{"paper_id":"25b0c4c7-2226-4b0d-85e9-e800705fb709","body_text":"A Minimal-Assumption Approach to Deriving a Unique Utility Function: Measuring the Psychological Utility of COVID-19 Vaccinations Worldwide | 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 A Minimal-Assumption Approach to Deriving a Unique Utility Function: Measuring the Psychological Utility of COVID-19 Vaccinations Worldwide Ka Yee Yeung This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7694489/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract “Psychic utility or satisfaction could scarcely be defined, let alone be measured”, a Nobel Prize laureate in Economic Sciences once said. Utility or objective functions are important for optimisation and strategic analysis across different fields, but it is challenging to identify the functions. Here, we present a pure mathematical method to solve an unknown utility function from a partial differential equation (PDE) β 2 U xx = U yy under minimal assumptions, where the solution is proved unique, stable, reliable, valid, and generalisable worldwide. A discount function measuring both pure time preference and shadow price can be derived from utility to infer vaccine hesitancy. A probability measure and a decision weight function are formulated by utility to compute the likelihood of vaccination behaviours. We prove the uniqueness and stability of the utility function in theory. For empirical evaluation using global data from 2020 to 2024, the psychometric measurement demonstrates strong internal-consistency reliability (|ρ|≥0.957), and strong convergent (ρ>0.83), discriminant (ρ=±0.2673) and predictive (ρ=0.8816, R 2 =0.984, RMSE=6.63×10 -5 ) validity. Our model addresses anomalies such as bounded rationality and inconsistent preferences. From first principles, we use the PDE to prove the properties of prospect theory's value function and the Friedman-Savage hypothesis. Despite its simplicity, this novel approach enables rich analysis and effectively handles complexity. Our ultimate goal is to derive a general equation to establish a theory of everything in economic science, under minimal assumptions and the least prerequisite data for modeling. Behavioral Economics Microeconomics Applied Mathematics Health Economics & Outcomes Research Psychology Decision Sciences Macroeconomics Health Policy Vaccine Development Economic Theory Social Policy Full Text Additional Declarations The authors declare no competing interests. Supplementary Files TechnicalBlueprintReadingGuide.pdf Technical Blueprint and Reading Guide Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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. We do this by developing innovative software and high quality services for the global research community. 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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-7694489\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":519959685,\"identity\":\"8db2da59-b2af-4cb1-b396-8f5c7b46dc4a\",\"order_by\":0,\"name\":\"Ka Yee Yeung\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYBACCRDxAcJmfEC0FsYZEDazAcwMglqYeSBsNgmitEi2H2D8wJtzWM7gdvu16sI9NnX80g2sGz7g0SLNk8AsIbntsLHBnTNlt2c8S5OQnHOA7eYMPFrkGBIYJAy3HU7ccCMn7TbPgcMSBjcS2G7z4NPC/4D5R+K2w/UgLcVwLX/wOUwigU3i4LbDCQY30o8xw7Xg9f6Mh22WjdvSDWfeyGGWnnEgTXLmjMS2mz14tEicTz58++82a3m+G+kPPxccsOHnl0g+duMHPmsYGBuARDMQ8xgwI4kQBHVAzP6AmRilo2AUjIJRMPIAAIIhUyrasoexAAAAAElFTkSuQmCC\",\"orcid\":\"\",\"institution\":\"\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Ka\",\"middleName\":\"Yee\",\"lastName\":\"Yeung\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2025-09-23 12:41:06\",\"currentVersionCode\":2,\"declarations\":{\"humanSubjects\":false,\"vertebrateSubjects\":false,\"conflictsOfInterestStatement\":false,\"humanSubjectEthicalGuidelines\":false,\"humanSubjectConsent\":false,\"humanSubjectClinicalTrial\":false,\"humanSubjectCaseReport\":false,\"vertebrateSubjectEthicalGuidelines\":false},\"doi\":\"10.21203/rs.3.rs-7694489/v2\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-7694489/v2\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":92536830,\"identity\":\"1249669b-c524-4372-b97e-c7542f59e9ab\",\"added_by\":\"auto\",\"created_at\":\"2025-09-30 17:36:58\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1592304,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"250314paper.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7694489/v2_covered_4a047921-0146-4267-98c7-69aa592e0188.pdf\"},{\"id\":92535783,\"identity\":\"e7c14d1c-4c5f-41c9-a01b-b29cc6bfb057\",\"added_by\":\"auto\",\"created_at\":\"2025-09-30 17:20:56\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"supplement\",\"size\":112277,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eTechnical Blueprint and Reading Guide\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"TechnicalBlueprintReadingGuide.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7694489/v2/0605faefb0a449b62f125c49.pdf\"}],\"financialInterests\":\"The authors declare no competing interests.\",\"formattedTitle\":\"\\u003cp\\u003eA Minimal-Assumption Approach to Deriving a Unique Utility Function: Measuring the Psychological Utility of COVID-19 Vaccinations Worldwide\\u003c/p\\u003e\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":true,\"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\":\"info@researchsquare.com\",\"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\":\"\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-7694489/v2\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-7694489/v2\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003e“Psychic utility or satisfaction could scarcely be defined, let alone be measured”, a Nobel Prize laureate in Economic Sciences once said. 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For empirical evaluation using global data from 2020 to 2024, the psychometric measurement demonstrates strong internal-consistency reliability (|ρ|≥0.957), and strong convergent (ρ\\u0026gt;0.83), discriminant (ρ=±0.2673) and predictive (ρ=0.8816, R\\u003csup\\u003e2\\u003c/sup\\u003e=0.984, RMSE=6.63×10\\u003csup\\u003e-5\\u003c/sup\\u003e) validity. Our model addresses anomalies such as bounded rationality and inconsistent preferences. From first principles, we use the PDE to prove the properties of prospect theory's value function and the Friedman-Savage hypothesis. Despite its simplicity, this novel approach enables rich analysis and effectively handles complexity. 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