When do noisy votes reveal the truth?

I. Caragiannis, A. Procaccia, Nisarg Shah
{"title":"When do noisy votes reveal the truth?","authors":"I. Caragiannis, A. Procaccia, Nisarg Shah","doi":"10.1145/2482540.2482570","DOIUrl":null,"url":null,"abstract":"A well-studied approach to the design of voting rules views them as maximum likelihood estimators; given votes that are seen as noisy estimates of a true ranking of the alternatives, the rule must reconstruct the most likely true ranking. We argue that this is too stringent a requirement, and instead ask: How many votes does a voting rule need to reconstruct the true ranking? We define the family of pairwise-majority consistent rules, and show that for all rules in this family the number of samples required from the Mallows noise model is logarithmic in the number of alternatives, and that no rule can do asymptotically better (while some rules like plurality do much worse). Taking a more normative point of view, we consider voting rules that surely return the true ranking as the number of samples tends to infinity (we call this property accuracy in the limit); this allows us to move to a higher level of abstraction. We study families of noise models that are parametrized by distance functions, and find voting rules that are accurate in the limit for all noise models in such general families. We characterize the distance functions that induce noise models for which pairwise-majority consistent rules are accurate in the limit, and provide a similar result for another novel family of position-dominance consistent rules. These characterizations capture three well-known distance functions.","PeriodicalId":194623,"journal":{"name":"ACM Trans. Economics and Comput.","volume":"27 5","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"122","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Trans. Economics and Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2482540.2482570","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 122

Abstract

A well-studied approach to the design of voting rules views them as maximum likelihood estimators; given votes that are seen as noisy estimates of a true ranking of the alternatives, the rule must reconstruct the most likely true ranking. We argue that this is too stringent a requirement, and instead ask: How many votes does a voting rule need to reconstruct the true ranking? We define the family of pairwise-majority consistent rules, and show that for all rules in this family the number of samples required from the Mallows noise model is logarithmic in the number of alternatives, and that no rule can do asymptotically better (while some rules like plurality do much worse). Taking a more normative point of view, we consider voting rules that surely return the true ranking as the number of samples tends to infinity (we call this property accuracy in the limit); this allows us to move to a higher level of abstraction. We study families of noise models that are parametrized by distance functions, and find voting rules that are accurate in the limit for all noise models in such general families. We characterize the distance functions that induce noise models for which pairwise-majority consistent rules are accurate in the limit, and provide a similar result for another novel family of position-dominance consistent rules. These characterizations capture three well-known distance functions.
嘈杂的投票什么时候能揭示真相?
一种被充分研究的投票规则设计方法将其视为最大似然估计器;考虑到投票被视为对备选方案真实排名的嘈杂估计,该规则必须重建最可能的真实排名。我们认为这是一个过于严格的要求,而是问:一个投票规则需要多少票才能重建真实的排名?我们定义了双多数一致规则族,并表明对于这个家族中的所有规则,从Mallows噪声模型所需的样本数量在可选的数量中是对数的,并且没有规则可以渐近地做得更好(而一些规则,如复数,做得更差)。从更规范的角度来看,我们认为当样本数量趋于无穷大时,投票规则肯定会返回真实的排名(我们称此属性为极限精度);这允许我们移动到更高的抽象层次。我们研究了由距离函数参数化的噪声模型族,并找到了在这些一般族中所有噪声模型的极限内准确的投票规则。我们描述了诱导噪声模型的距离函数,其中双多数一致规则在极限下是准确的,并为另一类新的位置优势一致规则提供了类似的结果。这些特征体现了三个众所周知的距离函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信