Measuring and Mismeasuring Income Polarization

Measuring and Mismeasuring Income Polarization | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Measuring and Mismeasuring Income Polarization Rodolfo Hoffmann, Ana Lucia Kassouf This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4139220/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The main contribution of this paper is to clarify some of the misconceptions about income polarization indices observed in the existing literature. Our analysis explores the domain of measures of polarization of the income distribution, with a specific emphasis on elucidating the importance of distinguishing between bipolarization and multipolarization measures. Additionally, we assert that a valid polarization metric must satisfy the principle of scale-invariance. Furthermore, in cases where the income distribution is categorized into relatively poor and relatively rich, a valid bipolarization measure should consistently increase when regressive transfers occur from poorer to richer individuals and when progressive transfers occur between two poorer or two richer individuals. The study identifies instances where bipolarization measures that fail to satisfy these criteria have been employed in previous research, leading to erroneous conclusions. The research also provides a succinct analysis of the challenges faced by scholars in employing Esteban and Ray’s multipolarization measure and its adapted versions. The study pinpoints errors in previously published works, particularly in those using the Median Relative Polarization measure with an additive median adjustment. Additionally, a real-world illustration is presented that depicts a declining trend of the bipolarization of income distribution in Brazil from 2001 to 2015, coinciding with a decrease in inequality during this period. polarization income distribution scale-invariant multipolarization inequality Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4139220","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":283352920,"identity":"694805e0-4c81-4e2d-9776-982a8490e9fd","order_by":0,"name":"Rodolfo Hoffmann","email":"","orcid":"","institution":"Universidade de São Paulo","correspondingAuthor":false,"prefix":"","firstName":"Rodolfo","middleName":"","lastName":"Hoffmann","suffix":""},{"id":283352921,"identity":"782c32d1-58d6-4d60-b5ed-7292e28f4777","order_by":1,"name":"Ana Lucia Kassouf","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxUlEQVRIiWNgGAWjYHACZih1+ACISiBBC1taAslacgyI08I/u/mxwY8/dXIGx3i+Sf7cwZBn3kBAi8SdY8aJvW2HjQ2O8W6T5j3DUCxzgJA1NxKMD/A2HEjccL93mzRjG0PiDEI65G+kfz74509d4oZjPM8kfxKjxeBGjnEyDxszSAubBC8xWgxv5BQbywL9InmMzdia94xEsQQhLXI30jdLvgGGGN8x5oc3f+6wySOoBRUwNpCoAaSFVB2jYBSMglEwEgAA635ASgP/5W4AAAAASUVORK5CYII=","orcid":"","institution":"Universidade de São Paulo","correspondingAuthor":true,"prefix":"","firstName":"Ana","middleName":"Lucia","lastName":"Kassouf","suffix":""}],"badges":[],"createdAt":"2024-03-20 19:29:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4139220/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4139220/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58068213,"identity":"26b4ae53-8d7d-446a-aa43-d2594a6a1257","added_by":"auto","created_at":"2024-06-10 18:07:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":483068,"visible":true,"origin":"","legend":"","description":"","filename":"HoffmannKassoufJEIMarch20.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4139220/v1_covered_ab3fcb87-42bb-4d9b-9815-842c889f8b16.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Measuring and Mismeasuring Income Polarization","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"polarization, income distribution, scale-invariant, multipolarization, inequality","lastPublishedDoi":"10.21203/rs.3.rs-4139220/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4139220/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe main contribution of this paper is to clarify some of the misconceptions about income polarization indices observed in the existing literature. 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