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This setting generalizes both the well-studied model of multiwinner voting and the recently introduced model of cake sharing. Under approval votes, we propose two variants of the extended justified representation (EJR) notion from multiwinner voting, a stronger one called <jats:italic>EJR for mixed goods (EJR-M)<\/jats:italic> and a weaker one called <jats:italic>EJR up to<\/jats:italic> 1 <jats:italic>(EJR-1)<\/jats:italic>. We extend three multiwinner voting rules to our setting\u2014GreedyEJR, the method of equal shares (MES), and proportional approval voting (PAV)\u2014and show that while all three generalizations satisfy EJR-1, only the first one provides EJR-M. In addition, we derive tight bounds on the proportionality degree implied by EJR-M and EJR-1, and investigate the proportionality degree of our proposed rules.<\/jats:p>","DOI":"10.1007\/s00355-024-01511-8","type":"journal-article","created":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T06:02:21Z","timestamp":1709013741000},"page":"643-677","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Approval-based voting with mixed goods"],"prefix":"10.1007","volume":"62","author":[{"given":"Xinhang","family":"Lu","sequence":"first","affiliation":[]},{"given":"Jannik","family":"Peters","sequence":"additional","affiliation":[]},{"given":"Haris","family":"Aziz","sequence":"additional","affiliation":[]},{"given":"Xiaohui","family":"Bei","sequence":"additional","affiliation":[]},{"given":"Warut","family":"Suksompong","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,2,27]]},"reference":[{"key":"1511_CR1","unstructured":"Abramowitz M, Stegun IA (eds) (1972) Handbook of mathematical functions with formulas, graphs, and mathematical tables, 10th edn. 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