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Opening up Echo Chambers via Optimal Content Recommendation

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Complex Networks and Their Applications XI (COMPLEX NETWORKS 2016 2022)

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Abstract

Online social platforms have become central in the political debate. In this context, the existence of echo chambers is a problem of primary relevance. These clusters of like-minded individuals tend to reinforce prior beliefs, elicit animosity towards others and aggravate the spread of misinformation. We study this phenomenon on a Twitter dataset related to the 2017 French presidential elections and propose a method to tackle it with content recommendations. We use a quadratic program to find optimal recommendations that maximise the diversity of content users are exposed to, while still accounting for their preferences. Our method relies on a theoretical model that can sufficiently describe how content flows through the platform. We show that the model provides good approximations of empirical measures and demonstrate the effectiveness of the optimisation algorithm at mitigating the echo chamber effect on this dataset, even with limited budget for recommendations.

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Notes

  1. 1.

    Differently distributed times induce similar equilibrium behaviour [8].

  2. 2.

    Other selection and eviction policies induce similar equilibrium behaviour [8].

  3. 3.

    Certain contexts might actually benefit from this simplification. For example mentions and replies on Twitter may sometimes represent support and sometimes hostility towards the initial content [22].

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Acknowledgements

The authors have no competing interests to declare. This project was funded by the UK EPSRC grant EP/S022503/1 that supports the Centre for Doctoral Training in Cybersecurity delivered by UCL’s Departments of Computer Science, Security and Crime Science, and Science, Technology, Engineering and Public Policy. The research of A.G. and E.P. is supported by the French National Agency of Research (ANR) through the FairEngine project under Grant ANR-19-CE25-0011.

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Correspondence to Antoine Vendeville .

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Appendix

Appendix

1.1 Empirical evaluation of p

First we label each tweet by the affiliation(s) of its original creator, or by ‘?’ if the affiliation is unknown. Because the size of the newsfeeds does not matter according to the model [8], we assume for simplicity that all users have newsfeeds of size 1. We do not know the initial content of each newsfeed and assume they all contain a post of unknown origin, labelled ‘?’. As soon as a user tweets or retweets something, the post is inserted into the newsfeeds of its followers, evicting any previous post that was there. Finally to obtain \(p_s^{(n)}\) we compute for each user n and label s the proportion of time their newsfeed contained a post labelled s. The original affiliation of most tweets is unknown and for each user we disregard periods during which the newsfeed contained a post labelled ‘?’.

1.2 Existence and Unicity of p With Recommendations

Let us write equation (5) in matrix form: \(p_s = \textbf{A}p_s +\textbf{b}.\) As long as the spectral radius \(\rho (\textbf{A})\) of \(\textbf{A}\) is stricly less than 1, the system has a unique solution \(p_s = (\textbf{I}-\textbf{A})^{-1}\textbf{b}\). The entries of \(\textbf{A}\) are given by

$$\begin{aligned} a_{ij} = (1-B) \frac{\mu ^{(j)}}{\sum _{k\in \mathcal {L}^{(i)}} \lambda ^{(k)}+\mu ^{(k)}} \textbf{1}_{j\in \mathcal {L}^{(i)}} \end{aligned}$$
(6)

and because \(B>0\) it holds that \(\sum _j a_{ij}<1\) for any row i. But from [11, Thm. 8.1.22] it we have \(\rho (\textbf{A}) \le \underset{i}{\text {max}}\sum _j a_{ij}\) and thus \(p_s\) exists and is unique.

1.3 Availability of code

The code for the optimisation problem is available at

https://github.com/AntoineVendeville/Opening-up-echo-chambers.

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Vendeville, A., Giovanidis, A., Papanastasiou, E., Guedj, B. (2023). Opening up Echo Chambers via Optimal Content Recommendation. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Miccichè, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1077. Springer, Cham. https://doi.org/10.1007/978-3-031-21127-0_7

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  • DOI: https://doi.org/10.1007/978-3-031-21127-0_7

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