Order Independence in Sequential, Issue-by-Issue Voting

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-12 DOI:10.1287/moor.2022.0342

Alex Gershkov, Benny Moldovanu, Xianwen Shi

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Abstract

We study when the voting outcome is independent of the order of issues put up for vote in a spatial multidimensional voting model. Agents equipped with norm-based preferences that use a norm to measure the distance from their ideal policy vote sequentially and issue by issue via simple majority. If the underlying norm is generated by an inner product—such as the Euclidean norm—then the voting outcome is order independent if and only if the issues are orthogonal. If the underlying norm is a general one, then the outcome is order independent if the basis defining the issues to be voted upon satisfies the following property; for any vector in the basis, any linear combination of the other vectors is Birkhoff–James orthogonal to it. We prove a partial converse in the case of two dimensions; if the underlying basis fails this property, then the voting order matters. Finally, despite existence results for the two-dimensional case and for the general lp case, we show that nonexistence of bases with this property is generic.Funding: The research of A. Gershkov is supported by the Israel Science Foundation [Grant 1118/22]. The research of B. Moldovanu is supported by the German Science Foundation through the Hausdorff Center for Mathematics and The Collaborative Research Center Transregio 224. The research of X. Shi is supported by the Social Sciences and Humanities Research Council of Canada.

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逐期顺序表决中的顺序独立性

我们研究了在一个空间多维投票模型中，当投票结果与提交投票的议题顺序无关时的情况。代理人具有基于规范的偏好，这种偏好使用规范来衡量与理想政策的距离，并通过简单多数按顺序逐项投票。如果基本准则是由内积（如欧几里得准则）生成的，那么当且仅当问题是正交的，投票结果才与顺序无关。如果底层规范是一般规范，那么如果定义待表决问题的基础满足以下性质，则表决结果与顺序无关；对于基础中的任何向量，其他向量的任何线性组合都是伯克霍夫-詹姆斯正交的。我们证明了二维情况下的部分反义；如果底层基础不符合这一性质，那么投票顺序就很重要。最后，尽管在二维情况和一般 lp 情况下有存在性结果，我们还是证明了具有这一性质的基础的不存在性是通用的：A. Gershkov 的研究得到了以色列科学基金会 [1118/22 号拨款] 的支持。B. Moldovanu 的研究由德国科学基金会通过豪斯多夫数学中心和 Transregio 224 合作研究中心资助。X. Shi 的研究得到了加拿大社会科学与人文研究理事会的支持。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.