[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82622-en":3,"doc-seo-82622-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82622,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","The General Stability of Ranking","Rankings produced by weighted scoring functions are widely used in university evaluation and employment selection, yet their conclusions depend on chosen attribute weights. Traditional exact stability measures the fraction of weight space yielding an identical ranking, which can be overly rigid when weight perturbations cause minor swaps or replace only the top item. This work introduces general stability, a distance-based metric that aggregates ranking regions by user-relevant changes. It develops stability computation algorithms, analyzes sampling limitations, and proposes Conv-SC for quasiconvex distances, enabling convex-volume approximation with polynomial-time randomized methods.","The General Stability of Ranking  \nHouming Chen  \nUniversity of Michigan Ann Arbor, Michigan, USA [houmingc@umich.edu](houmingc@umich.edu)  \nH. V. Jagadish  \nUniversity of Michigan Ann Arbor, Michigan, USA [jag@umich.edu](jag@umich.edu)  \narXiv :2607 .0 1546v 1 [ cs .DB] 1 Jul 2026  \nABSTRACT  \nRankings derived from weighted scoring functions are widely used in settings such as university rankings and employment candidate evaluations. Since ranking weights are often chosen by organizations or analysts, ranking stability asks whether a reported ranking persists under reasonable weight changes. Prior work on stable rankings formalizes this idea through volume-based stability, which measures the fraction of the weight space that induces the target ranking exactly.  \nThis exact-match requirement can be too blunt: once a perturbed weight vector produces a different ranking, exact stability gives it no credit, whether the change replaces the top-ranked item or only swaps two nearly tied lower-ranked items. We propose general stability, a distance-based generalization that aggregates ranking regions according to a user-defined distance from the target ranking. This lets users specify which ranking changes matter in the application, while recovering exact stability as a special case.  \nOur algorithmic focus is stability computation: given a reported or user-specified ranking and a distance function, estimate its general-stability score. We give a two-dimensional sweep algorithm and an unbiased multidimensional sampler that extend exactstability methods, and analyze why sampling can scale poorly as the dimension grows. Motivated by this scaling challenge, we identify quasiconvex distance functions as a tractable subclass and introduce Conv-SC, which reduces stability computation for this subclass to convex-volume approximation, where randomized polynomialtime methods are available. Experiments on eight real datasets and generated instances show that distance-sensitive stability gives informative real-data results, that our estimators are accurate and practical, and that Conv-SC improves scaling with dimension for quasiconvex distance functions.  \n1 INTRODUCTION  \nRankings are widely used in settings such as university evaluation, job hiring, and public review websites. For instance, organizations such as U.S. News and Quacquarelli Symonds rank universities, and the resulting rankings can influence public perception and institutional decisions. Such rankings are commonly produced by scoring each item on several attributes, assigning weights to those attributes, and then sorting items by their weighted scores.  \nThe choice of weights reflects a judgment about the relative importance of attributes, and is not driven by the data. Different reasonable choices of weights can lead to different rankings. This raises a robustness question: does the reported ranking reflect astable pattern in the data, or does it depend on a narrowly limited choice of weights? If small changes in the weights lead to very different outcomes, the reported ranking provides weak support  \nfor a robust conclusion. It may also raise concerns that the reported weights might have been cherry-picked for a particular outcome.  \nPrior work formalizes this idea through volume-based stability [3], which measures the fractional volume of the weight space that induces a target ranking. We refer to this original notion as exact stability. The following example illustrates the intuition: a ranking is robust when nearby weights support the same conclusion, and fragile when changes lead to different rankings.  \nExample 1 . Consider a hiring committee ranking candidates by a weighted sum of two criteria: an aptitude score 􀁇1 and an experience score 􀁇2 . Suppose three candidates have scores shown in Table 1 .  \n\n| Cand. 􀁇1 􀁇2 Weights and Corresponding Final Scores |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n|  |  |  | (0 .5, 0. 5) | (0 .6, 0.4) | (0 .7, 0. 3) | (","cbCaih68Sm5eeej7","https://ap.wps.com/l/cbCaih68Sm5eeej7","pdf",894229,1,13,"English","en",105,"# Introduction\n## Ranking stability and robustness\n## Exact stability and its limitations\n## General stability (distance-based)\n## Algorithmic approach and computation\n## Sampling vs. scaling in higher dimensions","[{\"question\":\"什么是排名稳定性（ranking stability）？\",\"answer\":\"排名稳定性衡量在属性权重发生合理变化时，所报告的排名是否仍能保持一致或保持在用户关心的变化范围内。\"},{\"question\":\"精确稳定性（exact stability）为何可能过于苛刻？\",\"answer\":\"精确稳定性要求扰动后的权重必须产生完全相同的排名。一旦权重变化导致排名不同，即使只是发生轻微交换或只影响顶部候选，也不会得到信用，从而可能低估“有用的鲁棒性”。\"},{\"question\":\"general stability 与 exact stability 的核心区别是什么？\",\"answer\":\"general stability 用基于距离的聚合方式，将与目标排名的偏离程度按用户定义的距离函数进行度量与汇总；当距离选择使其退化为“必须完全相同”的情形时，general stability 就能恢复为 exact stability。\"}]",1784181865,33,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"the-general-stability-of-ranking","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/the-general-stability-of-ranking/82622/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"什么是排名稳定性（ranking stability）？","Question",{"text":75,"@type":76},"排名稳定性衡量在属性权重发生合理变化时，所报告的排名是否仍能保持一致或保持在用户关心的变化范围内。","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"精确稳定性（exact stability）为何可能过于苛刻？",{"text":80,"@type":76},"精确稳定性要求扰动后的权重必须产生完全相同的排名。一旦权重变化导致排名不同，即使只是发生轻微交换或只影响顶部候选，也不会得到信用，从而可能低估“有用的鲁棒性”。",{"name":82,"@type":73,"acceptedAnswer":83},"general stability 与 exact stability 的核心区别是什么？",{"text":84,"@type":76},"general stability 用基于距离的聚合方式，将与目标排名的偏离程度按用户定义的距离函数进行度量与汇总；当距离选择使其退化为“必须完全相同”的情形时，general stability 就能恢复为 exact stability。","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":45,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":45,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]