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Throughout history, most of the focus is on deterministic methods to apportion seats among the groups which may favour bigger or smaller parties or may have some inherent mathematical limitations. We survey various randomized rules that achieve exact apportionment in expectation.<\/jats:p>","DOI":"10.1145\/3821540.3821548","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T12:25:47Z","timestamp":1781180747000},"page":"121-129","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Randomized Apportionment Methods for Exact Proportional Representation: A Short Survey"],"prefix":"10.1145","volume":"22","author":[{"given":"Haris","family":"Aziz","sequence":"first","affiliation":[{"name":"The University of New South Wales"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,6,11]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOCO.0000038913.96607.c2"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2019.06.004"},{"key":"e_1_2_1_3_1","first-page":"1750","volume-title":"Operations Research","author":"Aziz H.","year":"2024","unstructured":"H. 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