Designing Discontinuities

Designing Discontinuities | 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 Article Designing Discontinuities Ibtihal Ferwana, Suyoung Park, Ting-Yi Wu, Lav R. Varshney This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7243002/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 Discontinuities can be fairly arbitrary but also cause significant impacts on outcomes in larger systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression discontinuity from econometrics assumes the existence of a discontinuous variable, a threshold, that splits the population into distinct partitions to estimate the causal effects of a given phenomenon. Here we consider the design of partitions for a given discontinuous variable to optimize a certain effect previously studied using regression discontinuity. To do so, we propose a quantization-theoretic approach to optimize the effect of interest, first learning the causal effect size of a given discontinuous variable and then applying dynamic programming for optimal quantization design of discontinuities to balance the gain and loss in that effect size. We also develop a computationally-efficient reinforcement learning algorithm for a dynamic programming formulation of optimal quantization. We demonstrate our approach by designing optimal time zone borders for counterfactuals of social capital, social mobility, and health, including novel examples that may be of independent empirical interest. We further demonstrate our approach by designing letter grade breakpoints for college courses to improve motivation for students. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics 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-7243002","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":512181674,"identity":"3a2ae9d7-16fc-4243-b185-3fca76746fbb","order_by":0,"name":"Ibtihal Ferwana","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYBACNuYDYFqOn5m58UACAwMPiCeBVwtbApg2lmxmbCBOCwNUS+KGA0AtMEG8WvjYmI995t1hx7j5OFDLwx02MvINzAdv8+B1GFvybN4zycxmh4FaEs+k8RgcYEu2xqtFvseYObeNmQ2ipe0wjwEDj5k0flv4PwO11PMYN0O1yDfwfyOghYcZqOWwhAEzVAvDAR42AlrYjJn/th03kIA4DOiXw2zGlnPwaJFvY37MOLOtur6///DBhz/bbOzl25sf3niDRwsWwEya8lEwCkbBKBgFWAAA9WxEkSn/UlsAAAAASUVORK5CYII=","orcid":"","institution":"University of Illinois Urbana-Champaign","correspondingAuthor":true,"prefix":"","firstName":"Ibtihal","middleName":"","lastName":"Ferwana","suffix":""},{"id":512181675,"identity":"77d515a7-dbe7-4f07-8dde-e988b5047969","order_by":1,"name":"Suyoung Park","email":"","orcid":"","institution":"University of Illinois Urbana-Champaign","correspondingAuthor":false,"prefix":"","firstName":"Suyoung","middleName":"","lastName":"Park","suffix":""},{"id":512181676,"identity":"aa0cbb6d-42b8-4f32-85d4-9867f8ba0818","order_by":2,"name":"Ting-Yi Wu","email":"","orcid":"","institution":"University of Illinois Urbana-Champaign","correspondingAuthor":false,"prefix":"","firstName":"Ting-Yi","middleName":"","lastName":"Wu","suffix":""},{"id":512181677,"identity":"ed67aa8d-3e65-4316-8143-e9f937aceeaa","order_by":3,"name":"Lav R. 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