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In this paper, we provide a quantitative analysis of multiwinner voting rules using methods from the theory of approximation algorithms---we estimate how well multiwinner rules approximate two extreme objectives: a representation criterion defined via the Approval Chamberlin--Courant rule and a utilitarian criterion defined via Multiwinner Approval Voting. With both theoretical and experimental methods, we classify multiwinner rules in terms of their quantitative alignment with these two opposing objectives. Our results provide fundamental information about the nature of multiwinner rules and, in particular, about the necessary tradeoffs when choosing such a rule.","url_abs":"https://arxiv.org/abs/1801.01527v4","url_pdf":"https://arxiv.org/pdf/1801.01527v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-quantitative-analysis-of-multi-winner-rules","repo_url":"https://github.com/martinlackner/abcvoting","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-quantitative-analysis-of-multi-winner-rules","repo_url":"https://github.com/martinlackner/quantitative-multiwinner","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1801.01527","atlas_url":"https://app.syntology.ai/?focus=1801.01527","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1801.01527"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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