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arXiv · 2407.01382

Voting Profiles Admitting All Candidates as Knockout Winners

Bernard De Baets·Emilio De Santis
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Abstract

A set of $2^n$ candidates is presented to a commission. At every round, each member of this commission votes by pairwise comparison, and one-half of the candidates is deleted from the tournament, the remaining ones proceeding to the next round until the $n$-th round (the final one) in which the final winner is declared. The candidates are arranged on a board in a given order, which is maintained among the remaining candidates at all rounds. A study of the size of the commission is carried out in order to obtain the desired result of any candidate being a possible winner. For $2^n$ candidates with $n \geq 3$, we identify a voting profile with $4n -3$ voters such that any candidate could win simply by choosing a proper initial order of the candidates. Moreover, in the setting of a random number of voters, we obtain the same results, with high probability, when the expected number of voters is large.

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Bernard De Baets, Emilio De Santis. 2024-07-01. Voting Profiles Admitting All Candidates as Knockout Winners. https://arxiv.org/abs/2407.01382

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