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Quickly Determining Who Won an Election

Authors Lisa Hellerstein , Naifeng Liu , Kevin Schewior

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Author Details

Lisa Hellerstein
  • Department of Computer Science and Engineering, New York University Tandon School of Engineering, NY, USA
Naifeng Liu
  • Department of Computer Science, CUNY Graduate Center, New York, NY, USA
  • Department of Economics, University of Mannheim, Germany
Kevin Schewior
  • Department of Computer Science and Mathematics, University of Southern Denmark, Odense, Denmark

Funding

  • Hellerstein, Lisa: Partially supported by NSF Award IIS-1909335.
  • Liu, Naifeng: Partially supported by the Teaching Fellowship at City University of New York.
  • Schewior, Kevin: Partially supported by the Independent Research Fund Denmark, Natural Sciences, grant DFF-0135-00018B.

Acknowledgements

The authors thank R. Teal Witter and Devorah Kletenik for helpful discussions.

Cite AsGet BibTex

Lisa Hellerstein, Naifeng Liu, and Kevin Schewior. Quickly Determining Who Won an Election. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 61:1-61:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.61

Abstract

This paper considers elections in which voters choose one candidate each, independently according to known probability distributions. A candidate receiving a strict majority (absolute or relative, depending on the version) wins. After the voters have made their choices, each vote can be inspected to determine which candidate received that vote. The time (or cost) to inspect each of the votes is known in advance. The task is to (possibly adaptively) determine the order in which to inspect the votes, so as to minimize the expected time to determine which candidate has won the election. We design polynomial-time constant-factor approximation algorithms for both the absolute-majority and the relative-majority version. Both algorithms are based on a two-phase approach. In the first phase, the algorithms reduce the number of relevant candidates to O(1), and in the second phase they utilize techniques from the literature on stochastic function evaluation to handle the remaining candidates. In the case of absolute majority, we show that the same can be achieved with only two rounds of adaptivity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • stochastic function evaluation
  • voting
  • approximation algorithms

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