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The truncated geometric election algorithm: Duration of the election

par Louchard, Guy ;Ward, Mark Daniel
Référence Statistics & probability letters, 101, page (40-48)
Publication Publié, 2015-06

Article révisé par les pairs

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Résumé :

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.