Template-Type: ReDIF-Paper 1.0
Title: Monotonic Norms and Orthogonal Issues in Multidimensional 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: D71, D82
Keywords: 

Abstract: We study issue-by-issue voting by majority and incentive compatibility in multi-
dimensional frameworks where privately informed agents have preferences induced by
general norms and where dimensions are endogenously chosen. We uncover the deep
connections between dominant strategy incentive compatibility (DIC) on the one hand,
and several geometric/functional analytic concepts on the other. Our main results are:
1) Marginal medians are DIC if and only if they are calculated with respect to coor-
dinates de…ned by a basis such that the norm is orthant-monotonic in the associated
coordinate system. 2) Equivalently, marginal medians are DIC if and only if they are
computed with respect to a basis such that, for any vector in the basis, any linear
combination of the other vectors is Birkho¤-James orthogonal to it. 3) We show how
semi-inner products and normality provide an analytic method that can be used to …nd
all DIC marginal medians. 4) As an application, we derive all DIC marginal medians
for lp spaces of any …nite dimension, and show that they do not depend on p (unless
p = 2).

Note: 
Length: 36
Creation-Date: 2021-04
Revision-Date: 
File-URL: https://www.crctr224.de/research/discussion-papers/archive/dp290
File-Format: application/pdf
Handle: RePEc:bon:boncrc:CRCTR224_2021_290