Template-Type: ReDIF-Paper 1.0
Title: Order Independence in Sequential, Issue-by-Issue Voting
Author-Name: Alex Gershkov
Author-Email: alexg@huji.ac.il
Author-Name: Benny Moldovanu
Author-Email: mold@uni-bonn.de
Author-Name: Xianwen Shi
Author-Email: xianwen.shi@utoronto.ca
Classification-JEL: D72
Keywords: Sequential voting, order independence, norm-based preferences

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.

Note: 
Length: 29
Creation-Date: 2023-04
Revision-Date: 
File-URL: https://www.crctr224.de/research/discussion-papers/archive/dp413
File-Format: application/pdf
Handle: RePEc:bon:boncrc:CRCTR224_2023_413