Computational Complexity of Organizational Decision Hierarchies

Computational Complexity of Organizational Decision Hierarchies | 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Article Computational Complexity of Organizational Decision Hierarchies Michél Nguyễn This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7948428/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 We model organizational decision hierarchies as bounded-span monotone threshold circuits, capturing tradeoffs between decision latency, accuracy, and headcount. Aggregating n binary signals with span s requires depth at least ⌈logs n⌉;we formalize OrgTree-Design and evaluate a simple greedy heuristic. Full complexity analysis is out of scope. Simulations with n = 256, spans s ∈ {4, 8, 16}, and noise p ∈ {0.01, 0.05, 0.10, 0.20} show wider spans reduce latency butlower accuracy (e.g., at p = 0.10, s = 4 to s = 16 cuts latency from 3.6 to1.8 time units but drops accuracy from 100% to 89.7% (95% CI [82.1, 90.7])). Welch ANOVA on p = 0.10 data confirms span effects (F (2, 997.2) = 687.58,p < .001, ˆϵ2 = 0.479). Medium spans (s = 8) offer a balanced Pareto point for hybrid organizations Jacobsen (2023). Our framework links span-of-control theory to circuit complexity, providing a reproducible basis for hierarchy design. Organizational design threshold circuits decision latency span of control simulation ANOVA 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. 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-7948428","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":536308750,"identity":"aacdfbe6-43e2-488f-ace1-6a8666a4bf24","order_by":0,"name":"Michél Nguyễn","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYDACZgY2BoYCIIO9sYHhAQMDYwNxWgyADJ6DDQwJRGlhgGmRAKonSotuO/OzBx8MGPLkIx83fkioOCzbwH746AZ8WswOs5kbzjBgKDa8ndgskXDmsHEDT1raDfxaeNikeQwYEjfOTmxjSGw7nNggwWNGWMsfkJaZB0nRAvR+4nwJRqK1sJlJ9gC1bOAB+yXduI2gX84ffibxowJoS/vxhx8+VFjL9rMfPoZXCxT8ZzA4AGWyEaEcAuQbiFY6CkbBKBgFIw0AAEOnSkg3Lrn5AAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Michél","middleName":"","lastName":"Nguyễn","suffix":""}],"badges":[],"createdAt":"2025-10-27 10:58:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7948428/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7948428/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96361019,"identity":"80aaeeb3-dea6-4e71-a59e-3ff7d2c2ba5f","added_by":"auto","created_at":"2025-11-20 09:10:04","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2915,"visible":true,"origin":"","legend":"","description":"","filename":"c0f7a4ebc48d438ebbb238a67aa8f899.json","url":"https://assets-eu.researchsquare.com/files/rs-7948428/v1/2dbbba81e13388019edea737.json"},{"id":96361020,"identity":"7103e8d6-d25c-4e9c-bc90-1d0236a6bcdd","added_by":"auto","created_at":"2025-11-20 09:10:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":244164,"visible":true,"origin":"","legend":"","description":"","filename":"updatedspringerComputationalComplexity2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7948428/v1_covered_76698367-6256-49b6-9e3e-10d261e339b1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Computational Complexity of Organizational Decision Hierarchies","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":"[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":"Organizational design, threshold circuits, decision latency, span of control, simulation, ANOVA","lastPublishedDoi":"10.21203/rs.3.rs-7948428/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7948428/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We model organizational decision hierarchies as bounded-span monotone threshold circuits, capturing tradeoffs between decision latency, accuracy, and headcount. 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