{"title":"Approximate Single-Peakedness in Large Elections","authors":"Zhihuai Chen, Q. Li, Xiaoming Sun, Lirong Xia, Jialin Zhang","doi":"10.1109/ICBK50248.2020.00068","DOIUrl":null,"url":null,"abstract":"Single-peaked preferences are a natural way to avoid paradoxes and impossibility theorems in social choice and have recently been involved in the study of various computational aspects of social choice. Since strict single-peakedness is hard to achieve in practice, approximate single-peakedness appears more appropriate and is gaining popularity. In this paper, we study approximate single-peakedness of large, randomly-generated profiles. We focused on characterizing the asymptotically optimal social axis, which is asymptotically consistent with most agents’ preferences generated from a statistical model. We characterize all asymptotically optimal social axes under the Mallows model for two case: the case where the dispersion parameter $\\varphi$ is close to 0, and the case where $\\varphi$ is close to 1. We also design an algorithm to help characterize all asymptotically optimal social axes for all $\\varphi$ when the number of alternative is no more than 10. These results help us understand the structure of approximate single-peakedness in large elections.","PeriodicalId":432857,"journal":{"name":"2020 IEEE International Conference on Knowledge Graph (ICKG)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2020 IEEE International Conference on Knowledge Graph (ICKG)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICBK50248.2020.00068","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Single-peaked preferences are a natural way to avoid paradoxes and impossibility theorems in social choice and have recently been involved in the study of various computational aspects of social choice. Since strict single-peakedness is hard to achieve in practice, approximate single-peakedness appears more appropriate and is gaining popularity. In this paper, we study approximate single-peakedness of large, randomly-generated profiles. We focused on characterizing the asymptotically optimal social axis, which is asymptotically consistent with most agents’ preferences generated from a statistical model. We characterize all asymptotically optimal social axes under the Mallows model for two case: the case where the dispersion parameter $\varphi$ is close to 0, and the case where $\varphi$ is close to 1. We also design an algorithm to help characterize all asymptotically optimal social axes for all $\varphi$ when the number of alternative is no more than 10. These results help us understand the structure of approximate single-peakedness in large elections.