Order Independence in Sequential, Issue-by-Issue Voting

Alex Gershkov (), Benny Moldovanu () and Xianwen Shi ()
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Alex Gershkov: Department of Economics, Hebrew University of Jerusalem, Jerusalem 91905, Israel; and School of Economics, University of Surrey, Guildford GU2 7XH, United Kingdom
Benny Moldovanu: Department of Economics, University of Bonn, 53113 Bonn, Germany; and School of Economics, Tel Aviv University, Tel Aviv 6997801, Israel
Xianwen Shi: Department of Economics, University of Toronto, Toronto, Ontario M5S 3G7, Canada

Mathematics of Operations Research, 2025, vol. 50, issue 3, 1635-1653

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 l p case, we show that nonexistence of bases with this property is generic.

Keywords: Primary: 91B12; 91A27; 91A20; sequential voting; multidimensional types; Birkhoff–James orthogonality; order independence; median voter; Auerbach’s theorem (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:3:p:1635-1653

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