[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-274641-105":59,"doc-detail-274641-en":122},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":115,"head_meta":117,"extra_data":119,"updated_unix":121},105,"en","longer-lists-yield-better-matchings-serial-dictatorship-and-preference-list-length-june-6-2025","Longer Lists Yield Better Matchings - Serial Dictatorship and Preference-List Length - June 6, 2025","","The paper studies two-sided matching markets under incomplete or truncated preference lists, focusing on the Serial Dictatorship mechanism. It models a proposing side (students) whose preference lists are randomly generated with a fixed length, drawn uniformly from a set of schools with one seat each. The main findings show that when students mainly prefer being matched to any school in their list rather than being unmatched, longer lists improve preferences for sufficiently large numbers of schools; schools also consistently prefer longer lists. The work additionally analyzes how list length affects the rank of the matched school and supports designing reasonably long lists when demand does not exceed supply.",{"@graph":69,"@context":114},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/longer-lists-yield-better-matchings-serial-dictatorship-and-preference-list-length-june-6-2025/274641/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/longer-lists-yield-better-matchings-serial-dictatorship-and-preference-list-length-june-6-2025/274641.png","ImageObject",300,407,{"name":92,"@type":93},"4398046744996","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main result about preference-list length?","Question",{"text":112,"@type":113},"When students primarily care about being matched to any school in their list, students prefer markets with longer lists once the number of schools is large enough; schools also always prefer longer lists in the model.","Answer","https://schema.org",{"og:url":83,"og:type":116,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":118,"canonical":83},"index,follow",{"doc_id":120,"site_id":62},274641,1789480527,{"code":4,"msg":5,"data":123},{"doc_id":120,"user_id":124,"nickname":92,"user_avatar":66,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":125,"file_id":126,"file_url":127,"file_type":128,"file_size":129,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":130,"language":131,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":132,"faqs":133,"seo_title":134,"seo_description":67,"update_tm":121,"read_time":135,"preview_page_count":4},4398046744996,"arXiv :2506 .062 17v 1 [ cs .GT] 6 Jun 2025  \nLonger Lists Yield Better Matchings  \nYURI FAENZA AND AAPELI VUORINEN, IEOR, COLUMBIA UNIVERSITY  \nMany centralized mechanisms for two-sided matching markets that enjoy strong theoretical properties assume that the planner solicits full information on the preferences of each participating agent. In particular, they expect that participants compile and communicate their complete preference lists over agents from the other side of the market. However, real-world markets are often very large and agents cannot always be expected to even produce a ranking of all options on the other side. It is therefore important to understand the impact of incomplete or truncated lists on the quality of the resultant matching.  \nIn this paper, we focus on the Serial Dictatorship mechanism in a model where each agent of the proposing side (students) has a random preference list of length 􀀳, sampled independently and uniformly at random from 􀀽 schools, each of which has one seat. Our main result shows that if the students primarily care about being matched to any school of their list (as opposed to ending up unmatched), then all students in position 􀀸 ≤ 􀀽 will prefer markets with longer lists, when 􀀽 is large enough. Schools on the other hand will always prefer longer lists in our model. We moreover investigate the impact of 􀀳 on the rank of the school that a student gets matched to.  \nOur main result suggests that markets that are well-approximated by our hypothesis and where the demand of schools does not exceed supply should be designed with preference lists as long as reasonable, since longer lists would favor all agents.  \nContents  \nAbstract 0  \nContents 0  \n1 Introduction 1  \n1.1 Our Contributions 1  \n1.2 Organization of the Paper 2  \n1.3 Related Literature 3  \n1.4 Notation 4  \n2 Models and Results 4  \n2.1 A Discrete Random Market Model 4  \n2.2 A Continuous Market Model 6  \n2.3 From Continuous to Discrete 7  \n2.4 Implications and Extensions 10  \n2.5 Discussion of the Discrete Model 11  \n3 Proofs of Main Results 11  \n3.1 Connections Between the Discrete and Continuous Markets 11  \n3.2 Continuous Market 15  \n3.3 Discrete Market: Probability of Being Matched 16  \n3.4 Discrete Market: Impact on Rank 18  \n4 Numerical Experiments 18  \n5 Conclusions 19  \nReferences 20  \nA Background on Differential Equations and Stochastic Processes 21  \nB Extension to Schools Having Multiple Seats 24  \nC Missing Proofs 26  \nD Plots for Numerical Experiments 34  \nYuri Faenza and Aapeli Vuorinen, IEOR, Columbia University 1  \n1 Introduction  \nOne of the central objectives of theoretical research in matching markets is to design mechanismsand rigorously establish whether they, along with their outcomes, satisfy desirable properties. Depending on the specific market, the focus may be on concepts such as strategy-proofness, oneor two-sided optimality, or equilibria. These and other properties are often viewed as justifications for applying such mechanisms in practice, under the expectation that the valuable theoretical features will persist in the real world. However, in many applications, the assumptions that are necessary for such properties to hold may not be satisfied. For example, while in a static two-sided market one can compute a stable assignment efficiently, in real-world markets arising in public school allocation, a substantial number of agents often enter or leave the market after the first assignment has been decided (see for example [Ashlagi et al., 2023]) . The goal of the central planner becomes therefore less well-defined and, depending on the mathematical formalization, may lead to computationally hard problems, see for example [Bampis et al., 2023, Faenza et al., 2024, 2025, Miyazaki and Okamoto, 2019] .  \nIn this paper, we focus on one of the main restrictions encountered in real-world markets: imposing a limit on the maximum length of preference lists of agents. Such limits are common, for instance in ","cbCaiiGTt9UOuUya","https://ap.wps.com/l/cbCaiiGTt9UOuUya","pdf",1197233,37,"English","# Introduction\n## Our Contributions\n## Organization of the Paper\n## Related Literature\n## Notation\n# Models and Results\n## A Discrete Random Market Model\n## A Continuous Market Model\n## From Continuous to Discrete\n## Implications and Extensions\n## Discussion of the Discrete Model\n# Proofs of Main Results\n## Connections Between the Discrete and Continuous Markets\n## Continuous Market\n## Discrete Market: Probability of Being Matched\n## Discrete Market: Impact on Rank\n# Numerical Experiments\n# Conclusions\n# References\n# Appendices","[{\"question\":\"What is the main result about preference-list length?\",\"answer\":\"When students primarily care about being matched to any school in their list, students prefer markets with longer lists once the number of schools is large enough; schools also always prefer longer lists in the model.\"}]","Longer Lists Yield Better Matchings - Serial Dictatorship and Preference-List Length - June 6, 2025 | PDF",93]