Order Independence in Sequential, Issue-by-Issue Voting
研究在多维空间投票模型中，议题投票顺序何时不影响最终结果，发现若偏好由内积范数（如欧几里得范数）衡量，则顺序独立仅当议题正交；对一般范数，顺序独立需满足特定正交条件，且此类条件在一般情况下不存在。
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. 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.