Order Independence in Sequential, Issue-by-Issue Voting

• 成果类型: Article
• 署名作者: Gershkov, Alex; Moldovanu, Benny; Shi, Xianwen
• 署名单位: Hebrew University of Jerusalem; University of Surrey; University of Bonn; Tel Aviv University; University of Toronto
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0342
• 发表日期: 2025
• 关键词: Strategy-proofness; majority; equilibrium; subspaces

摘要

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.