Order Independence in Sequential, Issue-by-Issue Voting

Alex Gershkov (), Benny Moldovanu () and Xianwen Shi

CRC TR 224 Discussion Paper Series from University of Bonn and University of Mannheim, Germany

Abstract: We study when the voting outcome is independent of the order of issues put up for vote in a spacial multi-dimensional 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 the above property then the voting order matters. Finally, despite existence results for the two-dimensional case and for the general lp case, we show that non-existence of bases with the above property is generic.

Keywords: Sequential voting; order independence; norm-based preferences (search for similar items in EconPapers)
JEL-codes: D72 (search for similar items in EconPapers)
Pages: 29
Date: 2023-04
New Economics Papers: this item is included in nep-cdm, nep-des and nep-pol
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