{"title":"On rank dominance of tie‐breaking rules","authors":"Maxwell Allman, I. Ashlagi, Afshin Nikzad","doi":"10.3982/te4762","DOIUrl":null,"url":null,"abstract":"Lotteries are a common way to resolve ties in assignment mechanisms that ration resources. We consider a model with a continuum of agents and a finite set of resources with heterogeneous qualities, where the agents' preferences are generated from a multinomial‐logit (MNL) model based on the resource qualities. We show that all agents prefer a common lottery to independent lotteries at each resource if every resource is popular, meaning that the mass of agents ranking that resource as their first choice exceeds its capacity. We then prove a stronger result where the assumption that every resource is popular is not required and agents' preferences are drawn from a (more general) nested MNL model. By appropriately adapting the notion of popularity to resource types, we show that a hybrid tie‐breaking rule in which the objects in each popular type share a common lottery dominates independent lotteries at each resource.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.3982/te4762","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 1
Abstract
Lotteries are a common way to resolve ties in assignment mechanisms that ration resources. We consider a model with a continuum of agents and a finite set of resources with heterogeneous qualities, where the agents' preferences are generated from a multinomial‐logit (MNL) model based on the resource qualities. We show that all agents prefer a common lottery to independent lotteries at each resource if every resource is popular, meaning that the mass of agents ranking that resource as their first choice exceeds its capacity. We then prove a stronger result where the assumption that every resource is popular is not required and agents' preferences are drawn from a (more general) nested MNL model. By appropriately adapting the notion of popularity to resource types, we show that a hybrid tie‐breaking rule in which the objects in each popular type share a common lottery dominates independent lotteries at each resource.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
