{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T04:15:27Z","timestamp":1777090527367,"version":"3.51.4"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,7,23]],"date-time":"2020-07-23T00:00:00Z","timestamp":1595462400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,7,23]],"date-time":"2020-07-23T00:00:00Z","timestamp":1595462400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soc Choice Welf"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>I introduce a diagram for describing and analyzing single-winner elections in which voters rank the candidates\u2014a class of voting systems including positional methods (e.g. plurality, Borda count, anti-plurality), Condorcet methods, and instant-runoff voting (i.e. ranked-choice voting or the alternative vote). The diagram shows how the outcome of an election depends on each candidate\u2019s share of top rankings as a function of the voting system and the pattern of lower rankings. Using as examples two Brexit polls, a mayoral election in San Francisco, and the US\u2019s first instant-runoff congressional election (all since 2018), I show how the diagram can concisely present preferences and results under different voting systems, identify Condorcet cycles, highlight system properties such as join-inconsistency and the no-show paradox, and illuminate strategic voting incentives.<\/jats:p>","DOI":"10.1007\/s00355-020-01274-y","type":"journal-article","created":{"date-parts":[[2020,7,23]],"date-time":"2020-07-23T11:04:07Z","timestamp":1595502247000},"page":"143-171","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A diagram for analyzing ordinal voting systems"],"prefix":"10.1007","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2362-0654","authenticated-orcid":false,"given":"Andrew C.","family":"Eggers","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,23]]},"reference":[{"key":"1274_CR1","volume-title":"Social choice and individual values","author":"KJ Arrow","year":"1951","unstructured":"Arrow KJ (1951) Social choice and individual values. 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