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 de…ning the issues to be voted upon satis…es the following property: for any vector in the basis, any linear combination of the other vectors is Birkho¤-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 l p case, we show that non-existence of bases with the above property is generic.