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The truncated geometric election algorithm: Duration of the election

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  • Louchard, Guy
  • Ward, Mark Daniel

Abstract

The present paper makes three distinct improvements over an earlier investigation of Kalpathy and Ward. We analyze the length of the entire election process (not just one participant’s duration), for a randomized election algorithm, with a truncated geometric number of survivors in each round. We not only analyze the mean and variance; we analyze the asymptotic distribution of the entire election process. We also introduce a new variant of the election that guarantees a unique winner will be chosen; this methodology should be more useful in practice than the previous methodology. The method of analysis includes a precise analytic (complex-valued) approach, relying on singularity analysis of probability generating functions.

Suggested Citation

  • Louchard, Guy & Ward, Mark Daniel, 2015. "The truncated geometric election algorithm: Duration of the election," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 40-48.
    • Handle: RePEc:eee:stapro:v:101:y:2015:i:c:p:40-48
    DOI: 10.1016/j.spl.2015.02.018
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    References listed on IDEAS

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    1. Kalpathy, Ravi & Ward, Mark Daniel, 2014. "On a leader election algorithm: Truncated geometric case study," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 40-47.
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    Cited by:

    1. Goedhart, Joost & Haijema, René & Akkerman, Renzo, 2023. "Modelling the influence of returns for an omni-channel retailer," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1248-1263.

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