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An Approval-Based Model for Single-Step Liquid Democracy

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Algorithmic Game Theory (SAGT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12885))

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Abstract

We study a Liquid Democracy framework where voters can express preferences in an approval form, regarding being represented by a subset of voters, casting a ballot themselves, or abstaining from the election. We examine, from a computational perspective, the problems of minimizing (resp. maximizing) the number of dissatisfied (resp. satisfied) voters. We first show that these problems are intractable even when each voter approves only a small subset of other voters. On the positive side, we establish constant factor approximation algorithms for that case, and exact algorithms under bounded treewidth of a convenient graph-theoretic representation, even when certain secondary objectives are also present. The results related to the treewidth are based on the powerful methodology of expressing graph properties via Monadic Second Order logic. We believe that this approach can turn out to be fruitful for other graph related questions that appear in Computational Social Choice.

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Notes

  1. 1.

    For ease of presentation, we will also use some set operations that although they are not explicitly allowed, they can be easily replaced by equivalent MSO expressions. For instance, \(x\notin A\setminus B \equiv \lnot ((x \in A)\wedge \lnot (x\in B))\) and \(A\subseteq B \equiv (\forall x\in A\Rightarrow x\in B)\).

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Acknowledgements

This work has been supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “First Call for H.F.R.I. Research Projects to support faculty members and researchers and the procurement of high-cost research equipment” grant (Project Number: HFRI-FM17-3512).

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Authors and Affiliations

  1. Athens University of Economics and Business, Athens, Greece

    Evangelos Markakis & Georgios Papasotiropoulos

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  1. Evangelos Markakis
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  2. Georgios Papasotiropoulos
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Editors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Ioannis Caragiannis

  2. Aarhus University, Aarhus, Denmark

    Kristoffer Arnsfelt Hansen

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Markakis, E., Papasotiropoulos, G. (2021). An Approval-Based Model for Single-Step Liquid Democracy. In: Caragiannis, I., Hansen, K.A. (eds) Algorithmic Game Theory. SAGT 2021. Lecture Notes in Computer Science(), vol 12885. Springer, Cham. https://doi.org/10.1007/978-3-030-85947-3_24

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  • DOI: https://doi.org/10.1007/978-3-030-85947-3_24

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  • Online ISBN: 978-3-030-85947-3

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