{"title":"排列不变的社会福利秩序是匿名的","authors":"Jeremy Goodman","doi":"10.1016/j.jmateco.2025.103153","DOIUrl":null,"url":null,"abstract":"<div><div>We consider two widely discussed impartiality criteria for social welfare relations: Permutation Invariance, which says that every permutation of the population induces an automorphism of the relation, and Anonymity, which says that every permutation of the population induces a permutation that maps every social welfare distribution to one that is equally good. We show that these criteria are equivalent for social welfare orders (i.e., complete social welfare relations). The new result is that Permutation Invariance entails Anonymity for infinite populations. This is not a curiosity, as there are principled reasons (to do with upholding Pareto criteria) that have led many authors to reject Anonymity in favor of Permutation Invariance specifically in the case of infinite populations. A corollary of the present result is that such approaches are incompatible with the use of social welfare orders.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"120 ","pages":"Article 103153"},"PeriodicalIF":0.7000,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Permutation-invariant social welfare orders are anonymous\",\"authors\":\"Jeremy Goodman\",\"doi\":\"10.1016/j.jmateco.2025.103153\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We consider two widely discussed impartiality criteria for social welfare relations: Permutation Invariance, which says that every permutation of the population induces an automorphism of the relation, and Anonymity, which says that every permutation of the population induces a permutation that maps every social welfare distribution to one that is equally good. We show that these criteria are equivalent for social welfare orders (i.e., complete social welfare relations). The new result is that Permutation Invariance entails Anonymity for infinite populations. This is not a curiosity, as there are principled reasons (to do with upholding Pareto criteria) that have led many authors to reject Anonymity in favor of Permutation Invariance specifically in the case of infinite populations. A corollary of the present result is that such approaches are incompatible with the use of social welfare orders.</div></div>\",\"PeriodicalId\":50145,\"journal\":{\"name\":\"Journal of Mathematical Economics\",\"volume\":\"120 \",\"pages\":\"Article 103153\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Economics\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304406825000709\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304406825000709","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
Permutation-invariant social welfare orders are anonymous
We consider two widely discussed impartiality criteria for social welfare relations: Permutation Invariance, which says that every permutation of the population induces an automorphism of the relation, and Anonymity, which says that every permutation of the population induces a permutation that maps every social welfare distribution to one that is equally good. We show that these criteria are equivalent for social welfare orders (i.e., complete social welfare relations). The new result is that Permutation Invariance entails Anonymity for infinite populations. This is not a curiosity, as there are principled reasons (to do with upholding Pareto criteria) that have led many authors to reject Anonymity in favor of Permutation Invariance specifically in the case of infinite populations. A corollary of the present result is that such approaches are incompatible with the use of social welfare orders.
期刊介绍:
The primary objective of the Journal is to provide a forum for work in economic theory which expresses economic ideas using formal mathematical reasoning. For work to add to this primary objective, it is not sufficient that the mathematical reasoning be new and correct. The work must have real economic content. The economic ideas must be interesting and important. These ideas may pertain to any field of economics or any school of economic thought.