & Savarese, V. Manipulating an election in social networks through link addition. J Ambient Intell Human Comput 11, 4073–4088 (2020). https://doi.org/10.1007/s12652-019-01669-5

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