Ties in Multiwinner Approval Voting

{\L}ukasz Janeczko; Piotr Faliszewski

Ties in Multiwinner Approval Voting

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arxiv 2305.01769 v1 pith:EWHXGJRC submitted 2023-05-02 cs.GT

{L}ukasz Janeczko , Piotr Faliszewski This is my paper · ORCID

classification cs.GT

keywords tiescomplexitymultiwinnerrulessequentialsizealgorithmapproval

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We study the complexity of deciding whether there is a tie in a given approval-based multiwinner election, as well as the complexity of counting tied winning committees. We consider a family of Thiele rules, their greedy variants, Phragmen's sequential rule, and Method of Equal Shares. For most cases, our problems are computationally hard, but for sequential rules we find an FPT algorithm for discovering ties (parameterized by the committee size). We also show experimentally that in elections of moderate size ties are quite frequent.

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