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On the Complexity of Predicting Election Outcomes and Estimating Their Robustness

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Abstract

When dealing with real-world election data and preferences, it is often realistic to assume that the given data are incomplete or noisy. The reasons for such deficiencies are manifold and range from cost-intensive elicitation to transmission errors and manipulation. Therefore, we study the problem of evaluating elections with incomplete and noisy data and estimating the robustness of certain outcomes from a computational point of view. To cover a wide variety of different scenarios, we consider three different models for the distribution of preferences modeling the deficiencies: the uniform distribution over the completions of incomplete preferences inspired by the possible winner problem, the dispersion around complete preferences according to the Mallows noise model, and a general model in which the distribution over the possible preferences for each voter is explicitly given. We consider both approval vector preferences and linear order preferences and show that the computational complexity of the problems can vary remarkably with respect to the voting rule, the distribution model, and the parameterization. We study the problems both in terms of their weighted counting complexity and their decision complexity, and discuss the effects of the winner model and tie-breaking on the results.

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Funding

This work is supported by the DFG-grant BA6270/1-1.

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Authors and Affiliations

  1. Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, NRW, Germany

    Dorothea Baumeister & Tobias Hogrebe

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  1. Dorothea Baumeister
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  2. Tobias Hogrebe
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Correspondence to Dorothea Baumeister.

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Additional information

Communicated by Davide Grossi, Ariel Rosenfeld and Nimrod Talmon.

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Compared to the preliminary versions in AAMAS-2020 and EUMAS-2021 (see Baumeister and Hogrebe [1, 2]), this revision contains additional results, omitted proofs, further explanations, and an extended and updated section on related work.

This article is part of the topical collection “Advances in Multi-Agent Systems Research: EUMAS 2021 Extended Selected Papers” guest edited by Davide Grossi, Ariel Rosenfeld and Nimrod Talmon.

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Baumeister, D., Hogrebe, T. On the Complexity of Predicting Election Outcomes and Estimating Their Robustness. SN COMPUT. SCI. 4, 362 (2023). https://doi.org/10.1007/s42979-023-01725-0

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