Negative bloc rule: An axiomatic and probabilistic analysis

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December 21, 2023

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Marin Gohard, « Negative bloc rule: An axiomatic and probabilistic analysis », HAL-SHS : économie et finance, ID : 10670/1.48z9nz


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In single winner voting elections, the plurality rule is one of the most studied rules. Plurality has been extended to the field of multiwinner voting elections where instead of electing one candidate, k candidates have to be elected. This extension is called the Bloc rule and consists in voting for the k top preferred candidates. Antiplurality is another common voting rule, where voters vote for all the candidates except their last ranked candidate. In this paper, we introduce an extension of antiplurality in the field of multiwinner elections and call it Negative bloc rule. Axiomatic properties of this new rule are checked and compared to other multiwinner voting rules (k-plurality, k-antiplurality, k-Borda and Bloc). This axiomatic analysis is completed with a probabilistic approach on the similarity of results between Negative bloc rule and the four other rules. Finally, the behavior of Negative bloc rule according to some Condorcet properties is investigated.

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