Evaluating Log-Likelihood for Confidence Estimation in LLM-Based Multiple-Choice Question Answering

Evaluating Log-Likelihood for Confidence Estimation in LLM-Based Multiple-Choice Question Answering | 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 Evaluating Log-Likelihood for Confidence Estimation in LLM-Based Multiple-Choice Question Answering Christopher Boseak This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7038601/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 Reliable deployment of large language models (LLMs) in question-answering tasks requires well-calibrated confidence estimates. This work investigates whether token-level log-likelihoods—sums of log-probabilities over answer tokens—can serve as effective confidence signals in multiple-choice question answering (MCQA). We compare three methods: (1) raw log-likelihood, (2) length-normalized loglikelihood, and (3) conventional softmax-based choice probability. Across four diverse MCQA benchmarks, we find that no single scoring method is universally best. Length normalization can significantly improve calibration but may reduce accuracy, while softmax and raw log-likelihood yield identical predictions. These results highlight important trade-offs between calibration and accuracy, and offer insights into selecting or adapting confidence measures for different tasks. Our findings inform the design of more trustworthy LLM-based QA systems and lay groundwork for broader uncertainty quantification efforts. Artificial Intelligence and Machine Learning Large Language Models (LLMs) Confidence Estimation Log-Likelihood Calibration Multiple-Choice Question Answering (MCQA) Softmax Uncertainty Quantification Model Reliability Answer Scoring Methods NLP Evaluation Full Text Additional Declarations The authors declare no competing interests. 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7038601","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":480210460,"identity":"7655767b-b08d-408f-b626-4c00ead3e215","order_by":0,"name":"Christopher Boseak","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYDACCTCZIAciDzwgRYsxWEsCKVoSG8AUMTr4Zzcf/vChJi19ftjhh0Bb7OR0GwhZcudYmuSMYzm5G2+nGQC1JBubHSCgxUAix4yZh60id+PsBJCWA4nbiNBi/PnPv4p0w9npH4jWYiDN2JaTIC+dQ6QtYL/09qUZbpDOKTiQYECEX8Ah9uNbsrz87PTNHz5U2MkR1IJwIVilAbHKQUC+gRTVo2AUjIJRMKIAAJ0kRrItEaPDAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0004-4323-8016","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Christopher","middleName":"","lastName":"Boseak","suffix":""}],"badges":[],"createdAt":"2025-07-03 13:12:51","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7038601/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7038601/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86041147,"identity":"251f16cb-5c06-4a40-9c3e-3290152b4806","added_by":"auto","created_at":"2025-07-04 17:15:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":220907,"visible":true,"origin":"","legend":"","description":"","filename":"BoseakLLLLMConfidenceQA.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7038601/v1_covered_b57672f4-15b4-4b05-a872-d6ab190f3f95.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eEvaluating Log-Likelihood for Confidence Estimation in LLM-Based Multiple-Choice Question Answering\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Independent Researcher","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":"Large Language Models (LLMs), Confidence Estimation, Log-Likelihood, Calibration, Multiple-Choice Question Answering (MCQA), Softmax, Uncertainty Quantification, Model Reliability, Answer Scoring Methods, NLP Evaluation","lastPublishedDoi":"10.21203/rs.3.rs-7038601/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7038601/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eReliable deployment of large language models (LLMs) in question-answering tasks requires well-calibrated confidence estimates. 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